68 found
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  1.  33
    Johan Van Benthem, Patrick Girard & Olivier Roy (2009). Everything Else Being Equal: A Modal Logic for Ceteris Paribus Preferences. Journal of Philosophical Logic 38 (1):83 - 125.
    This paper presents a new modal logic for ceteris paribus preferences understood in the sense of "all other things being equal". This reading goes back to the seminal work of Von Wright in the early 1960's and has returned in computer science in the 1990' s and in more abstract "dependency logics" today. We show how it differs from ceteris paribus as "all other things being normal", which is used in contexts with preference defeaters. We provide a semantic analysis and (...)
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  2.  52
    Johan Van Benthem (2009). The Information in Intuitionistic Logic. Synthese 167 (2):251 - 270.
    Issues about information spring up wherever one scratches the surface of logic. Here is a case that raises delicate issues of 'factual' versus 'procedural' information, or 'statics' versus 'dynamics'. What does intuitionistic logic, perhaps the earliest source of informational and procedural thinking in contemporary logic, really tell us about information? How does its view relate to its 'cousin' epistemic logic? We discuss connections between intuitionistic models and recent protocol models for dynamic-epistemic logic, as well as more general issues that emerge.
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  3.  3
    Hajnal Andréka, István Németi & Johan van Benthem (1998). Modal Languages and Bounded Fragments of Predicate Logic. Journal of Philosophical Logic 27 (3):217 - 274.
  4.  22
    J. Benthem & E. Pacuit (2011). Dynamic Logics of Evidence-Based Beliefs. 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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  5. Johan Benthem (1984). Possible Worlds Semantics: A Research Program That Cannot Fail? Studia Logica 43 (4):379 - 393.
    Providing a possible worlds semantics for a logic involves choosing a class of possible worlds models, and setting up a truth definition connecting formulas of the logic with statements about these models. This scheme is so flexible that a danger arises: perhaps, any (reasonable) logic whatsoever can be modelled in this way. Thus, the enterprise would lose its essential tension. Fortunately, it may be shown that the so-called incompleteness-examples from modal logic resist possible worlds modelling, even in the above wider (...)
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  6.  6
    Johan Van Benthem, Jelle Gerbrandy, Tomohiro Hoshi & Eric Pacuit (2009). Merging Frameworks for Interaction. Journal of Philosophical Logic 38 (5):491 - 526.
    A variety of logical frameworks have been developed to study rational agents interacting over time. This paper takes a closer look at one particular interface, between two systems that both address the dynamics of knowledge and information flow. The first is Epistemic Temporal Logic (ETL) which uses linear or branching time models with added epistemic structure induced by agents' different capabilities for observing events. The second framework is Dynamic Epistemic Logic (DEL) that describes interactive processes in terms of epistemic event (...)
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  7.  35
    Johan Benthem, Davide Grossi & Fenrong Liu (2014). Priority Structures in Deontic Logic. Theoria 80 (2):116-152.
    This article proposes a systematic application of recent developments in the logic of preference to a number of topics in deontic logic. The key junction is the well-known Hansson conditional for dyadic obligations. These conditionals are generalized by pairing them with reasoning about syntactic priority structures. The resulting two-level approach to obligations is tested first against standard scenarios of contrary-to-duty obligations, leading also to a generalization for the Kanger-Anderson reduction of deontic logic. Next, the priority framework is applied to model (...)
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  8.  25
    Johan Benthem (1989). Polyadic Quantifiers. Linguistics and Philosophy 12 (4):437 - 464.
  9.  5
    Johan Van Benthem (2004). What One May Come to Know. Analysis 64 (2):95 - 105.
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  10.  17
    Johan Benthem (1982). The Logical Study of Science. Synthese 51 (3):431 - 472.
    The relation between logic and philosophy of science, often taken for granted, is in fact problematic. Although current fashionable criticisms of the usefulness of logic are usually mistaken, there are indeed difficulties which should be taken seriously — having to do, amongst other things, with different scientific mentalities in the two disciplines (section 1). Nevertheless, logic is, or should be, a vital part of the theory of science. To make this clear, the bulk of this paper is devoted to the (...)
