Arrow and turnstile interpolations are investigated in UCL [introduced by Sernadas et al. ], a logic that is a complete extension of classical propositional logic for reasoning about connectives that only behave as expected with a given probability. Arrow interpolation is shown to hold in general and turnstile interpolation is established under some provisos.

Fibring is recognized as one of the main mechanisms in combining logics, with great signicance in the theory and applications of mathematical logic. However, an open challenge to bring is posed by the collapsing problem: even when no symbols are shared, certain combinations of logics simply collapse to one of them, indicating that bring imposes unwanted interconnections between the given logics. Modulated bring allows a ner control of the combination, solving the collapsing problem both at the semantic and deductive levels. (...) Main properties like soundness and completeness are shown to be preserved, comparison with bring is discussed, and some important classes of examples are analyzed with respect to the collapsing problem. (shrink)

Motivated by applications in software engineering, we propose two forms of combination of logics: synchronization on formulae and synchronization on models. We start by reviewing satisfaction systems, consequence systems, one-step derivation systems and theory spaces, as well as their functorial relationships. We define the synchronization on formulae of two consequence systems and provide a categorial characterization of the construction. For illustration we consider the synchronization of linear temporal logic and equational logic. We define the synchronization on models of two satisfaction (...) systems and provide a categorial characterization of the construction. We illustrate the technique in two cases: linear temporal logic versus equational logic; and linear temporal logic versus branching temporal logic. Finally, we lift the synchronization on formulae to the category of logics over consequences systems. (shrink)

A completeness theorem is established for logics with congruence endowed with general semantics (in the style of general frames). As a corollary, completeness is shown to be preserved by fibring logics with congruence provided that congruence is retained in the resulting logic. The class of logics with equivalence is shown to be closed under fibring and to be included in the class of logics with congruence. Thus, completeness is shown to be preserved by fibring logics with equivalence and general semantics. (...) An example is provided showing that completeness is not always preserved by fibring ligics endowed with standard (non general) semantics. A categorial characterization of fibring is provided using coproducts and cocartesian liftings. (shrink)

Fibring is defined as a mechanism for combining logics with a first-order base, at both the semantic and deductive levels. A completeness theorem is established for a wide class of such logics, using a variation of the Henkin method that takes advantage of the presence of equality and inequality in the logic. As a corollary, completeness is shown to be preserved when fibring logics in that class. A modal first-order logic is obtained as a fibring where neither the Barcan formula (...) nor its converse hold. (shrink)

We introduce a general recipe for presenting non-classical logics in a modular and uniform way as labelled deduction systems. Our recipe is based on a labelling mechanism where labels are general entities that are present, in one way or another, in all logics, namely truth-values. More specifically, the main idea underlying our approach is the use of algebras of truth-values, whose operators reflect the semantics we have in mind, as the labelling algebras of our labelled deduction systems. The “truth-values as (...) labels” approach allows us to give generalized systems for multiple-valued logics within the same formalism: since we can take multiple-valued logics as meaning not only finitely or infinitely many-valued logics but also power-set logics, i.e. logics for which the denotation of a formula can be seen as a set of worlds, our recipe allows us to capture also logics such as modal, intuitionistic and relevance logics, thus providing a first step towards the fibring of these logics with many-valued ones. (shrink)

Fibring is a meta-logical constructor that applied to two logics produces a new logic whose formulas allow the mixing of symbols. Homogeneous fibring assumes that the original logics are presented in the same way . Heterogeneous fibring, allowing the original logics to have different presentations , has been an open problem. Herein, consequence systems are shown to be a good solution for heterogeneous fibring when one of the logics is presented in a semantic way and the other by a calculus (...) and also a solution for the heterogeneous fibring of calculi. The new notion of abstract proof system is shown to provide a better solution to heterogeneous fibring of calculi namely because derivations in the fibring keep the constructive nature of derivations in the original logics. Preservation of compactness and semi-decidability is investigated. (shrink)

