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A Computational Learning Semantics for Inductive Empirical Knowledge

In Alexandru Baltag & Sonja Smets (eds.), Johan van Benthem on Logic and Information Dynamics. Springer International Publishing. pp. 289-337 (2014)

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  1. The Geometry of Knowledge.Johan van Benthem & Darko Sarenac - unknown
    The most widely used attractive logical account of knowledge uses standard epistemic models, i.e., graphs whose edges are indistinguishability relations for agents. In this paper, we discuss more general topological models for a multi-agent epistemic language, whose main uses so far have been in reasoning about space. We show that this more geometrical perspective affords greater powers of distinction in the study of common knowledge, defining new collective agents, and merging information for groups of agents.
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  • Merging Frameworks for Interaction.Johan van Benthem Jelle Gerbrandy - unknown
    Many logical systems today describe intelligent interacting agents over time. Frameworks include Interpreted Systems (IS, Fagin et al. [8]), Epistemic-Temporal Logic (ETL, Parikh & Ramanujam [22]), STIT (Belnap et al. [5]), Process Algebra and Game Semantics (Abramsky [1]). This variety is an asset, as different modeling tools can be fine-tuned to specific applications. But it may also be an obstacle, when barriers between paradigms and schools go up. This paper takes a closer look at one particular interface, between two systems (...)
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  • A Brief History of Natural Logic.Johan van Benthem - unknown
    This paper is a brief history of natural logic at the interface of logic, linguistics, and nowadays also other disciplines. It merely summarizes some facts that deserve to be common knowledge.
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  • For Better or for Worse: Dynamic Logics of Preference.Johan van Benthem - unknown
    In the last few years, preference logic and in particular, the dynamic logic of preference change, has suddenly become a live topic in my Amsterdam and Stanford environments. At the request of the editors, this article explains how this interest came about, and what is happening. I mainly present a story around some recent dissertations and supporting papers, which are found in the references. There is no pretense at complete coverage of preference logic (for that, see Hanson 2001) or even (...)
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  • Inference, Promotion, and the Dynamics of Awareness.Johan van Benthem - unknown
    Classical epistemic logic describes implicit knowledge of agents about facts and knowledge of other agents, based on semantic information. The latter is produced by acts of observation or communication, that are described well by dynamic epistemic logics. What these logics do not describe, however, is how significant information is also produced by acts of inference – and key axioms of the system merely postulate “deductive closure”. In this paper, we take the view that all information is produced by acts, and (...)
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  • 'One is a Lonely Number': on the logic of communication.Johan van Benthem - unknown
    Logic is not just about single-agent notions like reasoning, or zero-agent notions like truth, but also about communication between two or more people. What we tell and ask each other can be just as 'logical' as what we infer in Olympic solitude. We show how such interactive phenomena can be studied systematically by merging epistemic and dynamic logic.
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  • The Stories of Logic and Information.Johan van Benthem, Maricarmen Martinez, David Israel & John Perry - unknown
    Information is a notion of wide use and great intuitive appeal, and hence, not surprisingly, different formal paradigms claim part of it, from Shannon channel theory to Kolmogorov complexity. Information is also a widely used term in logic, but a similar diversity repeats itself: there are several competing logical accounts of this notion, ranging from semantic to syntactic. In this chapter, we will discuss three major logical accounts of information.
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  • Preference logic, conditionals and solution concepts in games.Johan van Benthem - unknown
    Preference is a basic notion in human behaviour, underlying such varied phenomena as individual rationality in the philosophy of action and game theory, obligations in deontic logic (we should aim for the best of all possible worlds), or collective decisions in social choice theory. Also, in a more abstract sense, preference orderings are used in conditional logic or non-monotonic reasoning as a way of arranging worlds into more or less plausible ones. The field of preference logic (cf. Hansson [10]) studies (...)
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  • Comments On the Interpretation of Game Theory.Ariel Rubinstein - unknown
    The paper is a discussion of the interpretation of game theory. Game theory is viewed as an abstract inquiry into the concepts used in social reasoning when dealing with situations of conflict and not as an attempt to predict behavior. The first half of the paper..
