Electroencephalogram (EEG) recordings are increasingly used to evaluate patients with disorders of consciousness (DOC) or assess their prognosis outcome in the short-term perspective. However, there is a lack of information concerning the effectiveness of EEG in classifying long-term (many years) outcome in chronic DOC patients. Here we tested whether EEG operational architectonics parameters (geared towards consciousness phenomenon detection rather than neurophysiological processes) could be useful for distinguishing a very long-term (6 years) clinical outcome of DOC patients whose EEGs were (...) registered within 3 months post-injury. The obtained results suggest that EEG recorded at third month after sustaining brain damage, may contain useful information on the long-term outcome of patients in vegetative state: it could discriminate patients who remain in a persistent vegetative state from patients who reach a minimally conscious state or even recover a full consciousness in a long-term perspective (6 years) post-injury. These findings, if confirmed in further studies, may be pivotal for long-term planning of clinical care, rehabilitative programs, medical-legal decisions concerning the patients, and policy makers. (shrink)

The major contributions of operationism have been negative, largely because operationists failed to distinguish logical theories of reference from empirical accounts of language. Behaviorism never finished an adequate formulation of verbal reports and therefore could not convincingly embrace subjective terms. But verbal responses to private stimuli can arise as social products through the contingencies of reinforcement arranged by verbal communities.

Using theoretical analysis of self-consciousness concept and experimental evidence on the brain default mode network (DMN) that constitutes the neural signature of self-referential processes, we hypothesized that the anterior and posterior subnets comprising the DMN should show differences in their integrity as a function of meditation training. Functional connectivity within DMN and its subnets (measured by operational synchrony) has been measured in ten novice meditators using an electroencephalogram (EEG) recording in a pre-/post-meditation intervention design. We have found that while (...) the whole DMN was clearly suppressed, different subnets of DMN responded differently after 4 months of meditation training: The strength of EEG operational synchrony in the right and left posterior modules of the DMN decreased in resting post-meditation condition compared to a pre-meditation condition, whereas the frontal DMN module on the contrary exhibited an increase in the strength of EEG operational synchrony. These findings combined with published data on functional–anatomic heterogeneity within the DMN and on trait subjective experiences commonly found following meditation allow us to propose that the first-person perspective and the sense of agency (the witnessing observer) are presented by the frontal DMN module, while the posterior modules of the DMN are generally responsible for the experience of the continuity of ‘I’ as embodied and localized within bodily space. Significance of these findings is discussed. (shrink)

