In this paper we study 12 four-valued logics arisen from Belnap's truth and/or knowledge four-valued lattices, with or without constants, by adding one or both or none of two new non-regular operations—classical negation and natural implication. We prove that the secondary connectives of the bilattice four-valued logic with bilattice constants are exactly the regular four-valued operations. Moreover, we prove that its expansion by any non-regular connective (such as, e.g., classical negation or natural implication) is strictly functionally complete. Further, finding axiomatizations (...) of the quasi varieties generated by the 12 logics involved (that prove to be varieties), we find naturell equational axiomatizations of these logics. Finally, applying Pynko's general theory of algebraizable sequential consequence operations, we also find equivalent natural sequentiell axiomatizations of the logics under consideration that expand either of two Pynko's sequential calculi for the constant-free truth-lattice four-valued logic. (shrink)

The notion of an algebraizable logic in the sense of Blok and Pigozzi [3] is generalized to that of a possibly infinitely algebraizable, for short, p.i.-algebraizable logic by admitting infinite sets of equivalence formulas and defining equations. An example of the new class is given. Many ideas of this paper have been present in [3] and [4]. By a consequent matrix semantics approach the theory of algebraizable and p.i.-algebraizable logics is developed in a different way. (...) It is related to the theory of equivalential logics in the sense of Prucnal and Wroski [18], and it is extended to nonfinitary logics. The main result states that a logic is algebraizable (p.i.-algebraizable) iff it is finitely equivalential (equivalential) and the truth predicate in the reduced matrix models is equationally definable. (shrink)

Annotated logics were introduced by V.S. Subrahmanian as logical foundations for computer programming. One of the difficulties of these systems from the logical point of view is that they are not structural, i.e., their consequence relations are not closed under substitutions. In this paper we give systems of annotated logics that are equivalent to those of Subrahmanian in the sense that everything provable in one type of system has a translation that is provable in the other. Moreover these new (...) systems are structural. We prove that these systems are weakly congruential, namely, they have an infinite system of congruence 1-formulas. Moreover, we prove that an annotated logic is algebraizable (i.e., it has a finite system of congruence formulas,) if and only if the lattice of annotation constants is finite. (shrink)

In this paper we consider the implicational fragment of Abelian logic \ . We show that although the Abelian groups provide an semantics for the set of theorems of \ they do not for the associated consequence relation. We then show that the consequence relation is not algebraizable in the sense of Blok and Pigozzi . In the second part of the paper, we investigate an extension of \ in the same language and having the same set (...) of theorems and show that this new consequence relation is algebraizable with the Abelian groups as its equivalent algebraic semantics. Finally, we show that although \ is not algebraizable, it is order-algebraizable in the sense of Raftery. (shrink)

In this paper we define and study a generalized notion of a logical system that covers on an equal formal basis sentential, equational and sequential systems. We develop a general theory of equivalence between generalized logics that provides, first, a conception of algebraizable logic , second, a formal concept of equivalence between sequential systems and, third, a notion of equivalence between sentential and sequential systems. We also use our theory of equivalence for developing a general algebraic (...) approach to conjunctive non-pseudo-axiomatic self-extensional sentential logics. Finally, we consider within the framework of the mentioned approach various sequential formulations for some well-known sentential logics. (shrink)

The effect of recent experience on current behavior has been studied extensively in simple laboratory tasks. We explore the nature of sequential effects in the more naturalistic setting of automobile driving. Driving is a safety-critical task in which delayed response times may have severe consequences. Using a realistic driving simulator, we find significant sequential effects in pedal-press response times that depend on the history of recent stimuli and responses. Response times are slowed up to 100 ms in particular (...) cases, a delay that has dangerous practical consequences. Further, we observe a significant number of history-related pedal misapplications, which have recently been noted as a cause for concern in the automotive safety community. By anticipating these consequences of sequential context, driver assistance systems could mitigate the effects of performance degradations and thus critically improve driver safety. (shrink)

We respond to recent comments on our proposal to improve justice in ventilator triage, in which we used as an example New Jersey’s publicly available and legally binding Directive Number 2020-03. We agree with Bernard Lo and Doug White that equity implications of triage frameworks should be continually reassessed, which is why we offered six concrete options for improvement, and called for monitoring the consequences of adopted triage models. We disagree with their assessment that we mis-characterised their Model Guidance, as (...) included in the NJ Directive, in ways that undermine our conclusions. They suggest we erroneously described their model as a two-criterion allocation framework; that recognising other operant criterion reveals it ‘likely mitigate[s] rather than exacerbate[s] racial disparities during triage’, and allege that concerns about inequitable outcomes are ‘without evidence’. We highlight two major studies robustly demonstrating why concerns about disparate outcomes are justified. We also show that White and Lo seek to retrospectively—and counterfactually—correct the version of the Model Guideline included in the NJ Directive. However, as our facsimile reproductions show, neither the alleged four-criteria form, nor other key changes, such as dropping the Sequential Organ Failure Assessment score, are found in the Directive. These points matter because our conclusions hence stand, because the public version of the Model Guidance had not been updated to reduce the risk of inequitable outcomes until June 2021 and NJ’s Directive still does not reflect these revisions, and, hence, represents a less equitable version, as acknowledged by its authors. We comment on broader policy implications and call for ways of ensuring accurate, transparent and timely updates for users of high-stakes guidelines. (shrink)

It has received little attention that the truth values of sequential counterfactuals (i.e. counterfactuals in which the antecedent event precedes the consequent event) can shift over time. In the footsteps of Goodman, I develop a theory of sequential counterfactuals that can account for this feature. The theory (i) defends a semifactual test of cotenability, (ii) spells out the truth conditions for semifactuals in probabilistic terms and (iii) accounts for truth-value shifts by appealing to a dynamic view of time.

Uniform sequential continuity, a property classically equivalent to sequential continuity on compact sets, is shown, constructively, to be a consequence of strong continuity on a metric space. It is then shown that in the case of a separable metric space, uniform sequential continuity implies strong continuity if and only if one adopts a certain boundedness principle that, although valid in the classical, recursive and intuitionistic setting, is independent of Heyting arithmetic.

