We present a labelled version of Lambek Calculus without unit, and we use it to prove a completeness theorem for Lambek Calculus with respect to some relational semantics.

We present a sound and complete tableau calculus for the class of regular grammar logics. Our tableau rules use a special feature called automaton-labelled formulae, which are similar to formulae of automaton propositional dynamic logic. Our calculus is cut-free and has the analytic superformula property so it gives a decision procedure. We show that the known EXPTIME upper bound for regular grammar logics can be obtained using our tableau calculus. We also give an effective Craig interpolation (...) lemma for regular grammar logics using our calculus. (shrink)

We introduce an effective translation from proofs in the display calculus to proofs in the labelled calculus in the context of tense logics. We identify the labelled calculus proofs in the image of this translation as those built from labelled sequents whose underlying directed graph possesses certain properties. For the basic normal tense logic Kt, the image is shown to be the set of all proofs in the labelled calculus G3Kt.

Inspired by recent work on proof theory for modal logic, this paper develops a cut-free labelled sequent calculus obtained by imitating Herzberger’s limit rule for revision sequences as a clause in a possible world semantics. With the help of two completeness theorems, one between the labelled sequent calculus and the corresponding possible world semantics, and one between the axiomatic theory of truth PosFS and a neighbourhood semantics, together with the proof of the equivalence between the two (...) semantics, we show that the theory of truth obtained with the labelled sequent calculus based on Herzberger’s limit rule is equivalent to PosFS. (shrink)

This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic paradigms: labelled and nested sequent calculi. The formalism of labelled sequents has been successful in that cut-free calculi in possession of desirable proof-theoretic properties can be automatically generated for large classes of logics. Despite these qualities, labelled systems make use of a complicated syntax that (...) explicitly incorporates the semantics of the associated logic, and such systems typically violate the subformula property to a high degree. By contrast, nested sequent calculi employ a simpler syntax and adhere to a strict reading of the subformula property, making such systems useful in the design of automated reasoning algorithms. However, the downside of the nested sequent paradigm is that a general theory concerning the automated construction of such calculi (as in the labelled setting) is essentially absent, meaning that the construction of nested systems and the confirmation of their properties is usually done on a case-by-case basis. The refinement method connects both paradigms in a fruitful way, by transforming labelled systems into nested (or, refined labelled) systems with the properties of the former preserved throughout the transformation process. To demonstrate the method of refinement and some of its applications, we consider grammar logics, first-order intuitionistic logics, and deontic STIT logics. The introduced refined labelled calculi will be used to provide the first proof-search algorithms for deontic STIT logics. Furthermore, we employ our refined labelled calculi for grammar logics to show that every logic in the class possesses the effective Lyndon interpolation property. (shrink)

We present the design goals and metatheory of the Monadic Hybrid Calculus, a new formal system that has the same power as the Monadic Predicate Calculus. MHC allows quantification, including relative quantification, in a straightforward way without the use of bound variables, using a simple adaptation of modal logic notation. Thus “all Greeks are mortal” can be written as [G]M. MHC is also ‘hybrid’ in that it has individual constants, which allow us to formulate statements about particular individuals. (...) Thus “Socrates is Athenian and mortal” can be formalised as s.For our proof system, we use a simple adaptation of Beth-style tableaus. The availability of individual constants eliminates the need for labelled deduction.We discuss first the pragmatic and pedagogical advantages of MHC. Then we present the metatheory: formal syntax, semantics, proof rules, soundness, completeness and expressive equivalence with the Monadic Predicate Calculus. (shrink)

We prove a representation theorem for residuated algebras: each residuated algebra is isomorphically embeddable into a powerset residuated algebra. As a consequence, we obtain a completeness theorem for the Generalized Lambek Calculus. We use a Labelled Deductive System which generalizes the one used by Buszkowski [4] and Pankrat'ev [17] in completeness theorems for the Lambek Calculus.