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  11.  8
    Johan Van Benthem (2005). Minimal Predicates. Fixed-Points, and Definability. Journal of Symbolic Logic 70 (3):696 - 712.
    Minimal predicates P satisfying a given first-order description ϕ(P) occur widely in mathematical logic and computer science. We give an explicit first-order syntax for special first-order 'PIA conditions' ϕ(P) which quarantees unique existence of such minimal predicates. Our main technical result is a preservation theorem showing PIA-conditions to be expressively complete for all those first-order formulas that are preserved under a natural model-theoretic operation of 'predicate intersection'. Next, we show how iterated predicate minimization on PIA-conditions yields a language MIN(FO) equal (...)
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  12. Jon Barwise & Johan van Benthem (1999). Interpolation, Preservation, and Pebble Games. Journal of Symbolic Logic 64 (2):881 - 903.
    Preservation and interpolation results are obtained for L ∞ω and sublogics $\mathscr{L} \subseteq L_{\infty\omega}$ such that equivalence in L can be characterized by suitable back-and-forth conditions on sets of partial isomorphisms.
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  13.  11
    Johan Benthem, Nick Bezhanishvili & Ian Hodkinson (2012). Sahlqvist Correspondence for Modal Mu-Calculus. Studia Logica 100 (1-2):31-60.
    We define analogues of modal Sahlqvist formulas for the modal mu-calculus, and prove a correspondence theorem for them.
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  14.  21
    J. F. A. K. Van Benthem & W. J. Blok (1978). Transitivity Follows From Dummett's Axiom. Theoria 44 (2):117-118.
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  15.  9
    J. F. A. K. Benthem (1979). Critical Notice. Synthese 40 (2):353-373.
    Gabbay has gathered an enormous amount of results; some of them important and novel, others important but already known, many rather routine, however. The organization of this material shows grave defects, both in the exposition and in its logical structure. Intensional logic appears as a vast collection of (often duplicated) loosely connected results. This may be a true reflection of the present state of the subject, but it does not contribute to a better understanding of it, let alone advance it.
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  16.  14
    Johan Van Benthem (1984). Questions About Quantifiers. Journal of Symbolic Logic 49 (2):443 - 466.
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  17.  9
    Johan Van Benthem (2006). Modal Frame Correspondences and Fixed-Points. Studia Logica 83 (1/3):133 - 155.
    Taking Löb's Axiom in modal provability logic as a running thread, we discuss some general methods for extending modal frame correspondences, mainly by adding fixed-point operators to modal languages as well as their correspondence languages. Our suggestions are backed up by some new results -- while we also refer to relevant work by earlier authors. But our main aim is advertizing the perspectives, showing how modal languages with fixed-point operators are a natural medium to work with.
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  18.  31
    Johan Benthem (1985). The Variety of Consequence, According to Bolzano. Studia Logica 44 (4):389 - 403.
    Contemporary historians of logic tend to credit Bernard Bolzano with the invention of the semantic notion, of consequence, a full century before Tarski. Nevertheless, Bolzano's work played no significant rôle in the genesis of modern logical semantics. The purpose of this paper is to point out three highly original, and still quite relevant themes in Bolzano's work, being a systematic study of possible types of inference, of consistency, as well as their meta-theory. There are certain analogies with Tarski's concerns here, (...)
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  19.  8
    Johan van Benthem, Jelle Gerbrandy & Barteld Kooi (2009). Dynamic Update with Probabilities. Studia Logica 93 (1):67 - 96.
    Current dynamic-epistemic logics model different types of information change in multi-agent scenarios. We generalize these logics to a probabilistic setting, obtaining a calculus for multi-agent update with three natural slots: prior probability on states, occurrence probabilities in the relevant process taking place, and observation probabilities of events. To match this update mechanism, we present a complete dynamic logic of information change with a probabilistic character. The completeness proof follows a compositional methodology that applies to a much larger class of dynamic-probabilistic (...)
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  20.  18
    Johan Van Benthem (2006). Epistemic Logic and Epistemology: The State of Their Affairs. Philosophical Studies 128 (1):49 - 76.