Psychological Sequentialism holds that no causal constraint is necessary for the preservation of what matters in survival; rather, it is sufficient for preservation if two groups of mental states are similar enough and temporally close enough. Suppose that one’s body is instantaneously dematerialized and subsequently, by an amazing coincidence, a collection of molecules is configured to form a qualitatively identical human body. According to Psychological Sequentialism, these events preserve what matters in survival. In this article, I examine some of the (...) main arguments for the view and argue that they fail to establish that no causal constraint is necessary. I also argue that Psychological Sequentialism yields implausible consequences that render it hard to accept the view. (shrink)

Equivalences and translations between consequence relations abound in logic. The notion of equivalence can be defined syntactically, in terms of translations of formulas, and order-theoretically, in terms of the associated lattices of theories. W. Blok and D. Pigozzi proved in [4] that the two definitions coincide in the case of an algebraizable sentential deductive system. A refined treatment of this equivalence was provided by W. Blok and B. Jónsson in [3]. Other authors have extended this result to the (...) cases of k-deductive systems and of consequence relations on associative, commutative, multiple conclusion sequents. Our main result subsumes all existing results in the literature and reveals their common character. The proofs are of order-theoretic and categorical nature. (shrink)

Once assessments and continuers are focussed on as distinguishable phenomena it becomes clear that they differ from each other not just in the details of their sequential placement within an extended turn, but in other significant ways as well.First, though assessments can take the form of talk with clear lexical content (for example `Oh wow' and assessment adjectives such as ‘beautiful’), they can also be done with sounds such as ‘Ah:::’ whose main function seems to be the carrying of (...) an appropriate intonation contour, as well as gesturally (cf. M. Goodwin, 1980). In this they resemble continuers, which can be performed both with talk whose lexical status is not always granted, and with appropriate gestures such as nods. In view of the way in which both continuers and brief assessments are characteristically situated within a rather specialized environment, the ongoing talk of another, it is not surprising that they share these characteristics. Indeed in so far as these features provide minimal lexical and auditory interference with the other talk already in progress, they are precisely some of the adaptations that would be expected of action able to function in such an environment. Given such structural similarity in action that is also quite brief, the clarity with which assessments can be distinguished from continuers becomes interesting. If in fact these objects are doing different work in the same environment, the salience of their distinctness from each other becomes an important feature of the structure of each. In view of the economy and clarity that brief assessments require, it is all the more remarkable that many of them, through the details of the way in which they are pronounced and their intonation contour, are able to convey quite detailed, even intricate, information about their speaker's involvement in both the assessment and the talk of the moment.Second, while ‘uh huh’ seems to be restricted to placement in the midst of extended talk by another, assessments can occur at the completion of such extended turns as well. Indeed assessments are one of the prototypical ways of bringing an extended turn such as a story to completion. Such differential placement is quite compatible with what has already been noted about the organization of these phenomena. For example, insofar as a continuer treats the talk just heard as preliminary to further talk it would be quite inappropriate as a technique for marking completion of an extended turn. On the other hand by virtue of the way in which they appreciate the details of what has just been said without marking that talk as a prelude to something else, assessments are apt structures for doing terminal work on an extended sequence.Third, ‘uh huh’ seems to be an exclusively recipient action — indeed its work as a continuer is accomplished precisely through placement relative to more extended talk by another speaker. Assessments, however, can be done by speaker as well as recipient.Fourth, though analysis in the present paper has focussed on brief assessments (the type of assessment most similar in form to continuers), assessments unlike continuers can in fact take many shapes, some of them quite elaborate with, for example, extended sentences and even sequences of turns being devoted exclusively to the activity of doing an assessment.In sum, alternative types of action are available to recipients for constructing responses in the midst of another's extended talk. Though the responses themselves are typically brief, the presence of alternatives that can be placed in a variety of sequential positions provides recipients with resources that enable them to participate in speaker's emerging talk in a differentiated fashion, something which has consequences for speaker's actions as well. (shrink)

We introduce quantificational modal operators as dynamic modalities with (extensions of) Henkin quantifiers as indices. The adoption of matrices of indices (with action identifiers, variables and/or quantified variables as entries) gives an expressive formalism which is here motivated with examples from the area of multi-agent systems. We study the formal properties of the resulting logic which, formally speaking, does not satisfy the normality condition. However, the logic admits a semantics in terms of (an extension of) Kripke structures. As a (...) class='Hi'>consequence, standard techniques for normal modal logic become available. We apply these to prove completeness and decidability, and to extend some standard frame results to this logic. (shrink)

In a dynamic (sequential) framework, departures from the independence axiom (IND) are reputed to induce violations of dynamic consistency (DC), which may in turn have undesirable normative consequences. This result thus questions the normative acceptability of non expected-utility (non-EU) models, which precisely relax IND. This paper pursues a twofold objective. The main one is to discuss the normative conclusion: usual arguments linking violations of DC to departures from IND are shown to be actually based on specific (but usually remaining (...) implicit) assumptions which may rightfully be released, so that it is actually possible for a non-EU maximizer to be dynamically consistent and thus avoid normative difficulties. The second objective is to introduce a kind of `reality principle' (through two other evaluation criteria) in order to mitigate the normative requirement when examining adequate moods for non-EU decision making. (shrink)

Although great progress in neuroanatomy and physiology has occurred lately, we still cannot go directly to those levels to discover the neural mechanisms of higher cognition and consciousness. But we can use neurocomputational methods based on these details to push this project forward. Here we describe vector subtraction as an operation that computes sequential paths through high-dimensional vector spaces. Vector-space interpretations of network activity patterns are a fruitful resource in recent computational neuroscience. Vector subtraction also appears to be implemented (...) neurally in primate frontal eye field activity, which computes dimensions of saccadic eye movements. We use this apparent neural implementation as a model and construct from it a general neurocomputational account of an important type of sequential cognitive and conscious process. We defend the biological plausibility of all components of the general model and show that it yields testable anatomical and physiological predictions. We close by suggesting some interesting consequences for consciousness if our model characterizes correctly the neural mechanisms producing a common type of episode in our conscious streams. (shrink)

In an article published thirteen years ago, I tried to break new ground by showing that the texts transmitted under the titleCataleptonas the work of Virgil can be seen to form an elaborately arranged and highly allusive book of verse written by a single author. This latter, I argued, was identical with the anonymous poet who, in an epilogue, represents the preceding poems as the juvenilia of the author later known for hisBucolics,GeorgicsandAeneidand, consequently, is himself speaking in the alleged early (...) works asVirgil impersonator. This anonymous poet, however, cannot rightly be labelled a literary forger, since he repeatedly and quite unmistakably recalls each of Virgil's threeoperaas well as other texts written after the year 19b.c. Evidently, then, he is inviting his readers to take part in a literarylusus, one in which they are expected to be familiar not only with the texts ofBucolics,GeorgicsandAeneidbut also with the life of the man who wrote them. The fiction of a young Virgil is created, one who wrote his first poems—the verses referred to in the epilogue aselementaandrudis Calliope—primarily under the influence of Catullus, the said poems being, with the exception ofCatal.12 and 16, epigrams. My interpretation has borne fruit, with Irene Peirano and Markus Stachon each devoting, in 2012 and 2014 respectively, a monograph to this approach and offering what are often very thorough analytical readings of the poems as the creations of aVirgil impersonator. However, neither of these two Latinists has considered one particular interpretative aspect, which I myself had only been able to introduce very briefly into my paper: the recognition that, as many more recent studies have now further corroborated, Roman poetry books were designed for linear, sequential reading, that they have, as it were, a story to tell. Peirano, moreover, disregards in her study the threePriapeapositioned in editions before the other fifteen epigrams and shown there with their own separate numbering. In the manuscripts, however, the titleCataleptonrefers without exception to a unit comprising the threePriapeaand the fifteen epigrams. The titlePriapea, found in the catalogue of the Murbach manuscripts and in some codices, is always attached solely to the poemQuid hoc noui est?In theVita Suetoniana-Donatiana, the termsCatalepton,PriapeaandEpigrammatawere evidently used as three different titles; the author may not have seen thatCataleptonis the title of all the poems. Furthermore, I should like to point out that, counted together, ‘Virgil's’Priapeaand epigrams come to a total of seventeen poems and so match precisely both the total of seventeen books in the real Virgil's three works and the total number of Horace's epodes, of the poems, that is, which the not-so-real Virgil quite conspicuously evokes in his own penultimate poem. More significantly, however, a sequential reading of thePriapea et Epigrammatacan in fact build a watertight case for taking the texts to be, as it were, a composite whole, and that is what I intend to argue in the rest of the article. (shrink)