This article concerns the treatment of propositional quantification in a framework of labelled natural deduction for modal logic developed by Basin, Matthews and Viganò. We provide a detailed analysis of a basic calculus that can be used for a proof-theoretic rendering of minimal normal multimodal systems with quantification over stable domains of propositions. Furthermore, we consider variations of the basic calculus obtained via relational theories and domain theories allowing for quantification over possibly unstable domains of propositions. The (...) main result of the article is that fragments of the labelled calculi not exploiting reductio ad absurdum enjoy the Church–Rosser property and the strong normalization property; such result is obtained by combining Girard’s method of reducibility candidates and labelled languages of lambda calculus codifying the structure of modal proofs. (shrink)

The aim of this paper is to define a λ-calculus typed in aMixed (commutative and non-commutative) Intuitionistic Linear Logic. The terms of such a calculus are the labelling of proofs of a linear intuitionistic mixed natural deduction NILL, which is based on the non-commutative linear multiplicative sequent calculus MNL [RuetAbrusci 99]. This linear λ-calculus involves three linear arrows: two directional arrows and a nondirectional one (the usual linear arrow). Moreover, the -terms are provided with seriesparallel orders (...) on free variables. We prove a normalization theorem which explicitly gives the behaviour of the order during the normalization procedure. (shrink)

The logic of Conditional Beliefs has been introduced by Board, Baltag, and Smets to reason about knowledge and revisable beliefs in a multi-agent setting. In this article both the semantics and the proof theory for this logic are studied. First, a natural semantics forCDLis defined in terms of neighbourhood models, a multi-agent generalisation of Lewis’ spheres models, and it is shown that the axiomatization ofCDLis sound and complete with respect to this semantics. Second, it is shown that the neighbourhood semantics (...) is equivalent to the original one defined in terms of plausibility models, by means of a direct correspondence between the two types of models. On the basis of neighbourhood semantics, a labelled sequent calculus forCDLis obtained. The calculus has strong proof-theoretic properties, in particular admissibility of contraction and cut, and it provides a decision procedure for the logic. Furthermore, its semantic completeness is used to obtain a constructive proof of the finite model property of the logic. Finally, it is shown that other doxastic operators can be easily captured within neighbourhood semantics. This fact provides further evidence of the naturalness of neighbourhood semantics for the analysis of epistemic/doxastic notions. (shrink)

The notion of normal proof theory, and yet it has been somewhat neglected by the systems of equational logic. The intention here is then to show the normalization procedure for the equational logic of the Labelled Natural Deduction system . With this we believe we are making a step towards filling a gap in the literature on equational logic. Besides presenting a normalization procedure for the LND equational fragment, we employ a new method to prove the normalization theorems for (...) equational logic: proof transformation by rewriting, based on a algebraic calculus on the 'rewrite reasons'. (shrink)

Dynamic epistemic logic (DEL) is a multi-modal logic for reasoning about the change of knowledge in multi-agent systems. It extends epistemic logic by a modal operator for actions which announce logical formulas to other agents. In Hilbert-style proof calculi for DEL, modal action formulas are reduced to epistemic logic, whereas current sequent calculi for DEL are labelled systems which internalize the semantic accessibility relation of the modal operators, as well as the accessibility relation underlying the semantics of the actions. (...) We present a novel cut-free ordinary sequent calculus, called |$ \textbf{G4}_{P,A}[] $|⁠, for propositional DEL. In contrast to the known sequent calculi, our calculus does not internalize the accessibility relations, but—similar to Hilbert style proof calculi—action formulas are reduced to epistemic formulas. Since no ordinary sequent calculus for full S5 modal logic is known, the proof rules for the knowledge operator and the Boolean operators are those of an underlying S4 modal calculus. We show the soundness and completeness of |$ \textbf{G4}_{P,A}[] $| and prove also the admissibility of the cut-rule and of several other rules for introducing the action modality. (shrink)

This study investigates the engagement of family firms in corporate social responsibility. We first compare their corporate social performance to non-family firms. Then, following recent evidence on the heterogeneity of family firms, we examine two factors that may influence CSP within family firms: the level of family control and the governance orientation of the country in which they operate. This research is based on a theoretical framework which considers both agency and socioemotional wealth influences on family firms CSR engagements. Overall, (...) we find that family firms exhibit lower CSP than non-family firms. But when focusing on family firms, our analyses show a curvilinear relationship between family control and CSP. At lower levels of control, family owners invest more in social initiatives to protect their SEW. Beyond a threshold level of control that we estimate at 36 % in our sample, economic considerations prevail over SEW and social performance starts decreasing. We also find that family firms operating in stakeholder-oriented countries are more attentive to social concerns than those operating in more shareholder-oriented countries. (shrink)