The Build-Operate-Transfer (BOT) model is a financing model used especially in the financing of infrastructure projects in developing countries. It is one of the most common methods used by the countries to provide non-budgetary financing. The fact that becoming popular in the world as of the 20th Century, this model started to be implemented in the Islamic countries created the need for examining the model in terms of Islamic law. No substantive studies have been conducted on this matter in (...) Turkey. In the Arab world, the first significant development in this regard was the 23rd Term meeting of Al Baraka Group organized in Mecca in November 2002. Next, the Islamic Fiqh Community, which operates under the Organization of Islamic Cooperation, organized a meeting about the BOT model in 2009. At this meeting, ten experts from different countries presented papers on the BOT model, and a final declaration was announced at the end of the meeting. After this meeting, some independent studies were carried out on the BOT model. However, it was observed that these efforts did not reach a sufficient level, and generally remained within the framework of the papers presented at the meeting. The BOT model is a model that takes place in the form of the transfer of the facility to the relevant public institution or organization free of charge at the end of the period after the depreciation and profit of the invested capital are realized. All expenses are covered by the private enterprise. The public service or activity is operated for a certain period of time by the private enterprise. It was observed that the studies on the BOT model in Turkey mainly dated back to the last quarter of the Twentieth Century. In this context, the Law No. 3996 about the BOT model was enacted on 08 June 1994 in Turkey. Today, the BOT model is actively used in many areas, and the delivery of the service begins after the projects are completed. The BOT model has three main successive stages. In the first stage, the project is completed with the financing of OGS. In the second stage, the operating right of this project would be awarded to the investor in accordance with the contract. In the third stage, the ownership of the facility would be transferred to the relevant public institution. The BOT model was discussed in terms of Islamic law, firstly in general and then in terms of the interests and convictions. The BOT model contains many interests in terms of both the state and the society. In addition, it has certain disadvantages. There are many reasons and aims in selecting the BOT model. The most important of these reasons is the continuation of the projects and the required work without imposing a burden on the public budget. Islamic law has a structure that prioritizes public interest. In this context, the state must observe the public interest in its operations. In the BOT model, the existence of public interest is particularly notable with the projects implemented in the fields of hospitals, roads, bridges, airports and etc. Islamic jurists have different opinions regarding the contracts administered in the BOT model. Some of them consider this model as a new contract that does not exist in the tradition, while others compare it to a traditional contract. The analogies of the traditional contract have been compared to leasing, payment, foundation, fief, corporate (with partnership) and exception contracts. Others, on the other hand, considered the BOT model as an atramentous contract combining several different contracts. It seems difficult to argue that the BOT model is completely similar to any of the classical fiqh contracts. However, as a result of the BOT model, it is considered an agreement with a company to conclude a contract; therefore there is a more prominent similarity to an exception contract. Nonetheless, it is not possible to say that the BOT model fully complies with the traditional exception contract. As a matter of fact, while there is no time determination in the exception contract, the time is determined in the BOT model. In the exception contract, while the material must be completely covered by the private sector, in the BOT model, issues such as the right to land and building construction are covered by the employer. In addition, the classical exception contract does not contain many contracts as in the BOT model; and it is an agreement in which the fee is presented and terminated after the order is placed. Nonetheless, the BOT contract includes three basic contracts (construction-operation-transfer) as well as many contracts related to these contracts. Finally, considering that the BOT model was a contract, the issues in the context of the basic elements that should be included in a contract were discussed in this study. In addition, situations such as ignorance, gharar and interest in terms of affecting the validity of the contract were discussed and dealt with in terms of the BOT contract. (shrink)

Chapin reviewed this 1972 ZEITSCHRIFT paper that proves the completeness theorem for the logic of variable-binding-term operators created by Corcoran and his student John Herring in the 1971 LOGIQUE ET ANALYSE paper in which the theorem was conjectured. This leveraging proof extends completeness of ordinary first-order logic to the extension with vbtos. Newton da Costa independently proved the same theorem about the same time using a Henkin-type proof. This 1972 paper builds on the 1971 “Notes on a Semantic Analysis of (...) Variable Binding Term Operators” (Co-author John Herring), Logique et Analyse 55, 646–57. MR0307874 (46 #6989). A variable binding term operator (vbto) is a non-logical constant, say v, which combines with a variable y and a formula F containing y free to form a term (vy:F) whose free variables are exact ly those of F, excluding y. Kalish-Montague 1964 proposed using vbtos to formalize definite descriptions “the x: x+x=2”, set abstracts {x: F}, minimization in recursive function theory “the least x: x+x>2”, etc. However, they gave no semantics for vbtos. Hatcher 1968 gave a semantics but one that has flaws described in the 1971 paper and admitted by Hatcher. In 1971 we give a correct semantic analysis of vbtos. We also give axioms for using them in deductions. And we conjecture strong completeness for the deductions with respect to the semantics. The conjecture, proved in this paper with Hatcher’s help, was proved independently about the same time by Newton da Costa. (shrink)

Sub-Saharan emerging countries experience electrical shortages resulting in power rationing, which ends up hampering economic activities. This paper proposes an approach for very short-term blackout forecast in grid-tied PV systems operating in low reliability weak electric grids of emerging countries. A pilot project was implemented in Arusha-Tanzania; it mainly comprised of a PV-inverter and a lead-acid battery bank connected to the local electricity utility company, Tanzania Electric Supply Company Limited. A very short-term power outage prediction model framework based on a (...) hybrid random forest algorithm was developed using open-source Python machine learning libraries and using a dataset generated from the pilot project’s experimental microgrid. Input data sampled at a 15-minute interval included day of the month, weekday, hour, supply voltage, utility line frequency, and previous days’ blackout profiles. The model was composed of an adaptive similar day module that predicts 15 minutes ahead from a sliding window lookup table spanning 2 weeks prior to the prediction target day, after which ASD prediction was fused with RF prediction, giving a final optimised RF-ASD blackout prediction model. Furthermore, the efficacy analysis of the short-term blackout prediction of the formulated RF, ASD, and RF-ASD regression and classification algorithms was compared. Considering the stochastic nature of blackouts, their performance was found to be fair in short-term blackout predictions of the test site’s weak grid using limited input data from the point of coupling of the user. The models developed were only able to predict blackouts if they occurred frequently and contiguously, but they performed poorly if they were sparse or dispersed. (shrink)

