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  1. Modal Logic: An Introduction.Brian F. Chellas - 1980 - New York: Cambridge University Press.
    A textbook on modal logic, intended for readers already acquainted with the elements of formal logic, containing nearly 500 exercises. Brian F. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. Illustrative chapters focus on deontic logic and conditionality. Modality is a rapidly expanding branch of logic, and familiarity with the subject is now regarded as a necessary part of every philosopher's technical equipment. Chellas here offers an (...)
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  • (2 other versions)Counterfactuals.David Lewis - 1973 - Foundations of Language 13 (1):145-151.
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  • (2 other versions)Counterfactuals.David Lewis - 1973 - Philosophy of Science 42 (3):341-344.
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  • An essay in classical modal logic.Krister Segerberg - 1971 - Uppsala,: Filosofiska föreningen och Filosofiska institutionen vid Uppsala universitet.
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  • Universal grammar.Richard Montague - 1970 - Theoria 36 (3):373--398.
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  • Neighborhood Semantics for Modal Logic.Eric Pacuit - 2017 - Cham, Switzerland: Springer.
    This book offers a state-of-the-art introduction to the basic techniques and results of neighborhood semantics for modal logic. In addition to presenting the relevant technical background, it highlights both the pitfalls and potential uses of neighborhood models – an interesting class of mathematical structures that were originally introduced to provide a semantics for weak systems of modal logic. In addition, the book discusses a broad range of topics, including standard modal logic results ; bisimulations for neighborhood models and other model-theoretic (...)
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  • The Algebra of Topology.J. C. C. Mckinsey & Alfred Tarski - 1944 - Annals of Mathematics, Second Series 45:141-191.
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  • Advice on modal logic.D. Scott - 1980 - In Karel Lambert, Philosophical problems in logic: some recent developments. Hingham, MA: Sold and distributed in the U.S.A. and Canada by Kluwer Boston. pp. 143--173.
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  • Dynamic Logic.David Harel, Dexter Kozen & Jerzy Tiuryn - 2000 - MIT Press.
    This book provides the first comprehensive introduction to Dynamic Logic. Among the many approaches to formal reasoning about programs, Dynamic Logic enjoys the singular advantage of being strongly related to classical logic. Its variants constitute natural generalizations and extensions of classical formalisms. For example, Propositional Dynamic Logic (PDL) can be described as a blend of three complementary classical ingredients: propositional calculus, modal logic, and the algebra of regular events. In First-Order Dynamic Logic (DL), the propositional calculus is replaced by classical (...)
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  • Dynamic Logics of Evidence-Based Beliefs.Johan van Benthem & Eric Pacuit - 2011 - Studia Logica 99 (1):61-92.
    This paper adds evidence structure to standard models of belief, in the form of families of sets of worlds. We show how these more fine-grained models support natural actions of “evidence management”, ranging from update with external new information to internal rearrangement. We show how this perspective leads to new richer languages for existing neighborhood semantics for modal logic. Our main results are relative completeness theorems for the resulting dynamic logic of evidence.
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  • On the logic of ability.Mark A. Brown - 1988 - Journal of Philosophical Logic 17 (1):1 - 26.
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  • Dynamic Logics of Evidence-Based Beliefs.J. Benthem & E. Pacuit - 2011 - Studia Logica 99 (1-3):61-92.
    This paper adds evidence structure to standard models of belief, in the form of families of sets of worlds. We show how these more fine-grained models support natural actions of “evidence management”, ranging from update with external new information to internal rearrangement. We show how this perspective leads to new richer languages for existing neighborhood semantics for modal logic. Our main results are relative completeness theorems for the resulting dynamic logic of evidence.
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  • Topological reasoning and the logic of knowledge.Andrew Dabrowski, Lawrence S. Moss & Rohit Parikh - 1996 - Annals of Pure and Applied Logic 78 (1-3):73-110.
    We present a bimodal logic suitable for formalizing reasoning about points and sets, and also states of the world and views about them. The most natural interpretation of the logic is in subset spaces , and we obtain complete axiomatizations for the sentences which hold in these interpretations. In addition, we axiomatize the validities of the smaller class of topological spaces in a system we call topologic . We also prove decidability for these two systems. Our results on topologic relate (...)