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  • Constraints, Channels and the Flow of Information.Jon Barwise - 1993 - In Peter Aczel, David Israel, Yosuhiro Katagiri & Stanley Peters (eds.), Situation Theory and its Applications Vol. 3. CSLI Publications. pp. 3-27.
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  • Logics of Communication and Change. van Benthem, Johan, van Eijck, Jan & Kooi, Barteld - unknown
    Current dynamic epistemic logics for analyzing effects of informational events often become cumbersome and opaque when common knowledge is added for groups of agents. Still, postconditions involving common knowledge are essential to successful multi-agent communication. We propose new systems that extend the epistemic base language with a new notion of ‘relativized common knowledge’, in such a way that the resulting full dynamic logic of information flow allows for a compositional analysis of all epistemic postconditions via perspicuous ‘reduction axioms’. We also (...)
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  • Quantifiers and Working Memory.Jakub Szymanik & Marcin Zajenkowski - 2010 - In Maria Aloni & Katrin Schulz (eds.), Amsterdam Colloquium 2009, LNAI 6042. Springer.
    The paper presents a study examining the role of working<br>memory in quantifier verification. We created situations similar to the<br>span task to compare numerical quantifiers of low and high rank, parity<br>quantifiers and proportional quantifiers. The results enrich and support<br>the data obtained previously in and predictions drawn from a computational<br>model.
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  • A Note on some Neuroimaging Study of Natural Language Quantifiers Comprehension.Jakub Szymanik - 2007 - Neuropsychologia 45 (9):2158-2160.
    We discuss McMillan et al. (2005) paper devoted to study brain activity during comprehension of sentences with generalized quantifiers. According to the authors their results verify a particular computational model of natural language quantifier comprehension posited by several linguists and logicians (e. g. see van Benthem, 1986). We challenge this statement by invoking the computational difference between first-order quantifiers and divisibility quantifiers (e. g. see Mostowski, 1998). Moreover, we suggest other studies on quantifier comprehension, which can throw more light on (...)
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  • Quantifiers in TIME and SPACE. Computational Complexity of Generalized Quantifiers in Natural Language.Jakub Szymanik - 2009 - Dissertation, University of Amsterdam
    In the dissertation we study the complexity of generalized quantifiers in natural language. Our perspective is interdisciplinary: we combine philosophical insights with theoretical computer science, experimental cognitive science and linguistic theories. -/- In Chapter 1 we argue for identifying a part of meaning, the so-called referential meaning (model-checking), with algorithms. Moreover, we discuss the influence of computational complexity theory on cognitive tasks. We give some arguments to treat as cognitively tractable only those problems which can be computed in polynomial time. (...)
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  • Philosophical Explanations. [REVIEW]Robert Nozick - 1981 - Ethics 94 (2):326-327.
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  • Dynamics.Reinhard Muskens, Johan Van Benthem & Albert Visser - 1997 - In Johan Van Benthem & Alice Ter Meulen (eds.), Handbook of Logic and Language. Amsterdam: Elsevier. pp. 587-648.
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  • Pseudomonadic Algebras as Algebraic Models of Doxastic Modal Logic.Nick Bezhanishvili - 2002 - Mathematical Logic Quarterly 48 (4):624-636.
    We generalize the notion of a monadic algebra to that of a pseudomonadic algebra. In the same way as monadic algebras serve as algebraic models of epistemic modal system S5, pseudomonadic algebras serve as algebraic models of doxastic modal system KD45. The main results of the paper are: Characterization of subdirectly irreducible and simple pseudomonadic algebras, as well as Tokarz's proper filter algebras; Ordertopological representation of pseudomonadic algebras; Complete description of the lattice of subvarieties of the variety of pseudomonadic algebras.
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  • Logical Questions Concerning the $\mu$-Calculus: Interpolation, Lyndon and Los-Tarski.Giovanna D'agostino & Marco Hollenberg - 2000 - Journal of Symbolic Logic 65 (1):310-332.