This article proposes and empirically tests a theoretical framework incorporating Reidenbach and Robin’s (J Bus Ethics 10(4):273–284, 1991 ) conceptual model of corporate moral development. The framework is used to examine the relation between governance and business ethics, as proxied by diversity management (DM), and financial reporting quality, as proxied by the magnitude of earnings management (EM). The level of DM and governance quality are measured in accordance with the ratings of Jantzi Research (JR), a leading provider of social and (...) governance research for institutional investors. This DM score is part of an index developed by JR that investment managers use to integrate DM criteria into their investment decisions. As expected, a negative relation between corporate DM development and financial reporting quality is found while controlling for other factors known in the literatures on governance and accounting choices to affect earnings quality. Despite some caveats presented in conclusion, this study contributes to the ethics, governance, and financial reporting literatures by studying the dynamics between governance and ethics in the prevention of EM. (shrink)

In this paper I examine two theories of democracy that can be found in contemporary French philosophy. Both Cornelius Castoriadis and Jacques Rancière offer a critique of modern democracy with the purpose of refounding it. The ‘refoundation narratives’ they propose are both based on an account of the origins of democracy in ancient Greece. According to Castoriadis, ancient democracy is grounded in a ‘magma’ of ‘social imaginary significations’ in which ‘autonomy’ is considered the correct response to Being defined as an (...) insurmountable ‘Chaos’. On the contrary, modern democracy defines Being as a determinacy and consequently fails to grasp the notion of autonomy. According to Rancière, the origins of democracy are to be found in the invasion of the public space by ‘those without a part’ who consequently have no title to govern. The problem with the ‘domesticated’ modern democracy is that it denies the existence of Otherness; that is, of non-citizens excluded from the public space. Therefore it appears incapable of letting the ‘dis-agreement’ manifest itself and consequently incapable of transforming the ‘police’ order. After examining the meaning of both theories, I attempt to elucidate the difficulties encountered by each author in the attainment of his goal, which is that of refounding modern democracy. (shrink)

The book proposes a multi-dimensional understanding on sound and listening as capacities for challenging social and political structures of inequality and domination, supporting interpersonal exchange and modes of community-building based on empathy, care and compassion.

L’antéposition d’un verbe non conjugué (participe passé, infinitif) en ancien et en moyen français a été assimilée à l’antéposition stylistique de l’islandais. Nous montrons que dans le cas du français, ces antépositions illustrent trois constructions différentes, toutes distinctes de l’antéposition stylistique de l’islandais. Dans la construction la plus fréquente, étiquetée déplacement stylistique à gauche, l’expression antéposée s’insère dans une position interne à la proposition plutôt que dans la périphérie gauche, à la droite immédiate de la position canonique du sujet, qui (...) peut y être réalisé, contrairement à ce que l’on observe en islandais. La même analyse est étendue aux cas où le sujet est nul ou déplacé plus à gauche. Les deux autres cas sont ceux où 1) l’expression antéposée est l’élément initial d’une construction V2, une situation rare, ou 2) il y a mise en relief du verbe non fini à la gauche immédiate de la position canonique du sujet. (shrink)

Authored by leading sound studies scholar Brandon LaBelle, this book focuses on questions of acoustics as the basis for challenging normative structures.

The starting point of this article is that there is a kind of ‘hidden dialogue’ that Claude Lefort is trying to conduct with Leo Strauss on the theologico-political problem. If Strauss claims this problem to be ‘irresolvable’, Lefort seeks to show that the ‘permanence of the theologico-political’ in modernity is only an appearance, as democracy has, in the last instance, succeeded in ‘cutting’ the knot tied between the theological and the political in pre-modern societies. Moreover, while Strauss associates recognition of (...) the irresolvable character of the theologico-political problem with moderation, Lefort takes the exact opposite view, insisting on the lack of moderation, even excess, that weighs particularly on modern politics consequent to any attempt to amalgamate the theological with the political. (shrink)

Si les publics improbables sont, fondamentalement, des publics faibles, ils nous surprennent aussi – et c’est leur principal cadeau, leur caractère exemplaire. Par un art de la transgression, ils rappellent combien la vie publique est une affaire commune, façonnée par les gens à certains moments, en certains lieux, animés par la lutte et l’imagination, et par la joie de se découvrir les uns les autres. Cet article identifie quatre figures d’agentivité sonique pratiquées par ces improbables publics : l’invisible, l’entendu par-dessus (...) l’épaule, l’itinérant et le faible. (shrink)

