Ontology engineering is a hard and error-prone task, in which small changes may lead to errors, or even produce an inconsistent ontology. As ontologies grow in size, the need for automated methods for repairing inconsistencies while preserving as much of the original knowledge as possible increases. Most previous approaches to this task are based on removing a few axioms from the ontology to regain consistency. We propose a new method based on weakening these axioms to make them less restrictive, (...) employing the use of refinement operators. We introduce the theoretical framework for weakening DL ontologies, propose algorithms to repair ontologies based on the framework, and provide an analysis of the computational complexity. Through an empirical analysis made over real-life ontologies, we show that our approach preserves significantly more of the original knowledge of the ontology than removing axioms. (shrink)

In this paper we examine interactions of the reciprocal with distributive and collective operators, which are encoded by prefixes on verbs expressing the reciprocal relation: namely, the Czech distributive po and the collectivizing na-. The theoretical import of this study is two-fold. First, it contributes to our knowledge of how word-internal operators interact with phrasal syntax/semantics. Second, the prefixes po and na generate (a range of) readings of reciprocal sentences for which the Strongest Meaning Hypothesis (SMH) proposed by Dalrymple et (...) al. (1998) does not make the right predictions. The distributive prefix po prefers the Strong Reciprocity reading, although the SMH predicts that a weakening should take place, while with the prefix na we find cases where weaker reciprocal readings are preferable to the stronger ones predicted by the SMH. This behavior of po and na is, we propose, due to the way in which they modulate two factors that are crucial in the interpretation of reciprocal sentences: (i) the relevant subpluralities in the group denoted by the reciprocal's antecedent, and (ii) the strength of reciprocal relations. We provide a detailed analysis of the semantics of the prefixes po and na and their contribution to the meaning of reciprocal sentences within the general framework of event semantics with lattice structures. (shrink)

Every Berman’s variety \ which is the subvariety of Ockham algebras defined by the equation \ and \) determines a finitary substitution invariant consequence relation \. A sequent system \ is introduced as an axiomatization of the consequence relation \. The system \ is characterized by a single finite frame \ under the frame semantics given for the formal language. By the duality between frames and algebras, \ can be viewed as a \-valued logic as it is characterized by a (...) distributive lattice of \ elements with a unary operator. Moreover, a structural-rule-free, cut-free and terminating sequent system \ is established for \. The Craig interpolation property of \ is shown proof-theoretically utilizing \. (shrink)

Axiom weakening is a technique that allows for a fine-grained repair of inconsistent ontologies. Its main advantage is that it repairs on- tologies by making axioms less restrictive rather than by deleting them, employing the use of refinement operators. In this paper, we build on pre- viously introduced axiom weakening for ALC, and make it much more irresistible by extending its definitions to deal with SROIQ, the expressive and decidable description logic underlying OWL 2 DL. We extend the (...) definitions of refinement operator to deal with SROIQ constructs, in particular with role hierarchies, cardinality constraints and nominals, and illustrate its application. Finally, we discuss the problem of termi- nation of an iterated weakening procedure. (shrink)

The National Science Foundation's (NSF) role in, and influence on, the National Nanotechnology Initiative (NNI) can best be understood through an examination of the NSF's history. Because of the NSF's weakened position at its founding in 1950 and obstacles faced throughout its history, the NSF developed a discursive strategy that focuses on making a causal link between support for basic science and societal benefits, and an operational strategy focused on growing its constituency through infrastructural support. The hallmarks of both of (...) these strategies are present in the NNI. (shrink)

A. Tarski [21] proposed the study of infinitary consequence operations as the central topic of mathematical logic. He considered monotonicity to be a property of all such operations. In this paper, we weaken the monotonicity requirement and consider more general operations, inference operations. These operations describe the nonmonotonic logics both humans and machines seem to be using when infering dofeasible information from incomplete knowledge. We single out a number of interesting families of inference operations. This study of infinitary inference operations (...) is inspired by the results of [11] on finitary nonmonotonic operations, but this paper is self-contained. (shrink)

We treat emergence via reference to four ideas: (1) the different levels of emergence are characterised by distinct conservation laws, (2) the emergence process starts from some instability, (3) the driving force of emergence is given by selection processes allowing canalisation of specific (emerging) paths, and (4) new forms of stability are determined by new kinds of operations. At a quantum-mechanical level entropy is conserved in an isolated system or at global level and the only allowed operations are local shifts (...) in order and disorder – that implies weakening and strengthening correlations. The stable state is here represented by a highly symmetric state. Emergence of the classical physical world arises when energy is conserved and allowable operations include building and breaking of physical-chemical connections. The stable state is here the energy minimum. Emergence of the biotic world implies that the conserved quantity is energy efficiency. Energy is no longer locally conserved. The allowed operations are those that are consistent with the survival (persistence) of the organism. The emergence of the mind is grounded in selecting those operations that are rational (in the sense of maintaining biological self-organisation). Here, the rational value of behaviour is the quantity of interest. Mounting the ladder of (both cosmic and biological) evolution means to have more and more selection of the possible outcomes (and therefore of the relative operations) but in a growing space of possibilities: if selection would reduce more and more the space of possibilities, the final result would be a rigid order; at the other extreme, if we had only expansion of the possibilities without selection, the final result would be disorder. So growing complexity can be understood as a path in the evolutionary landscape of the systems in which a balance of order and disorder is maintained although each level emerges as a result of the selection. (shrink)

The minimal weakening \ of Belnap-Dunn logic under the polarity semantics for negation as a modal operator is formulated as a sequent system which is characterized by the class of all birelational frames. Some extensions of \ with additional sequents as axioms are introduced. In particular, all three modal negation logics characterized by a frame with a single state are formalized as extensions of \. These logics have the finite model property and they are decidable.