Several important terms in biology have recently been criticized for not being "operational." In this paper the course of operationism in physics, psychology and genetics is sketched to show what effect this particular view on the meaning of scientific terms had on these disciplines. Then the biological species concept and the concept of homology are examined to see in what respects they are or are not "operational." One of the primary conclusions of this investigation is that (...) few terms in science are completely operational or completely nonoperational. Some scientific terms, especially theoretical terms, are a good deal less operational than others; but, far from being regrettable, this situation is essential if theoretical terms are to fulfill their systematizing function and if scientific theories are to be capable of growth. (shrink)

-/- A variable binding term operator (vbto) is a non-logical constant, say v, which combines with a variable y and a formula F containing y free to form a term (vy:F) whose free variables are exact ly those of F, excluding y. -/- Kalish-Montague proposed using vbtos to formalize definite descriptions, set abstracts {x: F}, minimalization in recursive function theory, etc. However, they gave no sematics for vbtos. Hatcher gave a semantics but one that has flaws. We give a correct (...) semantic analysis of vbtos. We also give axioms for using them in deductions. And we conjecture strong completeness for the deductions with respect to the semantics. The conjecture was later proved independently by the authors and by Newton da Costa. -/- The expression (vy:F) is called a variable bound term (vbt). In case F has only y free, (vy:F) has the syntactic propreties of an individual constant; and under a suitable interpretation of the language vy:F) denotes an individual. By a semantic analysis of vbtos we mean a proposal for amending the standard notions of (1) "an interpretation o f a first -order language" and (2) " the denotation of a term under an interpretation and an assignment", such that (1') an interpretation o f a first -order language associates a set-theoretic structure with each vbto and (2') under any interpretation and assignment each vb t denotes an individual. (shrink)

Episodic memory often is conceptualized as a uniquely human system of long-term memory that makes available knowledge accompanied by the temporal and spatial context in which that knowledge was acquired. Retrieval from episodic memory entails a form of first–person subjectivity called autonoetic consciousness that provides a sense that a recollection was something that took place in the experiencer’s personal past. In this paper I expand on this definition of episodic memory. Specifically, I suggest that (a) the core features assumed unique (...) to episodic memory are shared by semantic memory, (b) episodic memory cannot be fully understood unless one appreciates that episodic recollection requires the coordinated function of a number of distinct, yet interacting, “enabling” systems. Although these systems – ownership, self, subjective temporality, and agency – are not traditionally viewed as memorial in nature, each is necessary for episodic recollection and jointly they may be sufficient, and (c) the type of subjective awareness provided by episodic recollection (autonoetic) is relational rather than intrinsic – i.e., it can be lost in certain patient populations, thus rendering episodic memory content indistinguishable from the content of semantic long-term memory. (shrink)

Predicates are term-to-sentence devices, and operators are sentence-to-sentence devices. What Kaplan and Montague's Paradox of the Knower demonstrates is that necessity and other modalities cannot be treated as predicates, consistent with arithmetic; they must be treated as operators instead. Such is the current wisdom.A number of previous pieces have challenged such a view by showing that a predicative treatment of modalities neednot raise the Paradox of the Knower. This paper attempts to challenge the current wisdom in another way as well: (...) to show that mere appeal to modal operators in the sense of sentence-to-sentence devices is insufficient toescape the Paradox of the Knower. A family of systems is outlined in which closed formulae can encode other formulae and in which the diagonal lemma and Paradox of the Knower are thereby demonstrable for operators in this sense. (shrink)