Cut elimination is shown, in a constructive way, to hold in sequent calculi labelled with truth values for a wide class of normal modal logics, supporting global and local reasoning and allowing a general frame semantics. The complexity of cut elimination is studied in terms of the increase of logical depth of the derivations. A hyperexponential worst case bound is established. The subformula property and a similar property for the label terms are shown to be satisfied by that class of (...) modal sequent calculi. Modal logics presented by these calculi are proven to be globally and locally consistent. (shrink)

Labelled sequent calculi are provided for a wide class of normal modal systems using truth values as labels. The rules for formula constructors are common to all modal systems. For each modal system, specific rules for truth values are provided that reflect the envisaged properties of the accessibility relation. Both local and global reasoning are supported. Strong completeness is proved for a natural two-sorted algebraic semantics. As a corollary, strong completeness is also obtained over general Kripke semantics. A duality result (...) is established between the category of sober algebras and the category of general Kripke structures. A simple enrichment of the proposed sequent calculi is proved to be complete over standard Kripke structures. The calculi are shown to be analytic in a useful sense. (shrink)

Satisfaction systems and reductions between them are presented as an appropriate context for analyzing the satisfiability and the validity problems. The notion of reduction is generalized in order to cope with the meet-combination of logics. Reductions between satisfaction systems induce reductions between the respective satisfiability problems and (under mild conditions) also between their validity problems. Sufficient conditions are provided for relating satisfiability problems to validity problems. Reflection results for decidability in the presence of reductions are established. The validity problem in (...) the meet-combination is proved to be decidable whenever the validity problem for the components are decidable. Several examples are discussed, namely, involving modal and intuitionistic logics, as well as the meet-combination of modal logic and intuitionistic logic. (shrink)

The novel notion of importing logics is introduced, subsuming as special cases several kinds of asymmetric combination mechanisms, like temporalization [8, 9], modalization [7] and exogenous enrichment [13, 5, 12, 4, 1]. The graph-theoretic approach proposed in [15] is used, but formulas are identified with irreducible paths in the signature multi-graph instead of equivalence classes of such paths, facilitating proofs involving inductions on formulas. Importing is proved to be strongly conservative. Conservative results follow as corollaries for temporalization, modalization and exogenous (...) enrichment. (shrink)

A new technique is presented for proving that a consequence system enjoys Craig interpolation or Maehara interpolation based on the fact that these properties hold in another consequence system. This technique is based on the existence of a back and forth translation satisfying some properties between the consequence systems. Some examples of translations satisfying those properties are described. Namely a translation between the global/local consequence systems induced by fragments of linear logic, a Kolmogorov-Gentzen-Gödel style translation, and a new translation between (...) the global consequence systems induced by full Lambek calculus and linear logic, mixing features of a Kiriyama-Ono style translation with features of a Kolmogorov-Gentzen-Gödel style translation. These translations establish a strong relationship between the logics involved and are used to obtain new results about whether Craig interpolation and Maehara interpolation hold in that logics . (shrink)

The essential structure of proofs is proposed as the basis for a measure of complexity of formulas in FOL. The motivating idea was the recognition that distinct theorems can have the same derivation modulo some non essential details. Hence the difficulty in proving them is identical and so their complexity should be the same. We propose a notion of complexity of formulas capturing this property. With this purpose, we introduce the notions of schema calculus, schema derivation and description complexity of (...) a schema formula. Based on these concepts we prove general robustness results that relate the complexity of introducing a logical constructor with the complexity of the component schema formulas as well as the complexity of a schema formula across different schema calculi. (shrink)

Fusion is a well-known form of combining normal modal logics endowed with a Hilbert calculi and a Kripke semantics. Herein, fusion is studied over logic systems using sequent calculi labelled with truth values and with a semantics based on a two-sorted algebra allowing, in particular, the representation of general Kripke structures. A wide variety of logics, including non-classical logics like, for instance, modal logics and intuitionistic logic can be presented by logic systems of this kind. A categorical approach of fusion (...) is defined in the context of these logic systems. Preservation of soundness and completeness by fusion is studied. Soundness is preserved without further requirements, completeness is preserved under mild assumptions. (shrink)

