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40
Compositional Model Checking
, 1999
"... We describe a method for reducing the complexity of temporal logic model checking in systems composed of many parallel processes. The goal is to check properties of the components of a system and then deduce global properties from these local properties. The main difficulty with this type of approac ..."
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Cited by 2407 (62 self)
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We describe a method for reducing the complexity of temporal logic model checking in systems composed of many parallel processes. The goal is to check properties of the components of a system and then deduce global properties from these local properties. The main difficulty with this type of approach is that local properties are often not preserved at the global level. We present a general framework for using additional interface processes to model the environment for a component. These interface processes are typically much simpler than the full environment of the component. By composing a component with its interface processes and then checking properties of this composition, we can guarantee that these properties will be preserved at the global level. We give two example compositional systems based on the logic CTL*.
Belief, awareness, and limited reasoning
 ARTIFICIAL INTELLIGENCE
, 1988
"... Several new logics for belief and knowledge are introduced and studied, all of which have the property that agents are not logically omniscient. In particular, in these logics, the set of beliefs of an agent does not necessarily contain all valid formulas. Thus, these logics are more suitable than t ..."
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Cited by 120 (12 self)
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Several new logics for belief and knowledge are introduced and studied, all of which have the property that agents are not logically omniscient. In particular, in these logics, the set of beliefs of an agent does not necessarily contain all valid formulas. Thus, these logics are more suitable than traditional logics for modelling beliefs of humans (or machines) with limited reasoning capabilities. Our first logic is essentially an extension of Levesque's logic of implicit and explicit belief, where we extend to allow multiple agents and higherlevel belief (i.e., beliefs about beliefs). Our second logic deals explicitly with "awareness," where, roughly speaking, it is necessary to be aware of a concept before one can have beliefs about it. Our third logic gives a model of "local reasoning," where an agent is viewed as a "society of minds," each with its own cluster of beliefs, which may contradict each other.
Modal logic S4f and the minimal knowledge paradigm
 In Proceedings of the Third Conference on Theoretical Aspects of Reasoning about Knowledge (TARK92
, 1992
"... ..."
A New Combination Procedure for the Word Problem that Generalizes Fusion Decidability Results in Modal Logics
 In David A. Basin and Michaël Rusinowitch, editors, IJCAR ’04
, 2004
"... Previous results for combining decision procedures for the word problem in the nondisjoint case do not apply to equational theories induced by modal logicswhose combination is not disjoint since they share the theory of Boolean algebras. Conversely, decidability results for the fusion of mod ..."
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Cited by 13 (7 self)
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Previous results for combining decision procedures for the word problem in the nondisjoint case do not apply to equational theories induced by modal logicswhose combination is not disjoint since they share the theory of Boolean algebras. Conversely, decidability results for the fusion of modal logics are strongly tailored towards the special theories at hand, and thus do not generalize to other equational theories.
Monotonic Modal Logics
, 2003
"... Monotonic modal logics form a generalization of normal modal logics... ..."
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Cited by 11 (0 self)
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Monotonic modal logics form a generalization of normal modal logics...
Everything else being equal: A modal logic approach to ceteris paribus preferences
, 2007
"... The notion of “preference ” has circulated in many disciplines in the first half of the 20th century, especially in economics and social choice theory (cf. [34]). In logic, Halldén [9] initiated a field of research that was quickly championed by G. H. von Wright in [33], a book that is usually taken ..."
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Cited by 8 (3 self)
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The notion of “preference ” has circulated in many disciplines in the first half of the 20th century, especially in economics and social choice theory (cf. [34]). In logic, Halldén [9] initiated a field of research that was quickly championed by G. H. von Wright in [33], a book that is usually taken to be the seminal work in preference logic. The present paper presents a modal logic for the formalization of preferences as initiated by von Wright. Beside historical concerns, a logic of preference finds an independent modern interest in various (sub)disciplines of economics, social choice theory, computer science and philosophy, to name a few. For instance, it proved indispensable to investigate the logic of solution concepts of game theory such as backward induction and Nash equilibrium (see [30]). Our preference logic can define a strict global binary relation between propositions which has an essential ceteris paribus rider. We achieve the first features with what we call the basic preference language. We start with a reflexive and transitive accessibility relation ≤ over states, where accessible states are those that are at least as good as the present one. To reason about strict preferences, we take the strict subrelation of ≤
Nonmonotonic Reasoning is Sometimes Simpler!