How can we critique political theory when all we have to use are its own conceptual tools? As Hannah Arendt observed, it can only be done through leaps, inversions, and the turning of concepts upside-down. But this twisting operation must be done in order to turn those who philosophize back to the hard work of real life change. In Turning Operations, renowned theorist Mary G. Dietz challenges specific contemporary modes of theorizing politics-from feminist theory to Habermasian discourse- -while appropriating some (...) of political theory's own approaches and some of its most striking figures, including Aristotle, Nietzsche, Weber, Beauvoir, and Arendt in order to foment some leaps, inversions, reversals and turns on politics along the way. Dietz confronts a number of current debates, arguing that most are filled with artificial division and empty terms. She argues that we must abandon commonly supported dichotomies-masculine versus feminine, speech versus action, liberty versus community -to create abetter discourse, and a better world. Turning Operations is an essential new contribution to democratic and feminist political thought. (shrink)

I shall be dealing, throughout this book, with a set of related problems: the relationship between morality and reasoning in general, the way in which moral reasoning is properly to be carried on, and why morality is not arbitrary. The solutions to these problems come out of the same train of argument. Morality is not arbitrary, I shall argue, because the acceptance of certain qualities of character as virtues and the rejection of others as vices is forced on us by (...) the co-operative basis of human life. The co-operation in human life is unavoidable; the alternative is a literal Hobbesian state of nature, and that is impossible. It is not that co-operation between people is a good thing or even a very good thing; it is simply unavoidable in human life, and it is impossible unless the qualities of character counted as virtues are encouraged and are at least fairly common. The possibility of human life presupposes a theory of human nature, and working out that theory of human nature is the main job of moral philosophy. These virtues or qualities of character or attitudes lead us towards a theory of reasons. A person with a sense of justice is a person inclined to accept certain sorts of facts as reasons for acting, and if the virtues are presupposed by human life then the acceptance of those sorts of facts as reasons for acting is presupposed by human life. A condition of the life of reasoning beings (a more accurate term here than 'human beings') is that moral reasons are reasons for acting and are at the very basis of reasoning. And from this it follows that properly conducted moral reasoning is ultimately guided by the virtues rather than ultimately guided by a set of rules. (shrink)

The general theory of variable binding term operators is an interesting recent development in logic. It opens up a rich class of semantic and model-theoretic problems. In this paper we survey the recent literature on the topic, and offer some remarks on its significances and on its connections with other branches of mathematical logic.

Concepts of space and time are widely developed in physics. However, there is a considerable lack of biologically plausible theoretical frameworks that can demonstrate how space and time dimensions are implemented in the activity of the most complex life-system – the brain with a mind. Brain activity is organized both temporally and spatially, thus representing space-time in the brain. Critical analysis of recent research on the space-time organization of the brain’s activity pointed to the existence of so-called operational space-time (...) in the brain. This space-time is limited to the execution of brain operations of differing complexity. During each such brain operation a particular short-term spatio-temporal pattern of integrated activity of different brain areas emerges within related operational space-time. At the same time, to have a fully functional human brain one needs to have a subjective mental experience. Current research on the subjective mental experience offers detailed analysis of space-time organization of the mind. According to this research, subjective mental experience (subjective virtual world) has definitive spatial and temporal properties similar to many physical phenomena. Based on systematic review of the propositions and tenets of brain and mind space-time descriptions, our aim in this review essay is to explore the relations between the two. To be precise, we would like to discuss the hypothesis that via the brain operational space-time the mind subjective space-time is connected to otherwise distant physical space-time reality. (shrink)

We study some operations that may be defined using the minimum operator in the context of a Heyting algebra. Our motivation comes from the fact that 1) already known compatible operations, such as the successor by Kuznetsov, the minimum dense by Smetanich and the operation G by Gabbay may be defined in this way, though almost never explicitly noted in the literature; 2) defining operations in this way is equivalent, from a logical point of view, to two clauses, one corresponding (...) to an introduction rule and the other to an elimination rule, thus providing a manageable way to deal with these operations. Our main result is negative: all operations that arise turn out to be Heyting terms or the mentioned already known operations or operations interdefinable with them. However, it should be noted that some of the operations that arise may exist even if the known operations do not. We also study the extension of Priestley duality to Heyting algebras enriched with the new operations. (shrink)