The main objective of this paper is to define a logic for reasoning about distributed time-stamped claims. Such a logic is interesting for theoretical reasons, i.e. as a logic per se, but also because it has a number of practical applications, in particular when one needs to reason about a huge amount of pieces of evidence collected from different sources, where some of the pieces of evidence may be contradictory and some sources are considered to be more trustworthy than others. (...) We introduce the time-stamped claim logic including a sound and complete sequent calculus. In order to show how time-stamped claim logic can be used in practice, we consider a concrete cyber-attribution case study. (shrink)

We give an axiomatization of first‐order logic enriched with the almost‐everywhere quantifier over finitely additive measures. Using an adapted version of the consistency property adequate for dealing with this generalized quantifier, we show that such a logic is both strongly complete and enjoys Craig interpolation, relying on a (countable) model existence theorem. We also discuss possible extensions of these results to the almost‐everywhere quantifier over countably additive measures.

The functional role of mirror neurons has been assessed in many different ways. They have been regarded, inter alia, as the core mechanism of mind reading, the mechanism of language understanding, the mechanism of imitation. In this paper we will discuss the thesis according to which MNs are a conceptual mechanism. This hypothesis is attractive since it could accommodate in an apparently simple way all the above-mentioned interpretations. We shall take into consideration some reasons suggesting the conceptualist characterization of MNs, (...) as well as some possible replies. We shall figure out how an argument for the conceptualist hypothesis could be deployed, focusing on the notion of off-line processes, which turns out to be the crucial property necessary to ascribe concept possession. Our conclusion will be that, despite of there being some evidence for the conceptualist account, the issue cannot be definitely settled, because there are both experimental shortages and conceptual difficulties. In particular, there are three distinct senses in which MNs can be regarded as a conceptual mechanism, but we shall argue that only one of these interpretations can be defended. (shrink)

Resumo: A Kehre (viragem) no pensamento de Heidegger foi amplamente discutida e debatida. A introdução da noção de metontologia (Metontologie), em 1927, informou proveitosamente esse debate, uma vez que implica uma preocupação com o domínio ôntico, por parte de Heidegger, que não está presente em trabalhos anteriores. O fato de essa noção desaparecer logo após ser introduzida, porém, desafia sua contribuição para esse debate. Neste artigo, mostra-se que o desaparecimento da metontologia não significa o desaparecimento da preocupação de Heidegger com (...) o ôntico, mas o contrário. Começa-se apresentando a visão de Freeman de uma tensão entre o ôntico e o ontológico, no pensamento de Heidegger, em meados da década de 1920, que resulta na introdução da metontologia, em 1927. Mais tarde, evidencia-se que a explicação de McNeill para o desaparecimento da metontologia, como consequência da visão de Heidegger, de meados dos anos 30, de que a projeção a priori do ser é uma retirada do ser (Entzug des Seins), permite dizer que esse desaparecimento não acarreta uma repentina falta de preocupação de Heidegger com o ôntico. Ao considerar a análise de Heidegger de “o matemático”, em Die Frage nach dem Ding, finalmente, argumenta-se que a metontologia desaparece do pensamento de Heidegger, porque sua dependência da ontologia a impede de explicar sua crescente preocupação com o ôntico, de maneira adequada. (shrink)

In The Grammar of Society, first published in 2006, Cristina Bicchieri examines social norms, such as fairness, cooperation, and reciprocity, in an effort to understand their nature and dynamics, the expectations that they generate, and how they evolve and change. Drawing on several intellectual traditions and methods, including those of social psychology, experimental economics and evolutionary game theory, Bicchieri provides an integrated account of how social norms emerge, why and when we follow them, and the situations where we are (...) most likely to focus on relevant norms. Examining the existence and survival of inefficient norms, she demonstrates how norms evolve in ways that depend upon the psychological dispositions of the individual and how such dispositions may impair social efficiency. By contrast, she also shows how certain psychological propensities may naturally lead individuals to evolve fairness norms that closely resemble those we follow in most modern societies. (shrink)