Examinations form part of the assessment processes that constitute the basis for benchmarking individual educational progress, and must consequently fulfill credibility, reliability, and transparency standards in order to promote learning outcomes and ensure academic integrity. A randomly selected question examination is considered to be an effective solution to mitigate sharing of questions between students by addressing replicated inter-examination questions that compromise examination integrity and sequential intra- examination questions that compromise examination comprehensivity. In this study, a Monte Carlo approach was (...) used to design six examination schemes for the purpose of generating and evaluating 600 RSQEs in order to investigate the effects of RSQE design on replicated inter-examination and sequential and intra-examination questions. Results revealed that the number of randomly selected questions from the pool and the number of sub-pools inversely affected the replication and sequencing of the examination questions. Thus, by designing the RSQE in many sub-pools, in equivalence to the number of examination questions and selecting only one question from each sub-pool, and updating the sub-pools after each examination, the passing of information can be prevented, ensuring the integrity of the examinations. (shrink)

The intuitionistic consequence operation restricted to the language with (equivalence) and (negation) as the only connectives is axiomatized by means of a finite set of sequential rules of inference.

Recently, a multinomial process tree model was developed to measure an agent’s consequence sensitivity, norm sensitivity, and generalized inaction/action preferences when making moral decisions (CNI model). However, the CNI model presupposed that an agent considersconsequences—norms—generalizedinaction/actionpreferences sequentially, which is untenable based on recent evidence. Besides, the CNI model generates parameters at the group level based on binary categorical data. Hence, theC/N/Iparameters cannot be used for correlation analyses or other conventional research designs. To solve these limitations, we developed the CAN algorithm (...) to computenormandconsequencesensitivities and overallaction/inactionpreferences algebraically in a parallel manner. We re-analyzed the raw data of the original CNI model to test the methodological predictions. Our results demonstrate that: (1) theCparameter is approximately equal between the CNI model and CAN algorithm; (2) theNparameter under the CNI model approximately equalsN/(1 −C) under the CAN algorithm; (3) theIparameter andAparameter are reversed around 0.5 – the larger theIparameter, the more the generalized inactionversusaction preference and the larger theAparameter, the more overall actionversusinaction preference; (4) tests of differences in parameters between groups with the CNI model and CAN algorithm led to almost the same statistical conclusion; (5) parameters from the CAN algorithm can be used for correlational analyses and multiple comparisons, and this is an advantage over the parameters from the CNI model. The theoretical and methodological implications of our study were also discussed. (shrink)

The purpose of this paper is an axiomatic study of the interrelations between certain continuity properties. We show that every mapping is sequentially continuous if and only if it is sequentially nondiscontinuous and strongly extensional, and that "every mapping is strongly extensional", "every sequentially nondiscontinuous mapping is sequentially continuous", and a weak version of Markov's principle are equivalent. Also, assuming a consequence of Church's thesis, we prove a version of the Kreisel-Lacombe-Shoenfield-Tsĕitin theorem.

The logic of (commutative integral bounded) residuated lattices is known under different names in the literature: monoidal logic [26], intuitionistic logic without contraction [1], H BCK [36] (nowadays called by Ono), etc. In this paper we study the -fragment and the -fragment of the logical systems associated with residuated lattices, both from the perspective of Gentzen systems and from that of deductive systems. We stress that our notion of fragment considers the full consequence relation admitting hypotheses. It results that (...) this notion of fragment is axiomatized by the rules of the sequent calculus for the connectives involved. We also prove that these deductive systems are non-protoalgebraic, while the Gentzen systems are algebraizable with equivalent algebraic semantics the varieties of pseudocomplemented (commutative integral bounded) semilatticed and latticed monoids, respectively. All the logical systems considered are decidable. (shrink)

A filter of a sentential logic ? is Leibniz when it is the smallest one among all the ?-filters on the same algebra having the same Leibniz congruence. This paper studies these filters and the sentential logic ?+ defined by the class of all ?-matrices whose filter is Leibniz, which is called the strong version of ?, in the context of protoalgebraic logics with theorems. Topics studied include an enhanced Correspondence Theorem, characterizations of the weak algebraizability of ?+ and of (...) the explicit definability of Leibniz filters, and several theorems of transfer of metalogical properties from ? to ?+. For finitely equivalential logics stronger results are obtained. Besides the general theory, the paper examines the examples of modal logics, quantum logics and Łukasiewicz's finitely-valued logics. One finds that in some cases the existence of a weak and a strong version of a logic corresponds to well-known situations in the literature, such as the local and the global consequences for normal modal logics; while in others these constructions give an independent interest to the study of other lesser-known logics, such as the lattice-based many-valued logics. (shrink)

The aim of this paper is to show that the calculi described by Anshakov and Rychkov are algebraizable in the sense of Blok and Pigozzi. As a consequence, a proof of the strong completeness of these calculi is obtained.