In this paper, we approach the problem of classical recapture for LP and K3 by using normality operators. These generalize the consistency and determinedness operators from Logics of Formal Inconsistency and Underterminedness, by expressing, in any many-valued logic, that a given formula has a classical truth value (0 or 1). In particular, in the rst part of the paper we introduce the logics LPe and Ke3 , which extends LP and K3 with normality operators, and we establish a classical recapture (...) result based on the two logics. In the second part of the paper, we compare the approach in terms of normality operators with an established approach to classical recapture, namely minimal inconsistency. Finally, we discuss technical issues connecting LPe and Ke3 to the tradition of Logics of Formal Inconsistency and Underterminedness. (shrink)

Two different concepts of iconicity compete in Peirce's diagrammatical logic. One is articulated in his general reflections on the role of diagrams in thought, in what could be termed his diagrammatology — the other is articulated in his construction of Existential Graphs as an iconic system for representing logic. One is operational and defines iconicity in terms of which information may be derived from a given diagram or diagram system — the other has stronger demands on iconicity, adding (...) to the operational criterion a demand for as high a degree of similarity as possible and may be termed optimal iconicity. Peirce himself does not clearly distinguish these two iconicity notions, a fact that has caused some confusion. By isolating them, we get a clearer and more refined conceptual apparatus for analyzing iconic signs, from pictures to logic. (shrink)

A series of representations must be semantics-driven if the members of that series are to combine into a single thought: where semantics is not operative, there is at most a series of disjoint representations that add up to nothing true or false, and therefore do not constitute a thought at all. A consequence is that there is necessarily a gulf between simulating thought, on the one hand, and actually thinking, on the other. A related point is that a popular doctrine (...) - the so-called 'computational theory of mind' (CTM) - is based on a confusion. CTM is the view that thought-processes consist in 'computations', where a computation is defined as a 'form-driven' operation on symbols. The expression 'form-driven operation' is ambiguous, as it may refer either to syntax-driven operations or to morphology-driven operations. Syntax-driven operations presuppose the existence of operations that are driven by semantic and extra-semantic knowledge. So CTM is false if the terms 'computation' and 'form-driven operation' are taken to refer to syntax-driven operations. Thus, if CTM is to work, those expressions must be taken to refer to morphology-driven operations. CTM therefore fails, given that an operation must be semantics-driven if it is to qualify as a thought. CTM therefore fails on each possible disambiguation of the expressions 'formal operation' and 'computation,' and it is therefore false. (shrink)

We study the extension of Feferman’s operational set theory provided by adding operational versions of unbounded existential quantification and power set and determine its proof-theoretic strength in terms of a suitable theory of sets and classes.

We study the forcing operators on MTL-algebras, an algebraic notion inspired by the Kripke semantics of the monoidal t -norm based logic . At logical level, they provide the notion of the forcing value of an MTL-formula. We characterize the forcing operators in terms of some MTL-algebras morphisms. From this result we derive the equality of the forcing value and the truth value of an MTL-formula.

Do neurobiologists aim to discover natural kinds? I address this question in this chapter via a critical analysis of classification practices operative across the 43-year history of research on long-term potentiation. I suggest that this 43-year history supports the idea that the structure of scientific practice surrounding LTP research has remained an obstacle to the discovery of natural kinds as philosophers of science have traditionally conceived them.

We trace the difference between the ways in which apes and humans co–operate to differences in communicative abilities, claiming that the pressure for future–directed co–operation was a major force behind the evolution of language. Competitive co–operation concerns goals that are present in the environment and have stable values. It relies on either signalling or joint attention. Future–directed co–operation concerns new goals that lack fixed values. It requires symbolic communication and context–independent representations of means and goals. We analyse these ways of (...) co–operating in game–theoretic terms and submit that the co–operative strategy of games that involve shared representations of future goals may provide new equilibrium solutions. (shrink)

In this paper we shall introduce the variety FWHA of frontal weak Heyting algebras as a generalization of the frontal Heyting algebras introduced by Leo Esakia in [10]. A frontal operator in a weak Heyting algebra A is an expansive operator r preserving finite meets which also satisfies the equation?? b V, for all a,b? A. These operators were studied from an algebraic, logical and topological point of view by Leo Esakia in [10]. We will study frontal operators in weak (...) Heyting algebras and we will consider two examples of them. We will give a Priestley duality for the category of frontal weak Heyting algebras in terms of relational spaces where is a WH space [6], and R is an additional binary relation used to interpret the modal operator. We will also study the WH- algebras with successor and the WTf- algebras with gamma. For these varieties we will give two topological dualities. The first one is based on the representation given for the frontal weak Heyting algebras. The second one is based on certain particular classes of WH-spaces. (shrink)