A. Tarski [22] proposed the study of infinitary consequence operations as the central topic of mathematical logic. He considered monotonicity to be a property of all such operations. In this paper, we weaken the monotonicity requirement and consider more general operations, inference operations. These operations describe the nonmonotonic logics both humans and machines seem to be using when infering defeasible information from incomplete knowledge. We single out a number of interesting families of inference operations. This study of infinitary inference operations (...) is inspired by the results of [12] on nonmonotonic inference relations, and relies on some of the definitions found there. (shrink)

A. Tarski [22] proposed the study of infinitary consequence operations as the central topic of mathematical logic. He considered monotonicity to be a property of all such operations. In this paper, we weaken the monotonicity requirement and consider more general operations, inference operations. These operations describe the nonmonotonic logics both humans and machines seem to be using when infering defeasible information from incomplete knowledge. We single out a number of interesting families of inference operations. This study of infinitary inference operations (...) is inspired by the results of [12] on nonmonotonic inference relations, and relies on some of the definitions found there. (shrink)

This paper is a companion to work of Feferman, Jäger, Glaß, and Strahm on the proof theory of the type two functionals μ and E1 in the context of Feferman-style applicative theories. In contrast to the previous work, we analyze these two functionals in the context of Schlüter's weakened applicative basis PRON which allows for an interpretation in the primitive recursive indices. The proof-theoretic strength of PRON augmented by μ and E1 is measured in terms of the two subsystems of (...) second order arithmetic, Π10-CA and Π11-CA, respectively. (shrink)

There are various contexts in which it is not pertinent to generate and attend to all the classical consequences of a given premiss—or to trace all the premisses which classically entail a given consequence. Such contexts may involve limited resources of an agent or inferential engine, contextual relevance or irrelevance of certain consequences or premisses, modelling everyday human reasoning, the search for plausible abduced hypotheses or potential causes, etc. In this paper we propose and explicate one formal framework for a (...) whole spectrum of consequence relations, flexible enough to be tailored for choices from a variety of contexts. We do so by investigating semantic constraints on classical entailment which give rise to a family of infra-classical logics with appealing properties. More specifically, our infra-classical reasoning demands (beyond ${\alpha\models\beta}$ ) that Mod(β) does not run wild, but lies within the scope (whatever that may mean in some specific context) of Mod(α), and which can be described by a sentence ${\bullet\alpha}$ with ${\beta\models\bullet\alpha}$ . Besides being infra-classical, the resulting logic is also non-monotonic and allows for non-trivial reasoning in the presence of inconsistencies. (shrink)

Weakening classical logic is one of the most popular ways of dealing with semantic paradoxes. Their advocates often claim that such weakening does not affect non-semantic reasoning. Recently, however, Halbach and Horsten have shown that this is actually not the case for Kripke’s fixed-point theory based on the Strong Kleene evaluation scheme. Feferman’s axiomatization $\textsf{KF}$ in classical logic is much stronger than its paracomplete counterpart $\textsf{PKF}$, not only in terms of semantic but also in arithmetical content. This paper (...) compares the proof-theoretic strength of an axiomatization of Kripke’s construction based on the paraconsistent evaluation scheme of $\textsf{LP}$, formulated in classical logic with that of an axiomatization directly formulated in $\textsf{LP}$, extended with a consistency operator. The ultimate goal is to find out whether paraconsistent solutions to the paradoxes that employ consistency operators fare better in this respect than paracomplete ones. (shrink)

Wittgenstein's conception of the general form of a truth function given in thesis 6 can be presented as a sort of a trade-off: the author of the Tractatus is unable to reconcile the simplicity of his original idea of a series of forms with the simplicity of his generalisation of Sheffer's stroke; therefore, he is forced to sacrifice one of them. As we argue in this paper, the choice he makes – to weaken the logical constraints put on the concept (...) of a series of forms, thus effectively metaphorising that concept for the sake of upholding the N-operation's role of generating the series – is unfortunate. An actual expansion of a series of truth functions as defined in 6 would require either making decisions at each step (Anscombe) or outwardly rejecting the concept of a series (Sundholm). However, neither is faithful to Wittgenstein's own fundamental intuitions regarding the nature of logic. For this reason, a different trade-off that prioritises upholding the basic features of a series of forms over the simplicity of the operation that generates that series seems to be much more reasonable. We offer such a trade-off by developing the schema already present in the Tractatus (5.101). The key element of our alternative solution is the construction of an operation that can perform the task of producing all consecutive truth functions of a given collection of atomic propositions as an invariant difference between any base and its successor throughout the series. We define it as a composition of three functions (in an algebraic sense): the first turns a symbol of a given truth function into a binary number, the second increments that number, the third turns the result back into a symbol of another truth function. We also show how the operation can be defined by means of a different notation without invoking binary arithmetic. (shrink)