Research on escalation of commitment has predominantly been studied in the context of a single decision without consideration for the psychological consequences of escalating. This study sought to examine a) the extent to which people escalate their commitment to a failing course of action in a sequential decision-making task, b) confidence and anger as psychological consequences of escalation of commitment, and c) the reciprocal relationship between escalation of commitment and confidence and anger. Participants were 110 undergraduate students who completed (...) a series of investment decisions regarding a failing endeavor. Results revealed that although a high proportion of individuals escalate through all decisions, the extent to which they escalated decreased with each decision as they were less willing to invest money in the project. Furthermore, as participants escalated, confidence in one’s decision decreased and anger increased. Lastly, the analyses revealed that the relationship between escalation and confidence is reciprocal. Escalation was negatively associated with confidence, and confidence predicted escalation in the subsequent decision. These results highlight the importance of considering both the determinants and psychological consequences of escalation of commitment. (shrink)

A logic is said to admit an equational completeness theorem when it can be interpreted into the equational consequence relative to some class of algebras. We characterize logics admitting an equational completeness theorem that are either locally tabular or have some tautology. In particular, it is shown that a protoalgebraic logic admits an equational completeness theorem precisely when it has two distinct logically equivalent formulas. While the problem of determining whether a logic admits an equational completeness theorem is shown (...) to be decidable both for logics presented by a finite set of finite matrices and for locally tabular logics presented by a finite Hilbert calculus, it becomes undecidable for arbitrary logics presented by finite Hilbert calculi. (shrink)

This chapter contains sections titled: Von Wright on Causality Actions, Events, and Intentionality; Results and Consequences Practical Inference and the Logical Connection Argument Two Kinds of Explanation and Their Compatibility and Congruence The Determinants of Action References Further reading.

In this paper, we investigate the social herding phenomenon known as informational cascades, in which sequential inter-agent communication might lead to epistemic failures at group level, despite availability of information that should be sufficient to track the truth. We model an example of a cascade, and check the correctness of the individual reasoning of each agent involved, using two alternative logical settings: an existing probabilistic dynamic epistemic logic, and our own novel logic for counting evidence. Based on this analysis, (...) we conclude that cascades are not only likely to occur but are sometimes unavoidable by "rational" means: in some situations, the group’s inability to track the truth is the direct consequence of each agent’s rational attempt at individual truth-tracking. Moreover, our analysis shows that this is even so when rationality includes unbounded higher-order reasoning powers, as well as when it includes simpler, non-Bayesian forms of heuristic reasoning. (shrink)

In the present paper we study systematically several consequence relations on the usual language of propositional intuitionistic logic that can be defined semantically by using Kripke frames and the same defining truth conditions for the connectives as in intuitionistic logic but without imposing some of the conditions on the Kripke frames that are required in the intuitionistic case. The logics so obtained are called subintuitionistic logics in the literature. We depart from the perspective of considering a logic just as (...) a set of theorems and also depart from the perspective taken by Restall in that we consider standard Kripke models instead of models with a base point. We study the relations between subintuitionistic logics and modal logics given by the translation considered by Došen. Moreover, we classify the logics obtained according to the hierarchy considered inAlgebraic Logic. (shrink)

In this paper we study the relations between the fragment L of classical logic having just conjunction and disjunction and the variety D of distributive lattices, within the context of Algebraic Logic. We prove that these relations cannot be fully expressed either with the tools of Blok and Pigozzi's theory of algebraizable logics or with the use of reduced matrices for L. However, these relations can be naturally formulated when we introduce a new notion of model of a sequent (...) calculus. When applied to a certain natural calculus for L, the resulting models are equivalent to a class of abstract logics (in the sense of Brown and Suszko) which we call distributive. Among other results, we prove that D is exactly the class of the algebraic reducts of the reduced models of L, that there is an embedding of the theories of L into the theories of the equational consequence (in the sense of Blok and Pigozzi) relative to D, and that for any algebra A of type (2,2) there is an isomorphism between the D-congruences of A and the models of L over A. In the second part of this paper (which will be published separately) we will also apply some results to give proofs with a logical flavour for several new or well-known lattice-theoretical properties. (shrink)

With any structural inference rule A/B, we associate the rule $${(A \lor p)/(B \lor p)}$$, providing that formulas A and B do not contain the variable p. We call the latter rule a join-extension ( $${\lor}$$ -extension, for short) of the former. Obviously, for any intermediate logic with disjunction property, a $${\lor}$$ -extension of any admissible rule is also admissible in this logic. We investigate intermediate logics, in which the $${\lor}$$ -extension of each admissible rule is admissible. We prove that (...) any structural finitary consequence operator (for intermediate logic) can be defined by a set of $${\lor}$$ -extended rules if and only if it can be defined through a set of well-connected Heyting algebras of a corresponding quasivariety. As we exemplify, the latter condition is satisfied for a broad class of algebraizable logics. (shrink)

As an Introduction to the Special Issue on “Formulation, generalization, and abstraction in interaction,” this paper discusses key problems of a conversation analytic (CA) approach to semantics in interaction. Prior research in CA and Interactional Linguistics has only rarely dealt with issues of linguistic meaning in interaction. It is argued that this is a consequence of limitations of sequential analysis to capture meaning in interaction. While sequential analysis remains the encompassing methodological framework, it is suggested that it (...) needs to be complemented by analyzing semantic relationships between choices of formulation in the interaction, ethnography, and structural techniques of comparing selected options with possible alternatives. The paper describes the methodological approach taken to interactional semantics by the papers in the Special Issue, which analyse practices of generalization and abstraction in interaction as they are accomplished by formulations of prior versions of reference and description. (shrink)

In the present paper we study systematically several consequence relations on the usual language of propositional intuitionistic logic that can be defined semantically by using Kripke frames and the same defining truth conditions for the connectives as in intuitionistic logic but without imposing some of the conditions on the Kripke frames that are required in the intuitionistic case. The logics so obtained are called subintuitionistic logics in the literature. We depart from the perspective of considering a logic just as (...) a set of theorems and also depart from the perspective taken by Restall in that we consider standard Kripke models instead of models with a base point. We study the relations between subintuitionistic logics and modal logics given by the translation considered by Došen. Moreover, we classify the logics obtained according to the hierarchy considered inAlgebraic Logic. (shrink)

In this paper we study the relations between the fragment L of classical logic having just conjunction and disjunction and the variety D of distributive lattices, within the context of Algebraic Logic. We prove that these relations cannot be fully expressed either with the tools of Blok and Pigozzi's theory of algebraizable logics or with the use of reduced matrices for L. However, these relations can be naturally formulated when we introduce a new notion of model of a sequent (...) calculus. When applied to a certain natural calculus for L, the resulting models are equivalent to a class of abstract logics (in the sense of Brown and Suszko) which we call distributive. Among other results, we prove that D is exactly the class of the algebraic reducts of the reduced models of L, that there is an embedding of the theories of L into the theories of the equational consequence (in the sense of Blok and Pigozzi) relative to D, and that for any algebra A of type (2,2) there is an isomorphism between the D-congruences of A and the models of L over A. In the second part of this paper (which will be published separately) we will also apply some results to give proofs with a logical flavour for several new or well-known lattice-theoretical properties. (shrink)

We study the matrices, reduced matrices and algebras associated to the systems SAT of structural annotated logics. In previous papers, these systems were proven algebraizable in the finitary case and the class of matrices analyzed here was proven to be a matrix semantics for them.We prove that the equivalent algebraic semantics associated with the systems SAT are proper quasivarieties, we describe the reduced matrices, the subdirectly irreducible algebras and we give a general decomposition theorem. As a consequence we (...) obtain a decision procedure for these logics. (shrink)