La 4e de couverture indique : "Avec l'accélération de la mondialisation, une opinion qui aurait, jusqu'il y a peu, été taxée d'incongruité, semble avoir gagné le statut d'évidence : le système étatique mondial serait menacé et appellerait à une profonde redéfinition des attributs, des structures et du rôle traditionnellement dévolus aux Etats. Malgré un échiquier géopolitique modifié, où les frontières s'évanouissent et où les cultures et les traditions nationales s'amalgament jusqu'à l'extinction, il faut cependant reconnaître que la mondialisation n'est pas (...) venue à bout des Etats, des sociétés qui les composent et des divers problèmes que crée la cohabitation au sein de leurs institutions traditionnelles. Bien au contraire, la mondialisation a souvent contribué à enclencher en série des situations qui se répercutent sur les plans social et étatique. Dans toutes ces situations, c'est aux Etats, à leur gouvernement et à la société entière qu'il appartient de restaurer, voire de réinventer, la trame des communautés politiques. Non pas en érigeant des barrages à la mondialisation, mais en contribuant à la création des institutions d'une gouvernance globale juste et efficace. Rassemblant des collaborateurs de l'Europe, du Québec, du Canada anglais et des Etats-Unis, ce livre questionne, sous des angles différents, la pertinence théorique de la notion de communauté politique lorsqu'il s'agit de penser le pluralisme résultant de l'immigration internationale. II pose aussi un regard critique sur le rôle que cette notion joue dans les approches courantes des phénomènes liés à la diversité. Car plusieurs questions se posent maintenant, dont celle, au premier chef, de la capacité des appareils d'Etats contemporains de cimenter des communautés politiques dans un contexte de mobilité spatiale accrue et de transnationalisme croissant.". (shrink)

Dans l’opinion publique, la mondialisation a ouvert les vannes de l’immigration internationale, les migrants circulant désormais aussi facilement que les capitaux et les marchandises. En phase avec cette représentation relevant du sens commun, le domaine de la migration internationale tend à subir l’influence des théories de la mobilité qui jouissent d’un véritable effet de mode. Cette pensée emprunte à des courants d’idées privilégiant l’effacement des frontières. Le concept de « mobilité » repose sur deux visions contradictoires. La première suppose que (...) les populations se déplacent à travers les frontières pour vendre et négocier leurs « capital social », là où les avantages économiques et sociaux sont les plus grands. La seconde considère que les obstacles à la mobilité sont la cause de nouvelles inégalités et de nouvelles hiérarchies dans le système mondial. Critiques de ces visions, certains spécialistes de l’immigration internationale estiment que les facteurs historico-structurels à l’œuvre dans les pays d’émigration et d’immigration ont une plus grande pertinence explicative que le recours à la question de la circulation. (shrink)

Les enjeux majeurs de l’éducation des adultes se résument en ces trois mots indissociables qu’éclaire ma théorie de la réciprocité éducative. S’éduquer, comme se nourrir, c’est à la fois recourir à l’action d’un autre et ne s’en remettre qu’à soi pour grandir, se conduire et s’épanouir. Le paradoxe de la mutualité réside en ce que j’adviens à ma singularité personnelle en voulant que tu sois toi-même par toi, et inversement. La transhumance est l’autre nom de l’éducabilité des personnes qui s’accomplissent (...) en parcourant ensemble leurs chemins, terrestres ou intérieurs. (shrink)