We study envy-free allocations in a many-to-many matching model with contracts in which agents on one side of the market (doctors) are endowed with substitutable choice functions and agents on the other side of the market (hospitals) are endowed with responsive preferences. Envy-freeness is a weakening of stability that allows blocking contracts involving a hospital with a vacant position and a doctor that does not envy any of the doctors that the hospital currently employs. We show that the set (...) of envy-free allocations has a lattice structure. Furthermore, we define a Tarski operator on this lattice and use it to model a vacancy chain dynamic process by which, starting from any envy-free allocation, a stable one is reached. (shrink)

Nichols’s view of empathy (in Sentimental Rules) in light of experimental moral psychology suffers from several deficiencies: (1) It operates with an impoverished view of the altruistic emotions (empathy, sympathy, concern, compassion, etc.) as mere short-term, affective states of mind, lacking any essential connection to intentionality, perception, cognition, and expressiveness. (2) It fails to keep in focus the moral distinction between two very different kinds of emotional response to the distress and suffering of others—other-directed, altruistic, emotions that have moral value, (...) and self-directed emotional responses, such as personal distress, that do not. (3) Nichols is correct to see morality as requiring affectivity, and the capability of emotional response to others; but his incorrect view of altruistic emotions (and of emotions in general) leads him to misstate the connection between morality and emotion. (4) Nichols’s specific attempt to ground moral judgment in emotion fails, but the argument he provides for it is part of the explanation of point (2), his failure to sustain the distinction between egoistic and altruistic emotions. (5) Without in any way denying that moral philosophy is strengthened by knowledge of empirical psychology, I suggest that the foregoing failures of Nichols’s argument are partly due to his misuse of particular empirical results and findings, and possibly in part to a weakened commitment to the distinctive contribution the humanistic methods of philosophy make to our understanding of the moral dimension of life. (shrink)

Working in the weakening of constructive Zermelo-Fraenkel set theory in which the subset collection scheme is omitted, we show that the binary refinement principle implies all the instances of the exponentiation axiom in which the basis is a discrete set. In particular binary refinement implies that the class of detachable subsets of a set form a set. Binary refinement was originally extracted from the fullness axiom, an equivalent of subset collection, as a principle that was sufficient to prove that (...) the Dedekind reals form a set. Here we show that the Cauchy reals also form a set. More generally, binary refinement ensures that one remains in the realm of sets when one starts from discrete sets and one applies the operations of exponentiation and binary product a finite number of times. (shrink)

I argue that the Stoic logic is explosive. The claim applies to the Stoics' syllogistic in the strictest sense, because there is a provable syllogism which qualifies as a principle of explosion. It applies also to the general consequence operation, in the sense that every sentence is derivable from any pair containing both a sentence and the negation of the sentence. Finally, it applies to the connective of implication (conditional), in the sense that any conditional is derivable, providing its antecedent (...) is a conjunction of a sentence and the negation of the sentence. All three claims allow weakening, i.e., additions of extra premises to an inference or extra conjuncts to the antecedent of an implication, respectively. Consequently, no concept of relevance, let alone paraconsistency or connexivity is applicable to the Stoic logic; in particular, the Stoics' connective of implication is either material (Boolean) or formal (strict). (shrink)

How does trust operate under conditions of oppression? Little attention has been paid to how distrust may be both necessary and costly to its bearer. Distrust is clearly warranted under certain conditions, but do those conditions contribute to a reduction in one's overall well-being? More importantly, is there something about distrust itself (rather than the conditions that warrant it) that contributes to this reduction in well-being? In this essay, I explore these questions in depth. I explain what the costs of (...) distrust are and how they impede our well-being. I argue that the weakened development of trust through oppression has some important downstream consequences: namely, it requires the cultivation of skepticism as a virtue of distrust, which I argue should be included as one of Lisa Tessman's burdened virtues—those that are required for survival but that do not necessarily lead to the agent's flourishing. (shrink)

This Dong Zhongshu (董仲舒BC179-104) is a philosopher who thought that the concept of yin and yang descending from whales was a very real existence code and a scientific code. He built a foundation stone with a scientific and yin-yang concept that was firmly established in establishing his huge ideological system, and established a universal human value on it. Therefore, his philosophical system has been sustained for over a thousand years without being firmly destroyed and contributed to the settlement of the (...) culture of the Orient as a culture of Yin and Yang. This yin and yang concept is derived from the origin of the universe, and is also the law of operation in the solar system. This concept is initially written as a sign character, and then converted into a character code, and its essence is embellished. Therefore, the logic of the code character has weakened and the emotionality of the character code has evolved. Dong zhongshu(董仲舒) who grasped the essence of this, used his philosophy back to the original purpose of the Yin and Yang concept in order to establish a logically solid philosophical system. Yin and Yang are originally an unchanging concept, so they are best judged to establish an irreversible truth system. From this, the truth system based on sociological statistics descending from Confucius was transformed into a scientific irreversible truth system in the East. The transition to the scientific truth system of the East and West has been a great success and has been enjoyed and denied in China for over 2,000 years. In fact, this is based on the fact that mankind on Earth is in the system of this sun and can not help but be applied to the law of yin and yang. This paper uses the term science and yin and yang because Yin and Yang, the first foundation stone concept of oriental philosophy, is a scientific code. (shrink)