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  • The modal logic of agency.Dag Elgesem - 1997 - Nordic Journal of Philosophical Logic 2:1-46.
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  • Normal monomodal logics can simulate all others.Marcus Kracht & Frank Wolter - 1999 - Journal of Symbolic Logic 64 (1):99-138.
    This paper shows that non-normal modal logics can be simulated by certain polymodal normal logics and that polymodal normal logics can be simulated by monomodal (normal) logics. Many properties of logics are shown to be reflected and preserved by such simulations. As a consequence many old and new results in modal logic can be derived in a straightforward way, sheding new light on the power of normal monomodal logic.
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  • A logic for deontic dilemmas.Lou Goble - 2005 - Journal of Applied Logic 3 (3-4):461-483.
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  • Resolving distributed knowledge.Thomas Ågotnes & Yì N. Wáng - 2017 - Artificial Intelligence 252 (C):1-21.
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  • Game Logic - An Overview.Marc Pauly & Rohit Parikh - 2003 - Studia Logica 75 (2):165-182.
    Game Logic is a modal logic which extends Propositional Dynamic Logic by generalising its semantics and adding a new operator to the language. The logic can be used to reason about determined 2-player games. We present an overview of meta-theoretic results regarding this logic, also covering the algebraic version of the logic known as Game Algebra.
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  • From Oughts to Goals: A Logic for Enkrasia.Dominik Klein & Alessandra Marra - 2020 - Studia Logica 108 (1):85-128.
    This paper focuses on the Enkratic principle of rationality, according to which rationality requires that if an agent sincerely and with conviction believes she ought to X, then X-ing is a goal in her plan. We analyze the logical structure of Enkrasia and its implications for deontic logic. To do so, we elaborate on the distinction between basic and derived oughts, and provide a multi-modal neighborhood logic with three characteristic operators: a non-normal operator for basic oughts, a non-normal operator for (...)
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  • A Propositional Dynamic Logic for Instantial Neighborhood Semantics.Johan van Benthem, Nick Bezhanishvili & Sebastian Enqvist - 2019 - Studia Logica 107 (4):719-751.
    We propose a new perspective on logics of computation by combining instantial neighborhood logic \ with bisimulation safe operations adapted from \. \ is a recent modal logic, based on an extended neighborhood semantics which permits quantification over individual neighborhoods plus their contents. This system has a natural interpretation as a logic of computation in open systems. Motivated by this interpretation, we show that a number of familiar program constructors can be adapted to instantial neighborhood semantics to preserve invariance for (...)
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  • Liquid Democracy: Potentials, Problems, and Perspectives.Christian Blum & Christina Isabel Zuber - 2015 - Journal of Political Philosophy 24 (2):162-182.
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  • Multiplex semantics for deontic logic.Lou Goble - 2000 - Nordic Journal of Philosophical Logic 5 (2):113-134.
    This multiplex semantics incorporates multiple relations of deontic accessibility or multiple preference rankings on alternative worlds to represent distinct normative standards. This provides a convenient framework for deontic logic that allows conflicts of obligation, due either to conflicts between normative standards or to incoherence within a single standard. With the multiplex structures, two general senses of "ought" may be distinguished, an indefinite sense under which something is obligatory when it is enjoined by some normative standard and a core sense for (...)
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  • Distributed knowledge.Floris Roelofsen - 2007 - Journal of Applied Non-Classical Logics 17 (2):255-273.
    This paper provides a complete characterization of epistemic models in which distributed knowledge complies with the principle of full communication (van der Hoek et al., 1999; Gerbrandy, 1999). It also introduces an extended notion of bisimulation and corresponding model comparison games that match the expressive power of distributed knowledge operators.
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  • On the Axiomatisation of Elgesem's Logic of Agency and Ability.Guido Governatori & Antonino Rotolo - 2005 - Journal of Philosophical Logic 34 (4):403-431.