In Norms in the Wild, distinguished philosopher Cristina Bicchieri argues that when it comes to human behavior, social scientists place too much stress on rational deliberation. In fact, she says, many choices occur without much deliberation at all. Two people passing in a corridor automatically negotiate their shared space; cars at an intersection obey traffic signals; we choose clothing based on our instincts for what is considered appropriate. Bicchieri's theory of social norms accounts for these automatic components of coordination, (...) where individuals react automatically to cues that focus their attention on what the norm is in that situation. Social norms thus act as rules for making choices in a social world where people expect others -- often unconsciously -- to follow the same rule. Some norms enable seamless social co-operation, while others are less beneficial to human flourishing.Bicchieri is famous for her interdisciplinary work on game theory and most recently her work on social norms, and Norms in the Wild represents her latest challenge to many of the fundamental assumptions of the social sciences. Bicchieri's work has broad implications not only for understanding human behavior, but for changing it for better outcomes. People have a strongly conditioned preference for following social norms, but that also means that manipulating their expectations can cause major behavioral changes. Bicchieri has been working recently with UNICEF and other NGO's to explore the applicability of her views to issues of human rights around the world. Is it possible to change social expectations around forced marriage, genital mutilations, and public health practices like vaccinations and sanitation? If so, how? What tools might we use? This short book explores how social norms work, and how changing them - changing preferences, beliefs, and especially social expectations - can potentially improve lives all around the world. It will appeal to an unusually broad range of readers including philosophers, psychologists and others in behavioral sciences, and anyone involved in public policy or at NGOs. (shrink)

A graph-theoretic account of logics is explored based on the general notion of m-graph (that is, a graph where each edge can have a finite sequence of nodes as source). Signatures, interpretation structures and deduction systems are seen as m-graphs. After defining a category freely generated by a m-graph, formulas and expressions in general can be seen as morphisms. Moreover, derivations involving rule instantiation are also morphisms. Soundness and completeness theorems are proved. As a consequence of the generality of the (...) approach our results apply to very different logics encompassing, among others, substructural logics as well as logics with nondeterministic semantics, and subsume all logics endowed with an algebraic semantics. (shrink)

The New Evil Demon Problem presents a serious challenge to externalist theories of epistemic justification. In recent years, externalists have developed a number of strategies for responding to the problem. A popular line of response involves distinguishing between a belief’s being epistemically justified and a subject’s being epistemically blameless for holding it. The apparently problematic intuitions the New Evil Demon Problem elicits, proponents of this response claim, track the fact that the deceived subject is epistemically blameless for believing as she (...) does, not that she is justified for so believing. This general strategy—which I call the “unjustified-but-blameless maneuver”—is motivated, in part, by the assumption that the distinction between epistemic justification and blamelessness is merely an extension of the familiar distinction between moral justification and blamelessness. In this paper, I consider three ways of drawing the distinction between justification and blamelessness familiar from the moral domain: the first in terms of a connection with reactive attitudes, the second in terms of the distinction between wrongness and wronging, and the third in terms of reasons-responsiveness. All three ways of drawing the distinction, I argue, make it difficult to see how an analogous distinction in the epistemic domain could help externalists explain away the intuitions which underwrite the New Evil Demon Problem. Motivating the unjustified-but-blameless maneuver, I conclude, is a much less straightforward task than its proponents tend to assume. (shrink)

Les études réunies et publiés dans ce volume sont d'abord concentrées sur les problèmes relatifs à la nature de l'âme en général, notamment par le biais d'une confrontation avec des penseurs antérieurs a Aristote ou qui leur sont contemporains - spécialement Platon et Xenocrate.