It is argued in this paper that a multimodal analysis of turn-taking, one of the core areas of conversation analytic research, is needed and has to integrate gaze as one of the most central resources for allocating turns, and that new technologies are available that can provide a solid and reliable empirical foundation for this analysis. On the basis of eye-tracking data of spontaneous conversations, it is shown that gaze is the most ubiquitous next-speaker-selection technique. It can function alone or (...) enhance other techniques. I also discuss the interrelationship between the strength for sequential projection and the choice of next-speaker-selection techniques by a current speaker. The appropriate consideration of gaze leads to a revision of the turn-taking model in that it reduces the domain of self-selection and expands that of the current-speaker-selects-next sub-rule. It also has consequences for the analysis of “simultaneous starts”. (shrink)

In this paper we show that axiomatic extensions of H. Wansing’s connexive logic $$\textsf{C}$$ ( $$\textsf{C}^{\perp }$$ ) are algebraizable (in the sense of J.W. Blok and D. Pigozzi) with respect to sub-varieties of $$\textsf{C}$$ ( $$\textsf{C}^{\perp }$$ )-algebras. We develop the structure theory of $$\textsf{C}$$ ( $$\textsf{C}^{\perp }$$ )-algebras, and we prove their representability in terms of twist-like constructions over implicative lattices (Heyting algebras). As a consequence, we further clarify the relationship between the aforementioned classes. Finally, taking (...) advantage of the above machinery, we provide some preliminary remarks on the lattice of axiomatic extensions of $$\textsf{C}$$ ( $$\textsf{C}^{\perp }$$ ) as well as on some properties of their equivalent algebraic semantics. (shrink)

Research in the field of planarian regeneration on the one hand, and a general survey of embryology on the other, throw doubt upon the reality of supra-cellular controls, which are still at the basis of all modern concepts of morphogenesis. The necessity of referring to such controls, which have never been convincingly demonstrated, is probably due to the fact that two aspects of cell behaviour have been underestimated: 1) the capacity of cells to change their individualities for a time independently (...) of other cells; 2) the social behaviour of cells, which is the consequence of the reciprocal exchange of information. Pattern formation and pattern remodeling in normal development results from readjustments of cell populations to local or global changes. The common responses of cell populations to disturbances are enhanced mitotic activity, cessation of specific syntheses and cell migration. In the young embryo these may promptly restore the unity of the injured primordium, leading to so-called restitution; this is based on a normal sequence of further readjustments in the primordium. In older organisms the same responses give rise to cell interactions which may be the starting point for further sequential readjustments — in some instances these are comparable to those that originally organized the primordium in question during development. The desirability of giving up the notion of morphogenetic field is discussed. (shrink)

In his seminal Discipline and Punish: The Birth of the Prison, Michel Foucault aims at outlining the historical course that led to the promulgation and consolidation of the institution of imprisonment as a means of punishment as well as narrating how the corresponding human type, i.e. the contemporary disciplined subject, has been shaped. Obviously, the disciplined subject gradually took the place of the tormented subject. Consequently, this study aims at describing the sequential mutations of the imposed punishment as it (...) progressively shifted from the spectacular slaughtering of the body to the strictly scientific manipulation of the non-material dimension of the human being. The reformation of the punitive practices “constructs” a docile body. It must be noticed, however, that this body is not necessarily guilty, since the disciplinary schemes concern everybody, even the most innocent sides of the everyday life as for example the hospital, the school or the barracks. Additionally, discipline is imposed through the division of the space, what Foucault calls the “art of allocation”, so that every working person is easily seen and supervised by the eye of the authority, while the disciplined subject is being forged gradually through the sense of responsibility before the flowing time. Foucault highlights the “political technology of the body”, that is its usurpation by the authorities, who aim at imposing to it adictated activity that produces palpable results in a binding frame of time. Although selective and brief, the present account of the punitive concepts of the three last centuries clarifies the fact that the authoritarian strategies are indissolubly interwoven with the different connotations of the human body, through the use of which they subdue human beings. (shrink)