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  21.  23
    Johan Benthem & Ştefan Minică (2012). Toward a Dynamic Logic of Questions. Journal of Philosophical Logic 41 (4):633 - 669.
    Questions are triggers for explicit events of 'issue management'. We give a complete logic in dynamic-epistemic style for events of raising, refining, and resolving an issue, all in the presence of information flow through observation or communication. We explore extensions of the framework to multiagent scenarios and long-term temporal protocols. We sketch a comparison with some alternative accounts.
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  22.  3
    Johan van Benthem & Fernando R. Velázquez-Quesada (2010). The Dynamics of Awareness. Synthese 177 (S1):5 - 27.
    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 hence (...)
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  23.  15
    J. F. A. K. Benthem (1980). Some Kinds of Modal Completeness. Studia Logica 39 (2-3):125 - 141.
    In the modal literature various notions of completeness have been studied for normal modal logics. Four of these are defined here, viz. (plain) completeness, first-order completeness, canonicity and possession of the finite model property — and their connections are studied. Up to one important exception, all possible inclusion relations are either proved or disproved. Hopefully, this helps to establish some order in the jungle of concepts concerning modal logics. In the course of the exposition, the interesting properties of first-order definability (...)
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  24.  18
    Johan Van Benthem (1984). Analytic/Synthetic: Sharpening a Philosophical Tool. Theoria 50 (2-3):106-137.
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  25.  14
    Johan Van Benthem, Sujata Ghosh & Fenrong Liu (2008). Modelling Simultaneous Games in Dynamic Logic. Synthese 165 (2):247 - 268.
    We make a proposal for formalizing simultaneous games at the abstraction level of player's powers, combining ideas from dynamic logic of sequential games and concurrent dynamic logic. We prove completeness for a new system of 'concurrent game logic' CDGL with respect to finite non-determined games. We also show how this system raises new mathematical issues, and throws light on branching quantifiers and independence-friendly evaluation games for first-order logic.
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  26.  16
    Johan Benthem (2012). The Logic of Empirical Theories Revisited. Synthese 186 (3):775 - 792.
    Logic and philosophy of science share a long history, though contacts have gone through ups and downs. This paper is a brief survey of some major themes in logical studies of empirical theories, including links to computer science and current studies of rational agency. The survey has no new results: we just try to make some things into common knowledge.
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  27.  18
    Johan Van Benthem (2011). Logic in a Social Setting. Episteme 8 (3):227-247.
    Taking Backward Induction as its running example, this paper explores avenues for a logic of information-driven social action. We use recent results on limit phenomena in knowledge updating and belief revision, procedural rationality, and a ‘Theory of Play’ analyzing how games are played by different agents.
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  28.  13
    Johan Benthem (1991). Language in Action. Journal of Philosophical Logic 20 (3):225 - 263.
    A number of general points behind the story of this paper may be worth setting out separately, now that we have come to the end.There is perhaps one obvious omission to be addressed right away. Although the word “information” has occurred throughout this paper, it must have struck the reader that we have had nothing to say on what information is. In this respect, our theories may be like those in physics: which do not explain what “energy” is (a notion (...)
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  29.  27
    J. F. A. K. Benthem (1974). Hintikka on Analyticity. Journal of Philosophical Logic 3 (4):419 - 431.
  30.  18
    J. F. A. K. Benthem (1979). What is Dialectical Logic? Erkenntnis 14 (3):333 - 347.
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  31.  25
    Johan Benthem (1987). Meaning: Interpretation and Inference. Synthese 73 (3):451 - 470.
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  32.  14
    Johan Benthem (1984). Foundations of Conditional Logic. Journal of Philosophical Logic 13 (3):303 - 349.
  33.  8
    Johan Benthem (1990). Categorial Grammar and Type Theory. Journal of Philosophical Logic 19 (2):115 - 168.