A graph-theoretic account of fibring of logics is developed, capitalizing on the interleaving characteristics of fibring at the linguistic, semantic and proof levels. Fibring of two signatures is seen as a multi-graph (m-graph) where the nodes and the m-edges include the sorts and the constructors of the signatures at hand. Fibring of two models is a multi-graph (m-graph) where the nodes and the m-edges are the values and the operations in the models, respectively. Fibring of two deductive systems is an (...) m-graph whose nodes are language expressions and the m-edges represent the inference rules of the two original systems. The sobriety of the approach is confirmed by proving that all the fibring notions are universal constructions. This graph-theoretic view is general enough to accommodate very different fibrings of propositional based logics encompassing logics with non-deterministic semantics, logics with an algebraic semantics, logics with partial semantics and substructural logics, among others. Soundness and weak completeness are proved to be preserved under very general conditions. Strong completeness is also shown to be preserved under tighter conditions. In this setting, the collapsing problem appearing in several combinations of logic systems can be avoided. (shrink)

Embora a relação entre subjectividade e tempo seja fulcral para a fenomenologia, é-o sempre com o intuito de fundamentar ontologicamente a consciência na sua verdade A grande originalidade de Levinas consiste em abandonar o plano do cogito e, consequentem.

Combined connectives arise in combined logics. In fibrings, such combined connectives are known as shared connectives and inherit the logical properties of each component. A new way of combining connectives (and other language constructors of propositional nature) is proposed by inheriting only the common logical properties of the components. A sound and complete calculus is provided for reasoning about the latter. The calculus is shown to be a conservative extension of the original calculus. Examples are provided contributing to a better (...) understanding of what are the common properties of any two constructors, say disjunction and conjunction. (shrink)

Dans Adv. math., X, 216-218, Sextus Empiricus rapporte une mystérieuse doctrine d' « Énésidème selon Héraclite » d'après laquelle le temps est identifié à un corps. L'hypothèse défendue ici est que cette formule exprime une théorie à usage dialectique et critique, construite par Énésidème afin d'inserer la thèse d' Héraclite dans un débat fictif où interviennent d'autres positions dogmatiques. Alors que la plupart des historiens de la philosophie nient l'authenticité héraclitéenne de ce témoignage, dans ses Leçons sur l'histoire de la (...) philosophie Hegel l'accepte sans réticence, aussi bien du point de vue historique que du point de vue théorique et y voit l'anticipation de sa propre notion du temps comme première forme du devenir. In Adv. Math., X, 216-218, Sextus Empiricus recalls a mysterious doctrine of a so-called « Enesidemus according to Heraclitus » according to which time is identified to a body. The hereby sustained hypothesis goes to saying that such a saying expresses some kind of theory meant to be used both dialectically and critically. It is said to have been erected by Enesidemes so as to be able to insert Heraclitus' thesis into a fictitious debate in which other dogmatic positions may interplay. Whereas most historians of philosophy deny the Heraclitean authenticity of such a testimony, Hegel, in his Lessons on the History of Philosophy, accepts it without any form of reticence, both on the historical point of view and on the theoretical point of view, thus viewing in it the foresight of his own concept of time as first form of the becoming. (shrink)

David Lewis may be regarded as an antiessentialist. The reason is that he is said to believe that individuals do not have essential properties independent of the ways they are represented. According to him, indeed, the properties that are determined to be essential to individuals are a matter of which similarity relations among individuals are salient, and salience, in turn, is a contextual matter also determined to some extent by the ways individuals are represented. Todd Buras argues that the acknowledgment (...) of natural properties in counterpart theoretic ontology affects Lewis’s theory with regard to essentialism. Buras’s reasoning is appealing. He claims that, since natural properties determine the existence of similarity relations among individuals that are salient independent of context, Lewis can no longer be claimed to be an antiessentialist. The aim of this paper is to argue, against Buras, that if counterpart theory was antiessentialist before natural properties were taken into account, then it remains so afterwards. (shrink)

The thesis of mental fragmentation has recently attracted increased attention as a way of explaining facts about mind and language. This volume provides an accessible introduction and essays on foundations and applications of fragmentation.