Logic in Action/Doron Avital Nothing is more difficult, and therefore more precious, than to be able to decide (Napoleon Bonaparte) Introduction -/- This book was born on the battlefield and in nights of secretive special operations all around the Middle East, as well as in the corridors and lecture halls of Western Academia best schools. As a young boy, I was always mesmerized by stories of great men and women of action at fateful cross-roads of decision-making. Then, like as today, (...) I felt the full weight of the moment of truth as it confronts the individual, the man or woman of action, with the imminent necessity to decide. Alongside, as I was climbing up the ladder of education, I found myself just as well captivated by the great intellectual stories of our times, in particular 20th century analytic philosophy and, at its core, the machinery of modern logic. How do then the cool contemplative modes of the philosophical and analytic outlooks, that are better fitting of the philosopher's armchair at the fireplace, hang together with the heat of the battlefield or the angst of the ticking clock of time left to the completion of a daring special operation? Growing up I was pondering exactly that. Not accidently, and in fact as consequence, I have chosen a course in life that challenged me to visit the poles of both theory and practice. I set myself on a mission to unravel the tension between the contemplative inquiry, supposedly theoretical, aiming at the logical structure of things, and the uncompromising test of life and action. The puzzle of the gap between theory and practice has become ever since the guiding question of my life. -/- Not long ago, I met two friends, Avner Shor, a veteran combat soldier of the special forces unit I eventually commanded, and Aviram Halevi, a fellow officer with whom I served. Why will we not put into writing the ideas that guided us during our years of military action, we wondered. At that time, I used to deliver the keynote lectures to the senior officers' course of Israel central intelligence organization, the Mossad. For this I already had to put some of these ideas in writing. Avner was quick to introduce me with a notable publisher and even helped me write the first chapter. With Aviram I sat to many meetings, where he would challenge me with key questions, and we followed them with memories of operations and battles, aiming to draw the required lessons. This served me well when I finally sat down to write the first draft of the book. The result was more extensive than me and my friends had expected. I had to add a particularly long chapter dealing with the story of modern philosophy and logic. This was required, I felt, as no decision-making process lives in an intellectual vacuum. Knowingly or subconsciously, the intellectual climate of the time guides us for better or worse with the decisions we finally take. The initial draft was naturally cumbersome and inaccessible. But here I had the privilege of meeting a particularly talented editor, Rami Rothholtz. I found in Rami both an editor and a critical reader. As an infantry combat soldier at youth and now a senior journalist and editor, Rami insisted on simplifying and refining my ideas. Had it not been for his work, this book would have been literally unreadable. *** I opened my book with a brief description of a single night of a special operation deep at the Lebanon Bekaa valley, far away from Israel northern border. The mission was to kidnap a senior terror leader known to be holding in captivity an Israeli pilot. This was also the last special operation I commanded in my military career. A single special operation night, but what had to precede it? For sure, many months of intense and skillful preparations. What is Planning? This is the question with which I open up chapter (2) of the book. I confront in this chapter two approaches to planning. The first is the one I saw as a mission to myself to cultivate in my many years of military service. The second is the one I saw as representing a deep-rooted fallacy that holds a firm grip on today's conventional wisdom about planning. To further examine the logic of the competing models, I was required in chapter (3) to analyze the concept of "The Standard". I argue that the false model of planning has its roots in an attitude of an uncompromising adherence to the power of literal obedience to standards and rules. The standard, or what is outlined by a rule as prescribing a future course of action, is seen as an answer to the fundamental tension between theory (planning) and practice (execution). I argue in contrast that the standard does not produce an answer but rather what I call: "A Well-Defined Question". In essence, it is a meticulously-well-planned invitation to exercise a fresh judgment. A judgement that has as an anchor the default answer that the standard produces but is open to extension as it confronts the new frame of reference of the test of reality. In chapter (4), I present a new tool for planning and execution: "The Polygon of Risks" or "The Polygon of Execution". The Polygon is a geometric illustration of the underlying tension that exists between all dimensions of the operational project. The construction and conceptualization of the trade-offs that exist between the various dimensions - segments of the polygon - is the first topic on the planner's agenda. I position the concepts of "Daring" and "Taking Proactive and Well-Informed Risks" as necessary logical constituents of the polygon and show how in contrast the false model of planning is responsible for an operational culture that is risk-averse. It encourages, in fact, the piling up of false securities at the segments' level that eventually lead to the collapse of the polygon. The necessary trade-offs relationships that exist between the segments of the polygon express the fundamental tension between partnership and competition: partnership in a joint goal and competition over resources, both material and abstract. When this tension is not managed well, that is, when the players' local optimizations overshadow the global optimization required for the success of the project, the execution polygon collapses. In this scenario, we may find the setting of the bar of "High Standards" in a players' spheres of responsibility to conceal a hidden agenda of personal insurances taken against a possible failure. Once the overall risk is not mitigated by way of collaborative joint executional dialogue, the process that leads to a collapse of the polygon is literally unstoppable. *** In chapter (5), I discuss "(Fateful) Decisions". I examine the way in which we should translate the polygon into sequential critical decisions on the timeline. The execution polygon is not a rigid scaffolding but a dynamic conceptual illustration of the -/- project. It will need now to be converted into successive decision junctions. We will find the content of a decision and its timing on the timeline to be inseparable. The right decision is the one that is taken at the right time. The moment of decision is in fact the last moment of deliberation, the first moment available for action, i.e. the first possible "Can" is also the latest possible "Must". Deciding too soon is analog to the "Jumping of the Gun". The decision maker is forcing a pre-conceived answer to a state of affairs not ripe for an answer, e.g. the target in the shooting range is not yet erected. Late to decide and the decision maker may envision what he or she should have done but reality is no longer available for them to harness it right, e.g. consider a tennis player's frustration when reviewing a too-late-to-react move in the video replay. I review in this chapter many fateful decisions, both historical, from Napoleon's Waterloo, to a Bridge Too Far of WWII, to the failed rescue attempt of American hostages at the time of the Iranian Revolution, as well as fateful decisions I had to take in the course of my military life, both in combat and in special operations, and show the sense in which they all answer to our analysis. The theme of chapter (6) is "The Moment of Truth". This is the moment when everything is on the line and from which there is no turning back. I discuss the formative repetitive structure of the schooling and simulation phase and contrast it with the "One Shot, One Opportunity" nature of the moment of truth. This is extremely helpful when we analyze the logical structure of failures as unwarranted repetitions of past lessons. The schooling curriculum indeed consists of important abstractions drawn from lessons of the past. However, it is when we project them in a fashion that is literal or mechanical that we cross path with the possibility of a failure. The paradox of education is that what we must repeat in school and simulation must be extended and not repeated in real life. What is required of us so we do not fall into the fallacy of repetition in face of the moment of truth is the core subject of the discussion of this chapter. In chapter (7), I took a lengthy philosophical detour surveying the intellectual drama of modern logic, and in general, the story of 20th century analytic philosophy. Readers who choose to bypass the somehow demanding narrative of this drama can do so and still keep the argumentative thread of the book. However, even by way of skipping the more technical parts, I would still urge the readers to delve into the discussion in this chapter as I believe this would grant them a deeper understanding of the overall conceptual framework. I explore here the work of two key figures: the logician Kurt Gödel and the philosopher Ludwig Wittgenstein, both were crowned in 2000 by TIME Magazine, as the leading Logician and Philosopher, respectively, of the 20th Century. I review the fascinating logical result of Gödel's Incompleteness Theorem and examine its relevance as setting a theoretical limit to the power of formalization. This amazing logical result - a result that shakes the logical foundations of 20th century thought in as much as the discovery of irrational numbers shook the foundations of the Pythagorean program of the ancient Greeks - bears significantly on the question of action and the blind trust we place in the power of formalization in the form of protocols and rules. It is here that Wittgenstein's philosophy enters in full force. We follow Wittgenstein as he dismantles our conception of rules as if there were "Railroads to Infinite", i.e. as prescribing for us in-advance their proper employments in all possible -/- future eventualities. Instead we propose that the dilemma of action demands of us an extension of rules rather than a mechanical or blind repetition of their literal imperative. In turn, this extension can serve as a new lesson added to the curriculum of school and simulation. The theme of chapter (8), the concluding chapter, is Strategy, Logic, and Ethics. The chapter comes to place the ethical dilemma in the conceptual map we presented in the book. I discuss here the tension between strategy as a process of setting goals and deriving backward as it were the steps that are necessary for achieving these goals, to the inescapable dictation of the ethical imperative. This unavoidable tension is particularly important against the backdrop of contemporary culture that is guided by a vision of personal success and achievement that may threaten our ability to do what is right. Most of all, I am troubled in this chapter, with the role logic may play, first as a liberating force enabling a change that is tuned to the ethical imperative, and second, as a force designed to justify on logical grounds, as it were, the existing power structure. It is in this junction that brave individuals will be called to challenge the governing logic of the zeitgeist - logic that operates now as an oppressive force that serves the vested interest of beneficials of the existing order. When success is favored over doing what is right, as we must admit is the prevailing cultural mood of our times, that the words of Emanuel Kant carry their full weight: "Do the Right thing and leave the Consequences to God". For this we need heroes and heroines that challenge the time by bearing the full weight of responsibility that comes with the doing of what is Right. *** This book was written more than anything from the perspective of the heroes and heroines of action. Sometimes they may be missing the exact words or the full insight into the solid logical complexity that stands between them and the doing of what is right. They feel what is right to do on the battlefield of life, whether in real battle, in political or economic life or whether in the life of creativity and the quest of the intellect. They do need, in analogy, proper logical and intellectual artillery. I hope they will find the logical cannons they require as they travel through the pages of this book. The rest is in their hands at the Moment of Truth. -/- Doron Avital, Tel Aviv 2011 -/- . (shrink)