Cooperative relations steeped in honesty and good faith are a necessity for any viable society. This is especially relevant to the police institution because the police are entrusted to promote justice and security. Despite the necessity of societal honesty and good faith, the police institution has embraced deception, dishonesty, and bad faith as tools of the trade for providing security. In fact, it seems that providing security is impossible without using deception and dishonesty during interrogations, undercover operations, pretextual detentions, and (...) other common scenarios. This presents a paradox related to the erosion of public faith in the police institution and the weakening of the police's legitimacy. -/- The book seeks to solve this puzzle by showing that many of our assumptions about policing and security are unjustified. Specifically, they are unjustified in the way many of our assumptions about security were unjustified after the 9/11 terrorist attacks, when state institutions embraced a variety of brutal rules and tactics in pursuit of perceived security enhancements. The police are likewise unjustified in their pursuit of many supposed security enhancements that rely on proactive deception, dishonesty, and bad faith. -/- There are compelling reasons to think that the police's widespread use of proactive deception and dishonesty is inconsistent with fundamental norms of political morality regarding fraud and the rule of law. Although there are times and places for such tactics in policing, those times and places should be much more limited than current practices suggest. (shrink)

Cybernetic governmentality weakens the capacity of resistant subjectivities to struggle against neoliberal rationality because digitalized subjectivation processes are constantly pushed towards the logics of the market and into codifications of competitive evaluation. Despite the potential for new forms of collectivity contained in the concept of virtuality, technological evolution has disseminated a systemic form of digitality that operates not through collective procedures but through subjective-individualistic ones. Hence arises a danger that was indicated by Deleuze decades ago: that of confusing the virtual (...) with the possible. By constructing a genealogy that is built around Pierre Levy’s optimistic representation of cyberspace, Bernard Stiegler’s work on the contemporary disenchantment of the computerized world, Baudrillard’s metaphysics of code and Antoinette Rouvroy’s analysis of algorithmic governmentality, we will demonstrate that digitality is between us and that this amounts to an irreversible fact entailing a critical confrontation with its current manifestation. (shrink)

Since at least 2016, many have worried that social media enables authoritarians to meddle in democratic politics. The concern is that trolls and bots amplify deceptive content. In this chapter I argue that these tactics have a more insidious anti-democratic purpose. Lies implanted in democratic discourse by authoritarians are often intended to be caught. Their primary goal is not to successfully deceive, but rather to undermine the democratic value of testimony. In well-functioning democracies, our mutual reliance on testimony also generates (...) a distinctively democratic value: decentralized testimonial networks evade control by the state or powerful actors. The deliberate exposure of deception in democratic testimonial networks undermines this value by implicating citizens in their own epistemic corruption, weakening the resilience of democratic society against authoritarian pressure. In this chapter I illustrate that danger through a close reading of recent Russian social media interference operations, showing both their epistemic underpinnings and their ongoing political threat. (shrink)

We present a game semantics in the style of Lorenzen for Girard's linear logic . Lorenzen suggested that the meaning of a proposition should be specified by telling how to conduct a debate between a proponent P who asserts and an opponent O who denies . Thus propositions are interpreted as games, connectives as operations on games, and validity as existence of a winning strategy for P. We propose that the connectives of linear logic can be naturally interpreted as the (...) operations on games introduced for entirely different purposes by Blass . We show that affine logic, i.e., linear logic plus the rule of weakening, is sound for this interpretation. We also obtain a completeness theorem for the additive fragment of affine logic, but we show that completeness fails for the multiplicative fragment. On the other hand, for the multiplicative fragment, we obtain a simple characterization of game-semantical validity in terms of classical tautologies. An analysis of the failure of completeness for the multiplicative fragment leads to the conclusion that the game interpretation of the connective is weaker than the interpretation implicit in Girard's proof rules; we discuss the differences between the two interpretations and their relative advantages and disadvantages. Finally, we discuss how Gödel's Dialectica interpretation , which was connected to linear logic by de Paiva , fits with game semantics. (shrink)

The relationships between various modal logics based on Belnap and Dunn’s paraconsistent four-valued logic FDE are investigated. It is shown that the paraconsistent modal logic \, which lacks a primitive possibility operator \, is definitionally equivalent with the logic \, which has both \ and \ as primitive modalities. Next, a tableau calculus for the paraconsistent modal logic KN4 introduced by L. Goble is defined and used to show that KN4 is definitionally equivalent with \ without the absurdity constant. (...) Moreover, a tableau calculus is defined for the modal bilattice logic MBL introduced and investigated by A. Jung, U. Rivieccio, and R. Jansana. MBL is a generalization of BK that in its Kripke semantics makes use of a four-valued accessibility relation. It is shown that MBL can be faithfully embedded into the bimodal logic \ over the non-modal vocabulary of MBL. On the way from \ to MBL, the Fischer Servi-style modal logic \ is defined as the set of all modal formulas valid under a modified standard translation into first-order FDE, and \ is shown to be characterized by the class of all models for \. Moreover, \ is axiomatized and this axiom system is proved to be strongly sound and complete with respect to the class of models for \. Moreover, the notion of definitional equivalence is suitably weakened, so as to show that \ and \ are weakly definitionally equivalent. (shrink)