  34.  12
    J. F. A. K. Benthem (1978). Two Simple Incomplete Modal Logics. Theoria 44 (1):25-37.
  35.  12
    J. F. A. K. Benthem (1978). Ramsey Eliminability. Studia Logica 37 (4):321 - 336.
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  36.  15
    J. F. A. K. Van Benthem (1979). Syntactic Aspects of Modal Incompleteness Theorems. Theoria 45 (2):63-77.
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  37.  17
    J. F. A. K. Benthem (1978). Four Paradoxes. Journal of Philosophical Logic 7 (1):49 - 72.
  38.  10
    Johan Benthem & Sonja Smets (2012). New Logical Perspectives on Physics. Synthese 186 (3):615 - 617.
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  39.  2
    Johan Van Benthem & David Pearce (1984). A Mathematical Characterization of Interpretation Between Theories. Studia Logica 43 (3):295 - 303.
    Of the various notions of reduction in the logical literature, relative interpretability in the sense of Tarski et al. [6] appears to be the central one. In the present note, this syntactic notion is characterized semantically, through the existence of a suitable reduction functor on models. The latter mathematical condition itself suggests a natural generalization, whose syntactic equivalent turns out to be a notion of interpretability quite close to that of Ershov [1], Szczerba [5] and Gaifman [2].
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  40.  8
    J. F. A. K. Van Benthem (1979). Canonical Modal Logics and Ultrafilter Extensions. Journal of Symbolic Logic 44 (1):1 - 8.
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  41.  10
    Johan Van Benthem (1993). Modelling the Kinematics of Meaning. Proceedings of the Aristotelian Society 93:105 - 122.
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  42.  15
    Johan Benthem (1985). Situations and Inference. Linguistics and Philosophy 8 (1):3 - 8.
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  43.  2
    J. F. A. K. Van Benthem (1975). A Note on Modal Formulae and Relational Properties. Journal of Symbolic Logic 40 (1):55 - 58.
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  44.  2
    J. F. A. K. Van Benthem (1976). Modal Reduction Principles. Journal of Symbolic Logic 41 (2):301 - 312.
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  45.  8
    Johan Van Benthem (2008). The Many Faces of Interpolation. Synthese 164 (3):451 - 460.
    We present a number of, somewhat unusual, ways of describing what Craig's interpolation theorem achieves, and use them to identify some open problems and further directions.
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  46. J. Benthem (2000). Information Transfer Across Chu Spaces. Logic Journal of the IGPL 8 (6):719-731.
    Chu spaces are a new model for information structure and mathematical structure in general. Their properties are usually developed as a form of category theory. In this note, we show how they may also be viewed as models for a two-sorted first-order language, and we determine the exact flow of information across the natural Chu transforms. Our analysis is akin to that of process graphs via bisimulation and modal formulas.
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  47.  3
    Johan Van Benthem (1986). Review: G. E. Hughes, M. J. Cresswell, A Companion to Modal Logic. [REVIEW] Journal of Symbolic Logic 51 (3):824-826.
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  48.  7
    J. Van Benthem, G. Bezhanishvili, B. Ten Cate & D. Sarenac (2006). Multimodal Logics of Products of Topologies. Studia Logica 84 (3):369 - 392.
    We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion ${\bf S4}\oplus {\bf S4}$ . We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies. We prove that both of these logics are complete for the product of rational numbers ${\Bbb Q}\times {\Bbb Q}$ (...)
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  49.  5
    Johan Van Benthem (2003). Logic Games Are Complete for Game Logics. Studia Logica 75 (2):183 - 203.
    Game logics describe general games through powers of players for forcing outcomes. In particular, they encode an algebra of sequential game operations such as choice, dual and composition. Logic games are special games for specific purposes such as proof or semantical evaluation for first-order or modal languages. We show that the general algebra of game operations coincides with that over just logical evaluation games, whence the latter are quite general after all. The main tool in proving this is a representation (...)
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  50.  5
    Johan Van Benthem (1983). Logical Semantics as an Empirical Science. Studia Logica 42 (2/3):299 - 313.
    Exact philosophy consists of various disciplines scattered and separated. Formal semantics and philosophy of science are good examples of two such disciplines. The aim of this paper is to show that there is possible to find some integrating bridge topics between the two fields, and to show how insights from the one are illuminating and suggestive in the other.
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