In this article we introduce and study the notion of operational closure: a transitive set d is called operationally closed iff it contains all constants of OST and any operation f∈d applied to an element a∈d yields an element fa∈d, provided that f applied to a has a value at all. We will show that there is a direct relationship between operational closure and stability in the sense that operationally closed sets behave like Σ1 substructures of the universe. (...) This leads to our final result that OST plus the axiom , claiming that any set is element of an operationally closed set, is proof-theoretically equivalent to the system KP+ of Kripke–Platek set theory with infinity and Σ1 separation. We also characterize the system OST plus the existence of one operationally closed set in terms of Kripke–Platek set theory with infinity and a parameter-free version of Σ1 separation. (shrink)

Do neurobiologists aim to discover natural kinds? I address this question in this chapter via a critical analysis of classification practices operative across the 43-year history of research on long-term potentiation (LTP). I argue that this 43-year history supports the idea that the structure of scientific practice surrounding LTP research has remained an obstacle to the discovery of natural kinds.

Storage operators have been introduced by J. L. Krivine in [5] they are closed λ-terms which, for a data type, allow one to simulate a "call by value" while using the "call by name" strategy. In this paper, we introduce the directed λ-calculus and show that it has the usual properties of the ordinary λ-calculus. With this calculus we get an equivalent--and simple--definition of the storage operators that allows to show some of their properties: $\bullet$ the stability of the (...) set of storage operators under the β-equivalence (Theorem 5.1.1); $\bullet$ the undecidability (and semidecidability) of the problem "is a closed λ-term t a storage operator for a finite set of closed normal λ-terms?" (Theorems 5.2.2 and 5.2.3); $\bullet$ the existence of storage operators for every finite set of closed normal λ-terms (Theorem 5.4.3); $\bullet$ the computation time of the "storage operation" (Theorem 5.5.2). (shrink)

Logic of proofs LP was introduced by S. Artemov in. It describes properties of the proof predicate “t is a proof of F” formalized by the formula ⟦t⟧ F. Proofs are represented by terms constructed by three elementary recursive operations on proofs. In this paper we extend the language of the logic of proofs by the additional storage predicate x ∋ F with the intended interpretation “x is a label for F”. The storage predicate can play the role of (...) syntax encoding, so it is useful for specification of operations on proofs, especially those that require formula arguments. We give a definition of a specification of an operation on proofs and introduce logics that describe such operations. For a large class of operations we prove the completeness of these logics with respect to the intended semantics. We also study the logic describing the operation of substitution. (shrink)

“Small” large cardinal notions in the language of ZFC are those large cardinal notions that are consistent with V = L. Besides their original formulation in classical set theory, we have a variety of analogue notions in systems of admissible set theory, admissible recursion theory, constructive set theory, constructive type theory, explicit mathematics and recursive ordinal notations (as used in proof theory). On the face of it, it is surprising that such distinctively set-theoretical notions have analogues in such disaparate and (...) relatively constructive contexts. There must be an underlying reason why that is possible (and, incidentally, why “large” large cardinal notions have not led to comparable analogues). My long term aim is to develop a common language in which such notions can be expressed and can be interpreted both in their original classical form and in their analogue form in each of these special constructive and semi-constructive cases. This is a program in progress. What is done here, to begin with, is to show how that can be done to a considerable extent in the settings of classical and admissible set theory (and thence, admissible recursion theory). The approach taken here is to expand the language of set theory to allow us to talk about (possibly partial) operations applicable both to sets and to operations and to formulate the large cardinal notions in question in terms of operational closure conditions; at the same time only minimal existence axioms are posited for sets. The resulting system, called Operational Set Theory, is a partial adaptation to the set-theoretical framework of the explicit mathematics framework Feferman (1975). The.. (shrink)