Résumé Cet article cherche à comprendre le rapport singulier que Maurice Merleau-Ponty a établi avec le christianisme au sein de la phénoménologie française. Sont rappelées les différentes positions successives adoptées par le philosophe à l’égard du christianisme. Après avoir d’abord situé sa réflexion philosophico-politique au sein de la foi chrétienne, Merleau-Ponty en vient ensuite à une critique de la théologie trinitaire et à une défense de l’athéisme qui, cependant, insiste pour conserver un certain nombre d’éléments propres au christianisme. Enfin, au (...) cours des années cinquante, il revient sur sa position antérieure afin de montrer que la philosophie doit s’engager dans une interrogation interminable de différentes formes de non-philosophie, y compris ce qui s’énonce du sein et au nom du christianisme.The goal of this paper is to understand the singular relation with Christianity established by Maurice Merleau-Ponty within French phenomenology. The successive different positions Merleau-Ponty adopted regarding Christianity are recalled. First, Merleau-Ponty placed his philosophy and his politics in the sphere of Christianity. Then he proposed a critique of Trinitarian theology and proclaimed himself an atheist. Finally, he held that philosophy, defined as a radical questioning, should endlessly question different forms of non-philosophy, including Christian thought and theology. (shrink)

Il y a un peu plus de vingt ans, Marcel Gauchet livrait ses réflexions sur le long et lent processus de désenchantement du monde qui, de l’intérieur même de la compréhension religieuse du monde, a abouti à l’affirmation de l’autonomie humaine et à la prise en main par les hommes de leur destin collectif. Cette thèse a fait l’objet de nombreuses discussions et controverses qui portaient sur la validité de la reconstruction historique générale, sur la méthode guidant cette dernière, et (...) enfin sur la vérité du diagnostic final. Ces questions ont leur intérêt et ont été déjà vivement débattues. Ce livre sur et à partir de la pensée de Gauchet sera toutefois différemment orienté. Il porte davantage sur les effets du désenchantement sur la démocratie elle-même que sur l’origine du désenchantement du monde. Il semble en effet que la démocratie contemporaine, en gros la démocratie des individus et des identités, subisse à son tour les effets du désenchantement et qu’elle tende à devenir une démocratie "contre elle-même". C’est du moins dans ce sens que l’on pourrait lire les ouvrages plus récents de Gauchet, La religion dans la démocratie (1998), La démocratie contre elle-même (2002) et La condition politique (2007). L’avènement de cette démocratie désenchantée ouvre tout un ensemble d’interrogations qui seront au coeur de cet ouvrage : un tel diagnostic est-il juste? Jusqu’à quel point la démocratie peut-elle se retourner contre elle-même? Un régime politique qui effacerait toute trace de croyable est-il possible? Comment la démocratie doit-elle réagir devant les tentatives idéologiques de réenchantement du monde? Quelles seraient les ressources internes à la démocratie pour corriger les excès provoqués par son propre désenchantement? (shrink)

This article examines whether and how the participation of women in the firm’s board of directors and senior management enhances financial performance. We use the Fama and French (1992, 1993) valuation framework to take the level of risk into consideration, when comparing firm performances, whereas previous studies used either raw stock returns or accounting ratios. Our results indicate that firms operating in complex environments do generate positive and significant abnormal returns when they have a high proportion of women officers. Although (...) the participation of women as directors does not seem to make a difference in this regard, firms with a high proportion of women in both their management and governance systems generate enough value to keep up with normal stock-market returns. These findings tend to support the policies currently being discussed or implemented in some countries and organizations to foster the advancement of women in business. (shrink)

Companies that are serious about corporate governance and business ethics are turning their attention to gender diversity at the most senior levels of business . Board gender diversity has been the subject of several studies carried out by international organizations such as Catalyst , the World Economic Forum , and the European Board Diversity Analysis . They all lead to reports confirming the overall relatively low proportion of women on boards and the slow pace at which more women are being (...) appointed. Furthermore, the proportion of women on corporate boards varies much across countries. Based on institutional theory, this study hypothesizes and tests whether this variation can be attributed to differences in cultural settings across countries. Our analysis of the representation of women on boards for 32 countries during 2010 reveals that two cultural characteristics are indeed associated with the observed differences. We use the cultural dimensions proposed by Hofstede to measure this construct. Results show that countries which have the greatest tolerance for inequalities in the distribution of power and those that tend to value the role of men generally exhibit lower representations of women on boards. (shrink)

The inconclusiveness of previous research on the association between gender diverse boards and corporate social performance has led us to revisit the question in light of stakeholder management and institutional theories. Given that corporate social responsibility is a multidimensional concept, we test the influence of GDB on various groups of stakeholders. By considering the interaction between stakeholders’ power and directors’ personal motivations toward the prioritization of stakeholders’ claims, we find that GDB are positively related to CSR dimensions that are related (...) to less powerful stakeholders such as the environment, contractors, and the community. However, GDB do not appear to have a significant impact on CSR dimensions that are associated with stakeholders who benefit from more institutionalized power, such as employees and customers. (shrink)