It is a widespread belief that the Kochen-Specker theorem imposes a contextuality constraint on the ontology of beables in quantum hidden variables theories. On the other hand, after Bell’s influential critique, the importance of von Neumann’s wrongly called ‘impossibility proof’ has been severely questioned. However, Max Jammer, Jeffrey Bub and Dennis Dieks have proposed insightful reassessments of von Neumann’s theorem: what it really shows is that hidden variables theories cannot represent their beables by means of Hermitian operators in Hilbert space. (...) Hereby I show that i) the very same constraint can be derived from Gleason’s theorem, and that ii) if we consider the import of von Neumann’s and Gleason’s theorems, the relevance of the Kochen-Specker theorem for hidden variables theories gets substantially weakened: it does not force them to be contextual in any interesting sense of the term. (shrink)

The problem of how to remove information from an agent's stock of beliefs is of paramount concern in the belief change literature. An inquiring agent may remove beliefs for a variety of reasons: a belief may be called into doubt or the agent may simply wish to entertain other possibilities. In the prominent AGM framework for belief change, upon which the work here is based, one of the three central operations, contraction, addresses this concern (the other two deal with the (...) incorporation of new information). Makinson has generalised this work by introducing the notion of a withdrawal operation. Underlying the account proffered by AGM is the idea of rational belief change. A belief change operation should be guided by certain principles or integrity constraints in order to characterise change by a rational agent. One of the most noted principles within the context of AGM is the Principle of Informational Economy. However, adoption of this principle in its purest form has been rejected by AGM leading to a more relaxed interpretation. In this paper, we argue that this weakening of the Principle of Informational Economy suggests that it is only one of a number of principles which should be taken into account. Furthermore, this weakening points toward a Principle of Indifference. This motivates the introduction of a belief removal operation that we call severe withdrawal. We provide rationality postulates for severe withdrawal and explore its relationship with AGM contraction. Moreover, we furnish possible worlds and epistemic entrenchment semantics for severe withdrawals. (shrink)

Family obligation, which has an exceptionally high salience in traditional Chinese society, continues to be significant in contemporary China. In family relations in particular sentiments and practices morphologically similar to those associated with xiao remains intact in so far as an enduring set of expectations concerning age-based obligation continues to structure behavior toward others. Researchers pursuing the theme of “individualization” in Chinese society, on the other hand, argue that family obligations and filial sentiments have substantially weakened. The present paper will (...) show that under conditions of cultural and social change in China filial behavior through family obligation continues to play an important role even though the conventions associated with the relevant expectations, attitudes and emotions have undergone significant change. The paper argues that the culture-system develops not merely through an internal dynamic and that family obligation must be understood in terms of the social and material context in which it operates and the nature of the motivations and imagery of the people that practice it. (shrink)

The role of moral intuition has been increasingly implicated in business decisions and ethical business behavior. But troublingly, because implicit processes often operate outside of conscious awareness, decision makers are generally unaware of their influence. We tested whether subtle contextual cues for identity can alter implicit beliefs. In two studies, we found that contextual cues which nonconsciously prime moral identity weaken the implicit association between the categories of “business” and “ethical,” an implicit association which has previously been linked to unethical (...) decision making. Further, changes in this implicit association mediated the relationship between contextually primed moral identity and concern for external stakeholder groups, regardless of self-reported moral identity. Thus, our results show that subtle contextual cues can lead individuals to render more ethical judgments, by automatically restructuring moral intuition below the level of consciousness. (shrink)

It is shown that Lewis’ ontological doctrine of Humean supervenience incorporates at its foundation the so-called separability principle of classical physics. In view of the systematic violation of the latter within quantum mechanics, the claim that contemporary physical science may posit non-supervenient relations beyond the spatiotemporal ones is reinforced on a foundational basis concerning constraints on the state representation of physical systems. Depending on the mode of assignment of states to quantum systems — unit state vectors versus statistical density operators (...) — we distinguish between strongly and weakly non-Humean, non-supervenient relations. It is demonstrated that in either case, the relations of quantum entanglement constitute prototypical examples of irreducible physical relations that do not supervene upon a spatiotemporal arrangement of Humean qualities, weakening, thereby, the thesis of Humean supervenience. In this respect, the status of Lewis’ recombination principle is examined, whereas his conception of lawhood is critically investigated. It is concluded that the assumption of ontological reductionism, as expressed in Lewis’ Humean doctrine, cannot be regarded as a reliable code of the nature of the physical world and its contents. It is proposed instead that due to the undeniable existence of non-supervenient relations, a metaphysic of relations of a moderate kind ought to be acknowledged as an indispensable part of our understanding of the natural world at a fundamental level. (shrink)

This short piece draws on political philosophy to show how social media interference operations can be used by hostile states to weaken the apparent legitimacy of democratic governments. Democratic societies are particularly vulnerable to this form of attack because democratic governments depend for their legitimacy on citizens' trust in one another. But when citizen see one another as complicit in the distribution of deceptive content, they lose confidence in the epistemic preconditions for democracy. The piece concludes with policy recommendations for (...) how democratic governments should protect themselves. (shrink)

Linear logic, introduced by Girard, is a refinement of classical logic with a natural, intrinsic accounting of resources. This accounting is made possible by removing the ‘structural’ rules of contraction and weakening, adding a modal operator and adding finer versions of the propositional connectives. Linear logic has fundamental logical interest and applications to computer science, particularly to Petri nets, concurrency, storage allocation, garbage collection and the control structure of logic programs. In addition, there is a direct correspondence between (...) polynomial-time computation and proof normalization in a bounded form of linear logic. In this paper we show that unlike most other propositional logics, full propositional linear logic is undecidable. Further, we prove that without the modal storage operator, which indicates unboundedness of resources, the decision problem becomes PSPACE-complete. We also establish membership in NP for the multiplicative fragment, NP-completeness for the multiplicative fragment extended with unrestricted weakening, and undecidability for fragments of noncommutative propositional linear logic. (shrink)