, 1993
"... We establish the complexity of decision problems associated with the nonmonotonic modal logic S4. We prove that the problem of existence of an S4expansion for a given set A of premises is \Sigma P 2 complete. Similarly, we show that for a given formula ' and a set A of premises, it is \Sigma P ..."
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Cited by 8 (1 self)
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We establish the complexity of decision problems associated with the nonmonotonic modal logic S4. We prove that the problem of existence of an S4expansion for a given set A of premises is \Sigma P 2 complete. Similarly, we show that for a given formula ' and a set A of premises, it is \Sigma P 2  complete to decide whether ' belongs to at least one S4expansion for A, and it is \Pi P 2 complete to decide whether ' belongs to all S4expansions for A. This refutes a conjecture of Gottlob that these problems are PSPACEcomplete. An interesting aspect of these results is that reasoning (testing satisfiability and provability) in the monotonic modal logic S4 is PSPACEcomplete. To the best of our knowledge, the nonmonotonic logic S4 is the first example of a nonmonotonic formalism which is computationally easier than the monotonic logic that underlies it (assuming PSPACE does not collapse to \Sigma P 2 ). 1 Introduction First nonmonotonic logics were proposed in late 70s and e...
On logics with coimplication
 Journal of Philosophical Logic
, 1998
"... This paper investigates (modal) extensions of HeytingBrouwer logic, i.e., the logic which results when the dual of implication (alias coimplication) is added to the language of intuitionistic logic. We rst develop matrix as well as Kripke style semantics for those logics. Then, by extending the God ..."
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Cited by 7 (1 self)
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This paper investigates (modal) extensions of HeytingBrouwer logic, i.e., the logic which results when the dual of implication (alias coimplication) is added to the language of intuitionistic logic. We rst develop matrix as well as Kripke style semantics for those logics. Then, by extending the Godelembedding of intuitionistic logic into S4, itisshown that all (modal) extensions of HeytingBrouwer logic can be embedded into tense logics (with additional modal operators). An extension of the BlokEsakiaTheorem is proved for this embedding. 1
On canonical modal logics that are not elementarily determined. Logique et Analyse
, 2003
"... There exist modal logics that are validated by their canonical frames but are not sound and complete for any elementary class of frames. Continuum many such bimodal logics are exhibited, including one of each degree of unsolvability, and all with the finite model property. Monomodal examples are als ..."
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Cited by 6 (5 self)
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There exist modal logics that are validated by their canonical frames but are not sound and complete for any elementary class of frames. Continuum many such bimodal logics are exhibited, including one of each degree of unsolvability, and all with the finite model property. Monomodal examples are also constructed that extend K4 and are related to the proof of noncanonicity of the McKinsey axiom. We dedicate this paper to Max Cresswell, a pioneer in the study of canonicity, on the occasion of his 65th birthday. 1
Canonicity for Intensional Logics without Iterative Axioms
 Journal of Philosophical Logic
, 1996
"... DAVID LEWIS proved in 1974 that all logics without iterative axioms are weakly complete. In this paper we extend LEWIS's ideas and provide a proof that such logics are canonical and so strongly complete. This paper also discusses the differences between relational and neighborhood frame semantics an ..."
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Cited by 5 (3 self)
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DAVID LEWIS proved in 1974 that all logics without iterative axioms are weakly complete. In this paper we extend LEWIS's ideas and provide a proof that such logics are canonical and so strongly complete. This paper also discusses the differences between relational and neighborhood frame semantics and poses a number of open questions about the latter. Canonicity for Intensional Logics Without Iterative Axioms Timothy J. Surendonk May 13, 1996 Keywords: Canonicity, strong completeness, nonnormal modal logics, neighborhood frame semantics, noniterative logics. Abstract DAVID LEWIS proved in 1974 that all logics without iterative axioms are weakly complete. In this paper we extend LEWIS's ideas and provide a proof that such logics are canonical and so strongly complete. This paper also discusses the differences between relational and neighborhood frame semantics and poses a number of open questions about the latter. 1 Introduction In 1974 DAVID LEWIS [13] showed that every intension...