Platelets have important hemostatic functions in repairing blood vessels upon tissue injury. Cytokines, growth factors, and metabolites stored in platelet α‐granules and dense granules are released upon platelet activation and clotting. Emerging evidence indicates that such platelet‐derived signaling factors are instrumental in guiding tissue regeneration. Here, we discuss the important roles of platelet‐secreted signaling factors in skeletal muscle regeneration. Chemokines secreted by platelets in the early phase after injury are needed to recruit neutrophils to injured muscles, and impeding this early (...) step of muscle regeneration exacerbates inflammation at later stages, compromises neo‐angiogenesis and the growth of newly formed myofibers, and reduces post‐injury muscle force production. Platelets also contribute to the recruitment of pro‐regenerative stromal cells from the adipose tissue, and the platelet releasate may also regulate the metabolism and proliferation of muscle satellite cells, which sustain myogenesis. Therefore, harnessing the signaling functions of platelets and the platelet secretome may provide new avenues for promoting skeletal muscle regeneration in health and disease. (shrink)

This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. Each aspect of the extraction process is motivated and detailed, showing that each nested calculus inherits favorable (...) proof-theoretic properties from its associated labelled calculus. (shrink)

We introduce translations between display calculus proofs and labeled calculus proofs in the context of tense logics. First, we show that every derivation in the display calculus for the minimal tense logic Kt extended with general path axioms can be effectively transformed into a derivation in the corresponding labeled calculus. Concerning the converse translation, we show that for Kt extended with path axioms, every derivation in the corresponding labeled calculus can be put into a special (...) form that is translatable to a derivation in the associated display calculus. A key insight in this converse translation is a canonical representation of display sequents as labeled polytrees. Labeled polytrees, which represent equivalence classes of display sequents modulo display postulates, also shed light on related correspondence results for tense logics. (shrink)

We employ a recently developed methodology -- called "structural refinement" -- to extract nested sequent systems for a sizable class of intuitionistic modal logics from their respective labelled sequent systems. This method can be seen as a means by which labelled sequent systems can be transformed into nested sequent systems through the introduction of propagation rules and the elimination of structural rules, followed by a notational translation. The nested systems we obtain incorporate propagation rules that are parameterized with (...) formal grammars, and which encode certain frame conditions expressible as first-order Horn formulae that correspond to a subclass of the Scott-Lemmon axioms. We show that our nested systems are sound, cut-free complete, and admit hp-admissibility of typical structural rules. (shrink)

The semilattice relevant logics ∪R, ∪T, ∪RW, and ∪TW are defined by semilattice models in which conjunction and disjunction are interpreted in a natural way. For each of them, there is a cut-free labelled sequent calculus with plural succedents . We prove that these systems are equivalent, with respect to provable formulas, to the restricted systems with single succedents . Moreover, using this equivalence, we give a new Hilbert-style axiomatizations for ∪R and ∪T and prove equivalence between two (...) semantics for the contractionless logics ∪RW and ∪TW. (shrink)

A proof-theoretical treatment of collectively accepted group beliefs is presented through a multi-agent sequent system for an axiomatization of the logic of acceptance. The system is based on a labelled sequent calculus for propositional multi-agent epistemic logic with labels that correspond to possible worlds and a notation for internalized accessibility relations between worlds. The system is contraction- and cut-free. Extensions of the basic system are considered, in particular with rules that allow the possibility of operative members or legislators. (...) Completeness with respect to the underlying Kripke semantics follows from a general direct and uniform argument for labelled sequent calculi extended with mathematical rules for frame properties. As an example of the use of the calculus we present an analysis of the discursive dilemma. (shrink)

A combination of epistemic logic and dynamic logic of programs is presented. Although rich enough to formalize some simple game-theoretic scenarios, its axiomatization is problematic as it leads to the paradoxical conclusion that agents are omniscient. A cut-free labelled Gentzen-style proof system is then introduced where knowledge and action, as well as their combinations, are formulated as rules of inference, rather than axioms. This provides a logical framework for reasoning about games in a modular and systematic way, and to (...) give a step-by-step reconstruction of agents omniscience. In particular, its semantic assumptions are made explicit and a possible solution can be found in weakening the properties of the knowledge operator. (shrink)