This paper explores whether MacIntyrean virtue ethics concepts are applicable in non-Western business contexts, specifically in SMEs in Taiwan, a country strongly influenced by the Confucian tradition. It also explores what differences exist between different polities in this respect, and specifically interprets observed differences between the Taiwanese study and previous studies conducted in Europe and Asia. Based on case study research, the findings support the generalizability of the MacIntyrean framework. Drawing on the institutional logics perspective and synthesizing this with MacIntyrean (...) concepts, the paper explains the differences between the studies largely by reference to the Confucian tradition operating at both the micro-level within firms and at the macro-level as a means of harmonizing the potentially competing institutional logics to which firms are subject. The recent weakening of this tradition, however, suggests that increased conflict may characterize the future. (shrink)

In this paper we define an augmentation mHC of the Heyting propositional calculus HC by a modal operator ?. This modalized Heyting calculus mHC is a weakening of the Proof-Intuitionistic Logic KM of Kuznetsov and Muravitsky. In Section 2 we present a short selection of attractive (algebraic, relational, topological and categorical) features of mHC. In Section 3 we establish some close connections between mHC and certain normal extension K4.Grz of the modal system K4. We define a translation of (...) mHC into K4.Grz and prove that this translation is exact, i. e. theorem-preserving and deducibility-invariant. We have established (however, in this note we do not present a proof of this) that the lattice of all extensions of mHC is isomorphic to the lattice of normal extensions of K4.Grz (a generalization of the Kuznetsov and Muravitsky theorem). (shrink)

The naïve idea of “size” for collections seems to obey both Aristotle’s Principle: “the whole is greater than its parts” and Cantor’s Principle: “1-to-1 correspondences preserve size”. Notoriously, Aristotle’s and Cantor’s principles are incompatible for infinite collections. Cantor’s theory of cardinalities weakens the former principle to “the part is not greater than the whole”, but the outcoming cardinal arithmetic is very unusual. It does not allow for inverse operations, and so there is no direct way of introducing infinitesimal numbers. Here (...) we maintain Aristotle’s principle, instead halving Cantor’s principle to “equinumerous collections are in 1–1 correspondence”. In this way we obtain a very nice arithmetic: in fact, our “numerosities” may be taken to be nonstandard integers. These numerosities appear naturally suited to sets of ordinals, but they depend, for generic sets, on a “labelling” of the universe by ordinals. The problem of finding a canonical way of attaching numerosities to all sets seems to be worth further investigation. (shrink)

COVID-19 continues to dominate 2020 and is likely to be a feature of our lives for some time to come. Given this, how should health systems respond ethically to the persistent challenges of responding to the ongoing impact of the pandemic? Relatedly, what ethical values should underpin the resetting of health services after the initial wave, knowing that local spikes and further waves now seem inevitable? In this editorial, we outline some of the ethical challenges confronting those running health services (...) as they try to resume non-COVID-related services, and the downstream ethical implications these have for healthcare professionals’ day-to-day decision making. This is a phase of recovery, resumption and renewal; a form of reset for health services.1 This reset phase will define the ‘new normal' for healthcare delivery, and it offers an opportunity to reimagine and change services for the better. There are difficulties, however, healthcare systems are already weakened by austerity and the first wave of COVID-19 and remain under stress as the pandemic continues. The reset period is operating alongside, rather than at the end, of the pandemic and this creates difficult ethical choices. ### Balancing the greater good with individual care Pandemics—and public health emergencies more generally—reinforce approaches to ethics that emphasise or derive from the interests of communities, rather than those grounded in the claims of the autonomous individual. The response has been to draw on more public health focused ethics, ‘if demand outstrips the ability to deliver to existing standards, more strictly utilitarian considerations will have to be applied, and decisions about how to meet the individual's need will give way to decisions about how to maximise overall benefit’.2 Alongside this, effective …. (shrink)

Under conditions of growing interconnectedness of the global economy, more and more stakeholders are exposed to risks and costs resulting from business activities that are neither regulated nor compensated for by means of national governance. The changing distribution of risks poses a threat to the legitimacy of business firms that normally derive their legitimacy from operating in compliance with the legal rules of democratic nation states. However, during the process of globalization, the regulatory power of nation states has been weakened (...) and many production processes have been shifted to states with weak regulatory frameworks where businesses operate outside the reach of the democratic nation state. As a result, business firms have to address the various legitimacy challenges of their operations directly and cannot rely upon the legitimacy of their regulatory environment. These developments challenge the dominant approach to corporate governance that regards shareholders as the only stakeholder group in need of special protection due to risks not covered by contracts and legal regulations. On the basis of these considerations, we argue for a democratization of corporate governance structures in order to compensate for the governance deficits in their regulatory environment and to cope with the changing allocation of risks and costs. By way of democratic involvement of various stakeholders, business firms may be able to mitigate the redistribution of individual risk and address the resulting legitimacy deficits even when operating under conditions of regulatory gaps and governance failure. (shrink)