Many expressions intuitively have different epistemic and modal profiles. For example, co-referring proper names are substitutable salva veritate in modal contexts but not in belief-contexts. Two-dimensional semantics, according to which terms have both a so-called primary and a secondary intension, is a framework that promises to accommodate and explain these diverging intuitions. The framework can be applied to indexicals, proper names or predicates. Graeme Forbes argues that the two-dimensional semantics of David Chalmers fails to account for so-called nested contexts. (...) These are linguistic contexts where a sentence is embedded under both epistemic and modal operators. Chalmers and Rabern suggest a two-dimensional solution to the problem. Their semantics solves the nesting-problem, but at the cost of invalidating certain plausible principles. We suggest a solution that is both simpler and avoids this cost. (shrink)

Many powerful logics exist today for reasoning about multi-agent systems, but in most of these it is hard to reason about an infinite or indeterminate number of agents. Also the naming schemes used in the logics often lack expressiveness to name agents in an intuitive way.To obtain a more expressive language for multi-agent reasoning and a better naming scheme for agents, we introduce a family of logics called term-modal logics. A main feature of our logics is the use of modal (...) operators indexed by the terms of the logics. Thus, one can quantify over variables occurring in modal operators. In term-modal logics agents can be represented by terms, and knowledge of agents is expressed with formulas within the scope of modal operators. (shrink)

The sum, difference, product and quotient of two functions with different domains are usually defined only on their common domain. This paper extends these definitions so that the sum and other operations are essentially defined anywhere that at least one of the components is defined. This idea is applied to propositions and events, expressed as indicator functions, to define conditional propositions and conditional events as three-valued indicator functions that are undefined when their condition is false. Extended operations of "and", "or", (...) "not" and "conditioning" are then defined on these conditional events with variable conditions. The probabilities of the disjunction and of the conjunction of two conditionals are expressed in terms of the conditional probabilities of the component conditionals. In a special case, these are shown to be weighted averages of the component conditional probabilities where the weights are the relative probabilities of the various conditions. Next, conditional random variables are defined to be random variables X whose domain has been restricted by a condition on a second random variable Y. The extended sum, difference, product and conditioning operations on functions are then applied to these conditional random variables. The expectation of a random variable and the conditional expectation of a conditional random variable are recounted. Theorem 1 generalizes the standard result that the conditional expectation of the sum of two conditional random variables with disjoint and exhaustive conditions is a weighted sum of the conditional expectations of the component conditional random variables. Because of the extended operations, the theorem is true for arbitrary conditions. Theorem 2 gives a formula for the expectation of the product of two conditional random variables. After the definition of independence of two random variables is extended to accommodate the extended operations, it is applied to the formula of Theorem 2 to simplify the expectation of a product of conditional random variables. Two examples end the paper. The first concerns a work force of n workers of different output levels and work shifts. The second example involves two radars with overlapping surveillance regions and different detection error rates. One radar's error rate is assumed to be sensitive to fog and the other radar's error rate is assumed to be sensitive to air traffic density. The combined error rate over the combined surveillance region given heavy fog and moderate air traffic is computed. (shrink)

Political interaction among citizens who hold opposing moral views commonly requires reaching beyond toleration, toward actual co‐operation with policies one opposes. On the more personal level, however, regarding (e.g.) interactions between healthcare providers and patients, several authors emphasise the importance of preserving integrity. But those who oppose any ‘complicity in evil’ often wrongly conflate instances in which the other's position is (and should be) totally rejected with instances of legitimate, although deep, disagreement. Starting with a striking example from the context (...) of a particular tradition, I argue generally that in the latter sort of disagreements, talk of ‘complicity’ should be largely replaced with a more co‐operative moral stance, grounded in a pluralistic framework. Co‐operation Despite Disagreement (CDD) should be sought either for institutional reasons – akin to the political – or for relational reasons. CDD involves sharing another's perspective and sometimes calls for adopting another's moral judgements in preference to one's own. I seek to identify some of the conditions and circumstances that would justify such a shift, particularly in scenarios involving assistance, such as physician‐assisted suicide (PAS) or the role of an anaesthesiologist in abortion. This discussion is meant to provide examples of the kind of second‐order reasons appropriate for determining the terms for CDD – in distinction from first‐order considerations (e.g., the much‐contested ‘active/passive’ distinction) which are likely to be the subject of the initial disagreement and hence cannot serve to resolve it. (shrink)