The Arabic version of the Enneads is the earliest datable text in which appears the term "anniyya", that features in Avicenna’s metaphysics and lies in the background of the Latin definition of the Causa prima as esse tantum, typical of the Liber de Causis. This paper examines some examples of the use of "to be" in the Arabic translation of the Enneads. It also discusses the description of the First Cause as ‘pure Being’ or ‘first Being’ in the Arabic Plotinus, (...) and compares it with the Divine Names of the pseudo-Dionysius. icona . (shrink)

Questo articolo presenta un quadro dei problemi che il frammento B85DK di Eraclito solleva e delle interpretazioni antiche e moderne che sono state suggerite. In particolare, è esaminata la testimonianza di Aristotele, la più antica e anche la più profonda e articolata. Una panoramica sui significati di thumos, punto centrale del frammento, mostra che per Aristotele questo concetto non si esaurisce nel pathos dell’ira. Il thumos è in primo luogo una dunamis, una facoltà dell’anima che rende possibile non solo il (...) pathos, l’affezione passeggera dell’ira, ma anche il coraggio, l’impulsività, l’affetto, il senso della libertà e dell’autorità. Questa nozione aristotelica, così ricca e polimorfica da sottrarsi a una traduzione unica esaustiva, proviene in realtà dalla sistematizzazione di un materiale molto antico, omerico e presocratico, legato ai proverbi. Eraclito stesso ne offre già una formulazione che sintetizza due aspetti che Aristotele accoglie e sottolinea: la forza irresistibile e inarrestabile dello slancio impulsivo naturale, una volta che sia stato innescato, e l'estrema conseguenza a cui puo' portare, e cioè la perdita della vita stessa. (shrink)

A probabilistic propositional logic, endowed with a constructor for asserting compatibility of diagonalisable and bounded observables, is presented and illustrated for reasoning about the random results of projective measurements made on a given quantum state. Simultaneous measurements are assumed to imply that the underlying observables are compatible. A sound and weakly complete axiomatisation is provided relying on the decidable first-order theory of real closed ordered fields. The proposed logic is proved to be a conservative extension of classical propositional logic.

We report the results of an experiment designed to determine the effects of psychological proximity—proxied by awareness of pain and friendship—on moral reasoning. Our study tests the hypotheses that a moral agent’s emphasis on justice decreases with proximity, while his/her emphasis on care increases. Our study further examines how personality, gender, and managerial status affect the importance of care and justice in moral reasoning. We find support for the main hypotheses. We also find that care should be split into two (...) components, one related to protection and the other to the preservation of relationships. Although gender does not affect moral reasoning directly, we find that it does so indirectly via personality, controlling for age, professional status, and professional background. We do not find a significant effect of managerial status on ethics of justice, but do find that holding a managerial position has a negative impact on ethics of care. Regarding personality, we detect significant positive effects of conscientiousness on ethics of justice and of neuroticism on ethics of care. (shrink)

This dissertation discusses friendship in relation to self-identity in the thought of Paul Ricoeur. Its main claim is that Ricoeur's notion of self-identity designates a hermeneutically mediated experience, and that this complex experience can only be illumined by a phenomenology that is sensitive to ethical aspects. Another finding is that, according to Ricoeur, whatever we do, say, or write, takes on the form of narrative experience. Finally, the dissertation shows that what looks like the force of the discourse, driving author (...) to reader, and readers to one another, is in fact the force of philia, and that the latter is a source that nourishes practical wisdom exercised in relations with others. The call to friendship is a call to esteem for the being-like-me, a call to recognize a likeness beyond question and doubt, which relates selfhood and alterity, sameness and difference. (shrink)