Continued failure to limit emissions of carbon dioxide and other greenhouse gases that are causing global climate change has brought increased attention to climate engineering technologies, which actively modify the global environment to counteract heating and climate disruptions caused by elevated greenhouse gases. Some proposed forms of CE, particularly spraying reflective particles in the upper atmosphere to reduce incoming sunlight, can cool the average temperature of the Earth rapidly and cheaply, thereby substantially reducing climate-related risks. Yet CE interventions provide only (...) imperfect corrections for the climatic and other environmental effects of elevated greenhouse gases, and carry their own environmental risks. Moreover, they may also increase other risks, by weakening political support for essential emissions reductions or providing new triggers for international conflict. These technologies thus require international governance, but also pose novel and severe challenges to current international laws and institutions. Effective governance of CE will require a capacity to make decisions regarding the conditions, if any, under which specific interventions are authorized, plus realtime operational oversight of any interventions that are conducted. Decision processes must be effectively linked with scientific research and assessment, and with institutions to manage and respond to threats of CE-related conflict. We advance preliminary suggestions to address two priority areas for early investigation: how international cooperation on early CE research can help develop shared norms that can grow robust enough to support future decision needs; and how early research and development on CE can be made to complement and encourage, rather than undermine, parallel efforts to reduce climate risks by cutting emissions. (shrink)

We argue that the rapid eye movement dream experiences owe their structure and meaning to inherent self-organizing properties of the brain itself. Thus, we offer a common meeting ground for brain based studies of dreaming and traditional psychological dream theory. Our view is that the dreaming brain is a self-organizing system highly sensitive to internally generated influences. Several lines of evidence support a process view of the brain as a system near the edge of chaos, one that is highly sensitive (...) to internal influences. Such sensitivity is due to several factors. First, the dreaming brain normally gates out external input and thus operates without the stabilizing influences of external feedback. Second, the pre-frontal cortex is only minimally activated during REM sleep, and hence the brain operates with weakened volition, reduced logic, and diminished self-reflection. Third, because the neuromodulatory inhibition mechanism is turned off during REM, the brain responds spontaneously to the least provocation. In addition, the dreaming brain is also subject to powerful intermittent cholinergic stimulation which may stimulate creative patterns of dream activity. (shrink)

We consider the connections between belief revision, conditional logic and nonmonotonic reasoning, using as a foundation the approach to theory change developed by Alchourrón, Gärdenfors and Makinson (the AGM approach). This is first generalized to allow the iteration of theory change operations to capture the dynamics of epistemic states according to a principle of minimal change of entrenchment. The iterative operations of expansion, contraction and revision are characterized both by a set of postulates and by Grove's construction based on total (...) pre-orders on the set of complete theories of the belief logic. We present a sound and complete conditional logic whose semantics is based on our iterative revision operation, but which avoids Gärdenfors's triviality result because of a severely restricted language of beliefs and hence the weakened scope of our extended postulates. In the second part of the paper, we develop a computational approach to theory dynamics using Rott's E-bases as a representation for epistemic states. Under this approach, a ranked E-base is interpreted as standing for the most conservative entrenchment compatible with the base, reflecting a kind of foundationalism in the acceptance of evidence for a belief. Algorithms for the computation of our iterative versions of expansion, contraction and revision are presented. Finally, we consider the relationship between nonmonotonic reasoning and both conditional logic and belief revision. Adapting the approach of Delgrande, we show that the unique extension of a default theory expressed in our conditional logic of belief revision corresponds to the most conservative belief state which respects the theory: however, this correspondence is limited to propositional default theories. Considering first order default theories, we present a belief revision algorithm which incorporates the assumption of independence of default instances and propose the use of a base logic for default reasoning which incorporates uniqueness of names. We conclude with an examination of the behavior of an implemented system on some of Lifschitz's benchmark problems in nonmonotonic reasoning. (shrink)

This essay describes how longstanding conceptions of professionalism in American medical care came under attack in the decades since the enactment of Medicare in 1965 and how the reform strategy and core provisions of the 2010 Affordable Care Act illustrate the weakening of those ideas and the institutional practices embodying them.The opening identifies the dominant role of physicians in American medical care in the two decades after World War II. By the time Medicare was enacted in 1965, associations of (...) American physicians were almost completely in charge of medical education, specialist certification, and the enforcement of professional norms on their members. Who could be a doctor, what education and training would be required, and what collegial oversight was operative was first a professional matter and only secondly implicated the state through malpractice or major corporations via the employment of physicians. (shrink)

Using a conviction-based measure, we find that local public corruption exerts a negative effect on the lending activity of US banks. Our baseline estimations show that the difference in public corruption between, for example, Alabama, where corruption is high, and Minnesota, where corruption is low, implies that banks headquartered in the former state grant 0.55% less credit ceteris paribus. Using proxies for relationship lending and monitoring, we also find that these bank characteristics weaken the negative effect of public corruption on (...) lending. These results are robust to tests that address endogeneity, to the use of perception-based measures of corruption, and after controlling for credit demand conditions. In further analysis, we show that these effects are more evident for smaller banks and banks operating in a single state. These findings provide evidence that public corruption could facilitate information asymmetry in the lending market and, thus, could hinder local development by reducing bank credit. (shrink)