Using labelled formulae, a cut-free sequent calculus for intuitionistic propositional logic is presented, together with an easy cut-admissibility proof; both extend to cover, in a uniform fashion, all intermediate logics characterised by frames satisfying conditions expressible by one or more geometric implications. Each of these logics is embedded by the Gödel–McKinsey–Tarski translation into an extension of S4. Faithfulness of the embedding is proved in a simple and general way by constructive proof-theoretic methods, without appeal to semantics other than (...) in the explanation of the rules. (shrink)

In the late forties, Stanisław Jaśkowski published two papers onthe discursive sentential calculus, D2. He provided a definition of it by an interpretation in the language of S5 of Lewis. The knownaxiomatization of D2 with discursive connectives as primitives was introduced by da Costa, Dubikajtis and Kotas in 1977. It turns out, however,that one of the axioms they used is not a thesis of the real Jaśkowski’s calculus. In fact, they built a new system, D∗2 for short, that (...) differs from D2 inmany respects. The aim of this paper is to introduce a direct Kripke-type semantics for the system, axiomatize it in a new way and prove soundness andcompleteness theorems. Additionally, we present labelled tableaux for D∗2.1. (shrink)

A general class of labeled sequent calculi is investigated, and necessary and sufficient conditions are given for when such a calculus is sound and complete for a finite -valued logic if the labels are interpreted as sets of truth values. Furthermore, it is shown that any finite -valued logic can be given an axiomatization by such a labeled calculus using arbitrary "systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is logarithmic (...) in the number of truth values, and it is shown that this bound is tight. (shrink)

Anti-realist epistemic conceptions of truth imply what is called the knowability principle: All truths are possibly known. The principle can be formalized in a bimodal propositional logic, with an alethic modality ${\diamondsuit}$ and an epistemic modality ${\mathcal{K}}$, by the axiom scheme ${A \supset \diamondsuit \mathcal{K} A}$. The use of classical logic and minimal assumptions about the two modalities lead to the paradoxical conclusion that all truths are known, ${A \supset \mathcal{K} A}$. A Gentzen-style reconstruction of the Church–Fitch paradox is presented (...) following a labelled approach to sequent calculi. First, a cut-free system for classical bimodal logic is introduced as the logical basis for the Church–Fitch paradox and the relationships between ${\mathcal {K}}$ and ${\diamondsuit}$ are taken into account. Afterwards, by exploiting the structural properties of the system, in particular cut elimination, the semantic frame conditions that correspond to KP are determined and added in the form of a block of nonlogical inference rules. Within this new system for classical and intuitionistic “knowability logic”, it is possible to give a satisfactory cut-free reconstruction of the Church–Fitch derivation and to confirm that OP is only classically derivable, but neither intuitionistically derivable nor intuitionistically admissible. Finally, it is shown that in classical knowability logic, the Church–Fitch derivation is nothing else but a fallacy and does not represent a real threat for anti-realism. (shrink)

De Finetti would claim that we can make sense of a draw in which each positive integer has equal probability of winning. This requires a uniform probability distribution over the natural numbers, violating countable additivity. Countable additivity thus appears not to be a fundamental constraint on subjective probability. It does, however, seem mandated by Dutch Book arguments similar to those that support the other axioms of the probability calculus as compulsory for subjective interpretations. These two lines of reasoning can (...) be reconciled through a slight generalization of the Dutch Book framework. Countable additivity may indeed be abandoned for de Finetti's lottery, but this poses no serious threat to its adoption in most applications of subjective probability. Introduction The de Finetti lottery Two objections to equiprobability 3.1 The ‘No random mechanism’ argument 3.2 The Dutch Book argument Equiprobability and relative betting quotients The re-labelling paradox 5.1 The paradox 5.2 Resolution: from symmetry to relative probability Beyond the de Finetti lottery. (shrink)

The axiomatic presentation of modal systems and the standard formulations of natural deduction and sequent calculus for modal logic are reviewed, together with the difficulties that emerge with these approaches. Generalizations of standard proof systems are then presented. These include, among others, display calculi, hypersequents, and labelled systems, with the latter surveyed from a closer perspective.