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  • Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
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  • Assertion.Robert Stalnaker - 1978 - In Maite Ezcurdia & Robert J. Stainton (eds.), The Semantics-Pragmatics Boundary in Philosophy. Broadview Press. pp. 179.
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  • Deontic Logic.Paul McNamara - 2006 - In Dov Gabbay & John Woods (eds.), The Handbook of the History of Logic, vol. 7: Logic and the Modalities in the Twentieth Century. Elsevier Press. pp. 197-288.
    Overview of fundamental work in deontic logic.
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  • Undecidable Theories.Alfred Tarski, Andrzej Mostowski & Raphael M. Robinson - 1953 - Philosophy 30 (114):278-279.
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  • Logik der Forschung.Karl Popper - 1934 - Erkenntnis 5 (1):290-294.
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  • Simplicity, Truth, and Probability.Kevin T. Kelly - unknown
    Simplicity has long been recognized as an apparent mark of truth in science, but it is difficult to explain why simplicity should be accorded such weight. This chapter examines some standard, statistical explanations of the role of simplicity in scientific method and argues that none of them explains, without circularity, how a reliance on simplicity could be conducive to finding true models or theories. The discussion then turns to a less familiar approach that does explain, in a sense, the elusive (...)
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  • God, the Devil, and Gödel.Paul Benacerraf - 2003 - Etica E Politica 5 (1):1-15.
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  • Relations between the logic of theory change and nonmonotonic logic.David Makinson & Peter Gärdenfors - 1991 - In André Fuhrmann & Michael Morreau (eds.), The Logic of Theory Change. Springer. pp. 183--205.
    Examines the link between nonmonotonic inference relations and theory revision operations, focusing on the correspondence between abstract properties which each may satisfy.
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  • Elusive Knowledge.David Lewis - 2000 - In Sven Bernecker & Fred I. Dretske (eds.), Knowledge: Readings in Contemporary Epistemology. Oxford University Press.
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  • Een zogenaamde denkfout.Frank Veltman - unknown
    Psychological experirnents have repeatedly shown that in judging the likelihood of uncertain events people do not follow the principles of probability theory. A notorious example is given by the so called conjunction fallacy. In this paper I argue that this fallacy is not really a fallacy when it is analysed in the light of a dynamic theory of default reasoning. The question that immediately rises is whether the fact that this theory conforms better to the way people actually think provides (...)
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  • What is information?David J. Israel & John Perry - 1990 - In Philip P. Hanson (ed.), Information, Language and Cognition. University of British Columbia Press.
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  • A paradox of information.David Miller - 1966 - British Journal for the Philosophy of Science 17 (1):59-61.
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  • Bridges from Classical to Nonmonotonic Logic.David Makinson - 2008 - Studia Logica 89 (3):437-439.
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  • Information and Architecture.David Israel & John Perry - 1991 - In Jon Barwise, Jean Mark Gawron, Gordon Plotkin & Syun Tutiya (eds.), Situation Theory and Its Applications Vol. 2. Stanford: CSLI Publications. pp. 147-160.
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  • Bewirken.Franz von Kutschera - 1986 - Erkenntnis 24 (3):253 - 281.
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  • Moorean Phenomena in Epistemic Logic.Wesley H. Holliday & Thomas F. Icard - 2010 - In Lev Beklemishev, Valentin Goranko & Valentin Shehtman (eds.), Advances in Modal Logic 8. College Publications. pp. 178-199.
    A well-known open problem in epistemic logic is to give a syntactic characterization of the successful formulas. Semantically, a formula is successful if and only if for any pointed model where it is true, it remains true after deleting all points where the formula was false. The classic example of a formula that is not successful in this sense is the “Moore sentence” p ∧ ¬BOXp, read as “p is true but you do not know p.” Not only is the (...)
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  • Convention: A Philosophical Study.David K. Lewis - 1971 - Philosophy and Rhetoric 4 (2):137-138.