Three-to-five-year-old French children were asked to add or remove objects to or from linear displays. The hypothesis of a universal tendency to represent increasing number magnitudes from left to right led to predict a majority of manipulations at the right end of the rows, whatever children's hand laterality. Conversely, if numbers are not inherently associated with space, children were expected to favour laterality-consistent manipulations. The results showed a strong tendency to operate on the right end of the rows in right-handers, (...) but no preference in left-handers. These findings suggest that the task elicited a left-to-right oriented representation of magnitudes that counteracted laterality-related responses in left-handed children. The young age of children and the lack of a developmental trend towards right preference weaken the hypothesis of a cultural origin of this oriented representation. The possibility that our results are due to weaker brain lateralisation in left-handers compared to right-handers is addressed in Discussion section. (shrink)

We present the logic $${\mathsf {LCB}}$$ LCB which is expressed in a propositional language constantly enriched by new atomic expressions. Our formal framework is the propositional doxastic logic $${\mathsf {KD45}}$$ KD 45 with the belief operator $${\mathcal {B}}$$ B, extended by the $${\mathcal {C}}$$ C operator, to be read it changes that.... We describe the changing beliefs of an agent who uses progressively expanding language. The approach presented here allows us to weaken pragmatic objections to the so-called principle (...) of negative retrospection accepted in $${\mathsf {KD45}}$$ KD 45 and the problem of logical omniscience. In what follows, we present the expanding propositional language used in our formalism, interpreted using an epistemic version of Kripke semantics. Next, we give a syntactic characterization of logic $${\mathsf {LCB}}$$ LCB and prove the soundness and completeness of $${\mathsf {LCB}}$$ LCB in respect to our semantics. Finally, we compare the idea of expanding language with the notion of agent awareness and we relate our formalism to two epistemic temporal logics. (shrink)

Performing an inference involves irreducibly dynamic cognitive procedures. The article proposes that a non-associative information frame, corresponding to a residuated pogroupoid, underpins the information structure involved. The argument proceeds by expounding the informational turn in logic, before outlining the cognitive actions at work in deductive inference. The structural rules of Weakening, Contraction, Commutation, and Association are rejected on the grounds that they cause us to lose track of the information flow in inferential procedures. By taking the operation of information (...) application as the primary operation, the fusion connective is retained, with commutative failure generating a double implication. The other connectives are rejected. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:GOOD MEN'S WOMEN: HUME ON CHASTITY AND TRUST At the very heart of Hume's philosophy in the Treatise, namely between his discussion of the artificial and the natural virtues, he places a short chapter entitled "Of Chastity and Modesty." Its central position is appropriate, since these supposed virtues present something of a test case for Hume's account of the relation between nature and artifice, and, more generally, beyond his (...) moral philosophy, for his views on regularity and constancy in and out of individual lives. For these theoretical reasons, as well as for the calm realism of his treatment of sexual inequality, the chapter warrants more attention than it has received. Perhaps Hume's most important contribution to moral philosophy is his account of the difference between natural virtues, displayed in actions which do good one by one, each act having value independently of whether similar acts are performed by oneself and others on other occasions, and artificial virtues displayed in acts in essential conformity to established socially useful conventions, which do good only in so far as they are supported by general conformity. Hume does not, like Kant, insist that we always see morally good action as obedience to law, nor does he neglect the importance of those areas where good can be done only if acts are correctly seen as conforming to general laws, general conformity to which is not only willed by the agent but assumed by him to be in effect. Hume gives a subtle and elaborate account of when we do and when we do not need moral and social conformity, of which virtues are and which virtues are not mediated by changeable public will or convention. Conventions must operate before any act can count as property-respecting, but there is no need to ask 'can I will this as universal law?' before comforting a frightened child. Whatever the conventions, whatever others do, such an act does some good, and is the sort of 2. act which displays the natural virtue of kindness. Hume requires of a virtuous act not merely that it be helpful or agreeable to someone (or some public) but that it display a durable character trait in the agent. An uncharacteristic act of kindness to a child may do good without displaying a virtue or a good character. Approval is given, according to Hume, to persons on account of theii durable character traits, as displayed in their actions and reactions. The natural response to virtue is to welcome its possessor: His company is a satisfaction to me (T588), and virtue in rags will be the exception in a smoothly functioning society. The fact that Hume's ethics is an agent ethics, and that the concept of welcome virtue is more fundamental to it than that of a useful action, commits Hume, throughout his moral philosophy and especial!, in his treatment of the natural virtues, to an emphasis on consistency or integrity of character, to a search for durable character traits and so for characteristic actions. Now a person might be characteristically kind, yet on occasion, under stress, give expression to unaccustomed malice. The uncharacteristic malicious act may weaken but not destroy the virtue of kindness which kind acts have both expressed and infixed (T411). When the malicious act is known, the person's reputation for benevolence may be slightly sullied, but certainly not ruined. Both within one person's life, and within one population, there will be reason to encourage consistently virtuous action, but no reason to feel that all is lost or spoiled if lapses from the natural virtues occur. Even when cruelty is the norm, the rare kind act may be appreciated, if not rewarded, the rare kind person may be welcome, if also exploited and victimized. With the artificial virtues there is a stronger demand and need for uniformity in a population, since the value of any one just act, or one person's character trait, depends upon the support received from the similar acts and 3. traits of others. Every single act is performed in the expectation that others are to perform the like (T498). To display artificial virtues, actions must be seen as rule... (shrink)