This paper, being a companion to the book [2] elaborates the deontology of sequential and compound actions based on relational models and formal constructs borrowed from formal linguistics. The semantic constructions presented in this paper emulate to some extent the content of [3] but are more involved. Although the present work should be regarded as a sequel of [3] it is self-contained and may be read independently. The issue of permission and obligation of actions is presented in the form (...) of a logical system. This system is semantically defined by providing its intended models in which the role of actions of various types is accentuated. Since the consequence relation is not finitary, other semantically defined variants of are defined. The focus is on the finitary system in which only finite compound actions are admissible. An adequate axiom system for it is defined. The strong completeness theorem is the central result. The role of the canonical model in the proof of the completeness theorem is emphasized. (shrink)

We continue the work of Blok and Jónsson by developing the theory of structural closure operators and introducing the notion of a representation between them. Similarities and equivalences of Blok-Jónsson turn out to be bijective representations and bijective structural representations, respectively. We obtain a characterization for representations induced by a transformer. In order to obtain a similar characterization for structural representations we introduce the notions of a graduation and a graded variable of an M-set. We show that several deductive systems, (...) Gentzen systems among them, are graded M-sets having graded variables, and describe the graded variables in each case. In the last section we show that, for a sentential logic, having an algebraic semantics is equivalent to being representable in an equational consequence. This motivates the extension of the notion of having an algebraic semantics for Gentzen systems, hypersequents systems, etc. We prove that if a closure operator is representable by a transformer, then every extension of it is also representable by the same transformer. As a consequence we obtain that if one of these systems has an algebraic semantics, then so does any of its extensions with the same defining equations. (shrink)

The human primate is a deeply cultural species, our cognition being shaped by culture, and cultural transmission amounting to an “epidemic of mental representations” (Sperber, 1996). The architecture of this aspect of human cognition has been shaped by our evolutionary past in ways that we can now begin to discern through comparative studies of other primates. Processes of social learning (learning from others) are important for cognitive science to understand because they are cognitively complex and take many interrelated forms; they (...) shape traditions, cultures and nonsocial aspects of cognition; and in turn they may be shaped by their cultural context. The study of primate social learning and culture has in recent years enjoyed a renaissance, providing a wealth of new findings, key aspects of which are reviewed. The focus is on cognitive issues, including learning about the consequences, sequential structure and hierarchical organization of actions; relating stored knowledge to the assimilation of new social knowledge; feedback guiding the construction of imitations; conceptual grasp of imitation; and the reciprocal relationship between social learning and culture. (shrink)

In this paper, I address a question in social epistemology about the unity of a scientic community to- wards its inner groups (teams, labs...). I investigate the reasons why these groups might want to \go it alone", working among themselves and hiding their discoveries from other groups. I concentrate on the intermediate results of a longer project, where the first steps can help to achieve a more advanced result. I study to what extent the isolation of research groups might be (...) damaging to the epistemic progress of the whole community. In order to get an idea of the reason why scientists might not share their intermediate results with others, consider for example Schawlow and Townes in the summer of 1958 (the historical material is drawn from Broberg, 1991, chap. 3): together they had just designed the principle of functioning of what would be known as the laser, with the intention of constructing the rst laser, relying on their theoretical ideas. Should they have published their theoretical discovery, or rather taken advantage of their advance on possible oppo- nents and start the experimental work? They chose to publish their theoretical ideas in a scientic journal, and they also led a patent application. On the one hand, it was a valuable choice: the patent was granted and their paper was published, making them soon famous. Further- more, another scientist called Gould was to le a simi- lar patent application a few months later, in March 1959; it was refused, because of the priority of Schawlow and Townes. If the latter had not submitted their idea in 1958, the patent would certainly have been acknowl- edged to Gould. In this sense, publishing their intermediate result was a worthy strategy. On the other hand, history showed that their publication had also some drawbacks for them. Schawlow and Townes' publication triggered a race among many American laboratories for the rst experimental construction of the laser. In addition to bringing them competitors, their publication helped these competitors in crucial ways; so much so that it was another scientist, Maiman, and not Schawlow and Townes, who was able to build the rst working laser, in May 1960, and to publish the result. If Schawlow and Townes had not published their theoretical idea, there are chances that they would have been the first ones to build a laser. Their publication of the first theoretical result certainly prevented them from getting the second experimental one. In short, the best publishing strategy about an intermediate result is no easy question for a scientist. Consider now the whole community, concerned with the results available to all and with the pace of the epistemic progress. Schawlow and Townes' publication enabled the rst laser to be built quicker, as other teams could rely on their theoretical work. More generally, being able to reuse other's works seems to be a rm basis of scientic progress. Thus, for the whole community, it seems that there are only benets if intermediate results are published. As this is not necessarily the best strategy for those who reach these intermediate results, there might be a conflict between the interests of individuals and those of the whole community. The question Schawlow and Townes faced was whether they should make their discovery publicly known, or keep it for themselves to progress alone. This alternative can also arise for an entire lab, when competing with other labs on some long-run project: should it make its discoveries known to its opponents, or only share them internally among its members? At a higher level still, this question arises for what can be called scientic schools, which are groups of labs sharing some particular approach|methodological, experimental or interpre- tational, for example. At each level within the scientic community, there are competitive groups of scientists which may decide to go it alone and to prevent their results from being accessible to others. If they had good reasons for doing so, there would be dramatic consequences for the whole community: other groups would not be able to reuse their results, labour force would be wasted in achieving them again, and the progress of the eld would be slowered. 9 The aim of this paper is to investigate this risk of division: to assess the conditions under which it may oc- cur, its damage for the community, and to draw the limit of an acceptable pluralism. The reasoning with benets and drawbacks which has been sketched for Schawlow and Townes seems to be implicitly an informal economic argument. In order to clarify and to rene such an argument, I will investigate it in a rational decision framework, supposing some utility or preferences for the groups of scientists, and I will propose a formal model, in game theory. In social epistemology of science, formal models have been proposed for various questions (for example, Kitcher 1990, 1993, Goldman 2009, Strevens 2003, 2006, Weisberg and Muldoon, forthcoming, Zollman 2007, 2008, 2009, 2010), but not for the question of the division of the scientic community. I will concentrate on the normative aspect of the question, ignoring the descriptive and historical question of whether groups do go it alone or not. The model I propose is sequential: two groups are competing on a research program, which consists of several results which have to be obtained in order. The groups always carry out some research for the next result, which they reach with some probability per unit of time. When a group, say A, reaches a result, it can either make it public for the other group, or continue its research. After a result is made public, the competitor B can start from it so as to continue its own research. Thus, when A publishes it loses its lead, and its competitor will be able to compete with it in the near future. But it is also recognized as the rst to reach this step. I consider two dierent cases, one in which the number of steps is limited, another where the limit concerns the number of temporal intervals. In both cases, assuming that all steps are equally dicult and equally rewarding, it turns out that the best strategy for a group concerned with its own reward is to make public every step it takes. Thus, there is no risk that groups might separate: a scientist, whatever its group, will publish for all. Finally, I turn to more complex situations, where results have varying size or diculty: there, groups can indeed be better o going it alone. (shrink)