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  • Perspectival act utilitarianism.John Horty - unknown
    This paper works within a particular framework for reasoning about actions—sometimes known as the framework of “stit semantics”—originally due to Belnap and Perloff, based ultimately on the theory of indeterminism set out in Prior’s indeterministic tense logic, and developed in full detail by Belnap, Perloff, and Xu [3]. The issues I want to consider arise when certain normative, or decision theoretic, notions are introduced into this framework: here I will focus on the notion of a right action, and so on (...)
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  • Homotopy theoretic models of identity types.Steve Awodey & Michael A. Warren - unknown
    Quillen [17] introduced model categories as an abstract framework for homotopy theory which would apply to a wide range of mathematical settings. By all accounts this program has been a success and—as, e.g., the work of Voevodsky on the homotopy theory of schemes [15] or the work of Joyal [11, 12] and Lurie [13] on quasicategories seem to indicate—it will likely continue to facilitate mathematical advances. In this paper we present a novel connection between model categories and mathematical logic, inspired (...)
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  • Truth.J. L. Austin - 1950 - Aristotelian Society Supp 24 (1):111--29.
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  • Representation= grounded information.Mary-Anne Williams - 2008 - In Tu-Bao Ho & Zhi-Hua Zhou (eds.), Pricai 2008: Trends in Artificial Intelligence. Springer. pp. 473--484.
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  • Assertion.Robert Stalnaker - 1978 - Syntax and Semantics (New York Academic Press) 9:315-332.
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  • Logics of Time and Computation.Robert Goldblatt - 1990 - Studia Logica 49 (2):284-286.
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  • Synchronic information, knowledge and common knowledge in extensive games.Giacomo Bonanno - 1999 - Research in Economics 53 (1):77-99.
    Restricting attention to the class of extensive games defined by von Neumann and Morgenstern with the added assumption of perfect recall, we specify the information of each player at each node of the game-tree in a way which is coherent with the original information structure of the extensive form. We show that this approach provides a framework for a formal and rigorous treatment of questions of knowledge and common knowledge at every node of the tree. We construct a particular information (...)
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  • Relevant and substructural logics.Greg Restall - unknown
    This essay is structured around the bifurcation between proofs and models: The first section discusses Proof Theory of relevant and substructural logics, and the second covers the Model Theory of these logics. This order is a natural one for a history of relevant and substructural logics, because much of the initial work — especially in the Anderson–Belnap tradition of relevant logics — started by developing proof theory. The model theory of relevant logic came some time later. As we will see, (...)
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  • How to make our ideas clear.C. S. Peirce - 1878 - Popular Science Monthly 12 (Jan.):286-302.
    This is one of the seminal articles of the pragmatist tradition where C.S. Peirce sets out his doctrine of doubt and belief --and their relationship to inquiry and clarity of our concepts. Originally published in the Popular Science Monthly; and widely available in reprints and collections of Peirce's writings.
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  • Direct reference and propositional attitudes.Scott Soames - 1989 - In John Perry, J. Almog & Howard K. Wettstein (eds.), Themes From Kaplan. Oxford University Press. pp. 393--419.
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  • Philosophical Explanations.Robert Nozick - 1981 - Mind 93 (371):450-455.
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  • Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games.Reinhard Selten - 1975 - International Journal of Game Theory 4:25-55.
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  • The Will to Believe.W. James - 1896 - Philosophical Review 6:88.
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  • A Theory of Truth and Semantic Representation.Hans Kamp - 1981 - In P. Portner & B. H. Partee (eds.), Formal Semantics - the Essential Readings. Blackwell. pp. 189--222.
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  • Memory and perfect recall in extensive games.Giacomo Bonanno - 2004 - Games and Economic Behavior 47 (2):237-256.
    The notion of perfect recall in extensive games was introduced by Kuhn (1953), who interpreted it as "equivalent to the assertion that each player is allowed by the rules of the game to remember everything he knew at previous moves and all of his choices at those moves''. We provide a characterization and axiomatization of perfect recall based on two notions of memory: (1) memory of past knowledge and (2) memory of past actions.
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