    In this paper we show that the Hilbert system of agency and ability presented by Dag Elgesem is incomplete with respect to the intended semantics. We argue that completeness result may be easily regained. Finally, we shortly discuss some issues related to the philosophical intuition behind his approach. This is done by examining Elgesem's modal logic of agency and ability using semantics with different flavours.
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  • A New Game Equivalence, its Logic and Algebra.Sebastian Enqvist, Nick Bezhanishvili & Johan Benthem - 2019 - Journal of Philosophical Logic 48 (4):649-684.
    We present a new notion of game equivalence that captures basic powers of interacting players. We provide a representation theorem, a complete logic, and a new game algebra for basic powers. In doing so, we establish connections with imperfect information games and epistemic logic. We also identify some new open problems concerning logic and games.
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  • A Propositional Dynamic Logic for Instantial Neighborhood Semantics.Sebastian Enqvist, Nick Bezhanishvili & Johan Benthem - 2019 - Studia Logica 107 (4):719-751.
    We propose a new perspective on logics of computation by combining instantial neighborhood logic INL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {INL}$$\end{document} with bisimulation safe operations adapted from PDL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {PDL}$$\end{document}. INL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {INL}$$\end{document} is a recent modal logic, based on an extended neighborhood semantics which permits quantification over individual neighborhoods plus their contents. This system has a natural interpretation as a (...)
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  • A New Game Equivalence, its Logic and Algebra.Johan van Benthem, Nick Bezhanishvili & Sebastian Enqvist - 2019 - Journal of Philosophical Logic 48 (4):649-684.
    We present a new notion of game equivalence that captures basic powers of interacting players. We provide a representation theorem, a complete logic, and a new game algebra for basic powers. In doing so, we establish connections with imperfect information games and epistemic logic. We also identify some new open problems concerning logic and games.
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  • “That Will Do”: Logics of Deontic Necessity and Sufficiency.Frederik Van De Putte - 2017 - Erkenntnis 82 (3):473-511.
    We study a logic for deontic necessity and sufficiency, as originally proposed in van Benthem :36–41, 1979). Building on earlier work in modal logic, we provide a sound and complete axiomatization for it, consider some standard extensions, and study other important properties. After that, we compare this logic to the logic of “obligation as weakest permission” from Anglberger et al. :807–827, 2015).
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  • Preference Semantics for Deontic Logic - Part II: Multiplex Models.Lou Goble - 2004 - Logique Et Analyse 47.
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  • “That Will Do”: Logics of Deontic Necessity and Sufficiency.Frederik Putte - 2017 - Erkenntnis 82 (3):473-511.
    We study a logic for deontic necessity and sufficiency, as originally proposed in van Benthem :36–41, 1979). Building on earlier work in modal logic, we provide a sound and complete axiomatization for it, consider some standard extensions, and study other important properties. After that, we compare this logic to the logic of “obligation as weakest permission” from Anglberger et al. :807–827, 2015).
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  • Pooling Modalities and Pointwise Intersection: Axiomatization and Decidability.Frederik Van De Putte & Dominik Klein - 2020 - Studia Logica 109 (1):47-93.
    We establish completeness and the finite model property for logics featuring the pooling modalities that were introduced in Van De Putte and Klein. The definition of our canonical models combines standard techniques with a so-called “puzzle piece construction”, which we first illustrate informally. After that, we apply it to the weakest classical logics with pooling modalities and investigate the technique’s potential for the axiomatization of stronger logics, obtained by imposing well-known frame conditions on the models.
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  • Pointwise Intersection in Neighbourhood Modal Logic.Frederik van De Putte & Dominik Klein - 2018 - In Guram Bezhanishvili, Giovanna D'Agostino, George Metcalfe & Thomas Studer, Advances in Modal Logic, Vol. 12. College Publications. pp. 591-610.
    We study the logic of neighbourhood models with pointwise intersection, as a means to characterize multi-modal logics. Pointwise intersection takes us from a set of neighbourhood sets Ni (one for each member i of a set G used to interpret the modality □) to a new neighbourhood set NG, which in turn allows us to interpret the operator □G Here, X is in the neighbourhood for G if and only if X equals the intersection of some Y {Yi | Yi (...)
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