We introduce a deductive system Bal which models the logic of balance of opposing forces or of balance between conflicting evidence or influences. ‘‘Truth values’’ are interpreted as deviations from a state of equilibrium, so in this sense, the theorems of Bal are to be interpreted as balanced statements, for which reason there is only one distinguished truth value, namely the one that represents equilibrium. The main results are that the system Bal is algebraizable in the sense of [5] (...) and its equivalent algebraic semantics BAL is definitionally equivalent to the variety of abelian lattice ordered groups, that is, the categories of the algebras in BAL and of ℓ–groups are isomorphic (see [10], Ch.4, 4). We also prove the deduction theorem for Bal and we study different kinds of semantic consequence associated to Bal. Finally, we prove the co-NP-completeness of the tautology problem of Bal. (shrink)

Maher (1992b) advances an objection to dynamic Dutch-book arguments, partly inspired by the discussion in Levi (1987; in particular by Levi's case 2, p. 204). Informally, the objection is that the decision maker will "see the dutch book coming" and consequently refuse to bet, thus escaping the Dutch book. Maher makes this explicit by modeling the decision maker's choices as a sequential decision problem. On this basis he claims that there is a mistake in dynamic coherence arguments. There is (...) really no formal mistake in classical dynamic coherence arguments, but the discussions in Maher and Levi do suggest interesting ways in which the definition of dynamic coherence might be strengthened. Such a strengthened "sequentialized" notion of dynamic coherence is explored here. It so happens that even on the strengthened standards for a Dutch book, the classic dynamic coherence argument for conditioning still goes through. (shrink)

Prior research on sustainable supply chain management (SSCM) has almost exclusively focused on environmental aspects (GSCM—green supply chain management) and the study of its external drivers and consequences. Framing our study within the “strategy‐conduct‐performance” paradigm, we consider the focal firm's role in the implementation of sustainable supply chain initiatives, social as well as environmental. We use data on the S&P 500 Index retrieved from Bloomberg, including variables for two relevant focal firm strategies: (a) reducing the environmental footprint of the supply (...) chain and (b) reducing social risks in the supply chain (SRSS). Hierarchical logit modeling is carried out to examine the sequential impact of governance board characteristics and the focal firm's adoption of related internal policies and practices on the likelihood of implementing these initiatives along the supply chain. Controlling for industry, firm size, and resources, we find that board structure and diversity influence the implementation of sustainable supply chain initiatives by increasing organizational commitment to environmentally friendly and socially responsible policies and practices. Consequently, empirical evidence exists for the importance of strategic factors, namely a proactive corporate stance on sustainability associated with governance board characteristics, as antecedents of sustainable (environmental and social) supply chain initiatives. (shrink)

We provide a finite axiomatization of the consequence , i.e. of the set of common sequential rules for and . Moreover, we show that has no proper non-trivial strengthenings other than and . A similar result is true for , but not, e.g., for +.

High-dose chemotherapy and autologous stem cell transplantation is used to treat some advanced malignancies. It is a traumatic procedure, with a high complication rate and significant mortality. ASCT patients and their carers draw on many sources of information as they seek to understand the procedure and its consequences. Some seek information from beyond orthodox medicine. Alternative beliefs and practices may conflict with conventional understanding of the theory and practice of ASCT, and ‘contested understandings’ might interfere with patient adherence to the (...) strict and demanding protocols required for successful ASCT.The present study, conducted in Sydney, Australia, examines narrative-style interviews with 10 sequentially recruited ASCT patients and nine of their carers conducted at the time of transplant and three months later. Transcripts were read for instances of mention of alternative advice, and for instances of contested understanding of information relevant to the transplant.Patients and carer pairs expressed closely concordant views about alternative advice. Five pairs were consulting alternative practitioners. Contested understanding was expressed in four domains—understandings of the transplant itself and its underlying theory, of the relationship between the components of the ‘transplant’, of the nature and role of stem cells, and of beliefs about bodily function and life-style. Contested understandings of the transplant treatment were expressed as predominantly personal interpretations of orthodox informationPatients and carers seemed to recognise that alternative and conventional systems were discordant, yet they were able to separate the two, and adhere to each practice without prejudicing their medical treatment. A single case of late, post-transplant repudiation of Western medicine is discussed to emphasise some of the possible determinants of dissonance when it does occur. (shrink)

Quantum information science is a source of task-related axioms whose consequences can be explored in general settings encompassing quantum mechanics, classical theory, and more. Quantum states are compendia of probabilities for the outcomes of possible operations we may perform on a system: ''operational states.'' I discuss general frameworks for ''operational theories'' (sets of possible operational states of a system), in which convexity plays key role. The main technical content of the paper is in a theorem that any such theory naturally (...) gives rise to a ''weak effect algebra'' when outcomes having the same probability in all states are identified and in the introduction of a notion of ''operation algebra'' that also takes account of sequential and conditional operations. Such frameworks are appropriate for investigating what things look like from an ''inside view,'' i.e., for describing perspectival information that one subsystem of the world can have about another. Understanding how such views can combine, and whether an overall ''geometric'' picture (''outside view'') coordinating them all can be had, even if this picture is very different in structure from the perspectives within it, is the key to whether we may be able to achieve a unified, ''objective'' physical view in which quantum mechanics is the appropriate description for certain perspectives, or whether quantum mechanics is truly telling us we must go beyond this ''geometric'' conception of physics. (shrink)

Monitoring ongoing clinical trials for early signs of effectiveness is an option for improving cost-effectiveness of trials that is becoming increasingly common. Alongside the obvious advantages made possible by monitoring, however, there are some downsides. In particular, there is growing concern in the medical community that trials stopped early for benefit tend to overestimate treatment effect. In this paper, I examine this problem from the point of view of statistical methodology, starting from the observation that the overestimation is caused by (...) the statistical method adopted. Consequently, I argue that some modifications can and should be made to the present statistical framework in order not to miss the advantages the possibility of monitoring can grant. (shrink)