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59
Logic in Computer Science: Modelling and Reasoning about Systems
, 1999
"... ion. ACM Transactions on Programming Languages and Systems, 16(5):15121542, September 1994. Bibliography 401 [Che80] B. F. Chellas. Modal Logic  an Introduction. Cambridge University Press, 1980. [Dam96] D. R. Dams. Abstract Interpretation and Partition Refinement for Model Checking. PhD thesi ..."
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Cited by 245 (8 self)
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ion. ACM Transactions on Programming Languages and Systems, 16(5):15121542, September 1994. Bibliography 401 [Che80] B. F. Chellas. Modal Logic  an Introduction. Cambridge University Press, 1980. [Dam96] D. R. Dams. Abstract Interpretation and Partition Refinement for Model Checking. PhD thesis, Institute for Programming research and Algorithmics. Eindhoven University of Technology, July 1996. [Dij76] E. W. Dijkstra. A Discipline of Programming. Prentice Hall, 1976. [DP96] R. Davies and F. Pfenning. A Modal Analysis of Staged Computation. In 23rd Annual ACM Symposium on Principles of Programming Languages. ACM Press, January 1996. [EN94] R. Elmasri and S. B. Navathe. Fundamentals of Database Systems. Benjamin/Cummings, 1994. [FHMV95] Ronald Fagin, Joseph Y. Halpern, Yoram Moses, and Moshe Y. Vardi. Reasoning about Knowledge. MIT Press, Cambridge, 1995. [Fit93] M. Fitting. Basic modal logic. In D. Gabbay, C. Hogger, and J. Robinson, editors, Handbook of Logic in Artificial In...
Towards a Logic of Rational Agency
, 2003
"... Rational agents are important objects of study in several research communities, including economics, philosophy, cognitive science, and most recently computer science and artificial intelligence. Crudely, a rational agent is an entity that is capable of acting on its environment, and which chooses t ..."
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Cited by 53 (6 self)
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Rational agents are important objects of study in several research communities, including economics, philosophy, cognitive science, and most recently computer science and artificial intelligence. Crudely, a rational agent is an entity that is capable of acting on its environment, and which chooses to act in such a way as to further its own best interests. There has recently been much interest in the use of mathematical logic for developing formal theories of such agents. Such theories view agents as practical reasoning systems, deciding moment by moment which action to perform nexi, given the beliefs they have about the world and their desires with respect to how they would like the world to be. In this article, we survey the state of the art in developing logical theories of rational agency. Following a discussion on the dimensions along which such theories can vary, we briefly survey the logical tools available in order to construct such theories. We then review and critically assess three of the best known theories of rational agency: Cohen and Levesque's intention logic, Rao and Georgeff's BDI logics, and the KARO framework of Meyer et al. We then discuss the various roles that such logics can play in helping us to engineer rational agents, and conclude with a discussion of open problems.
Formalizing action and change in modal logic I: the frame problem
, 1999
"... We present the basic framework of a logic of actions and plans defined in terms of modal logic combined with a notion of dependence. The latter is used as a weak causal connection between actions and literals. In this paper we focus on the frame problem and demonstrate how it can be solved in our fr ..."
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Cited by 47 (15 self)
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We present the basic framework of a logic of actions and plans defined in terms of modal logic combined with a notion of dependence. The latter is used as a weak causal connection between actions and literals. In this paper we focus on the frame problem and demonstrate how it can be solved in our framework in a simple and monotonic way. We give the semantics, and associate an axiomatics and a decision procedure to it. The decision procedure is based on a sound and complete tableau method with single step rules to treat dependence. We show how it can be used to generate plans. Our solution is formally assessed by a translation of Gelfond and Lifschitz' logic A. We briefly sketch the second part of the paper, showing how we can go beyond A by some examples involving nondeterminism and ramifications.
Coalgebras and Modal Logic
 Coalgebraic Methods in Computer Science, Volume 33 in Electronic Notes in Theoretical Computer Science
, 2000
"... Coalgebras are of growing importance in theoretical computer science. To develop languages for them is significant for the specification and verification of systems modelled with them. Modal logic has proved to be suitable for this purpose. So far, most approaches have presented a language to descri ..."
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Cited by 33 (0 self)
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Coalgebras are of growing importance in theoretical computer science. To develop languages for them is significant for the specification and verification of systems modelled with them. Modal logic has proved to be suitable for this purpose. So far, most approaches have presented a language to describe only deterministic coalgebras. The present paper introduces a generalization that also covers nondeterministic systems. As a special case, we obtain the "usual" modal logic for Kripkestructures. Models for our modal language L F are Fcoalgebras where the functor F is inductively constructed from constant sets and the identity functor using product, coproduct, exponentiation, and the power set functor. We define a language L F and show that it embeds into L F . We prove that, for imagefinite coalgebras, L F is expressive enough to distinguish elements up to bisimilarity and therefore L F does so, too. Moreover, we also give a complete calculus for L F in case the constants...
A Finite Model Construction For Coalgebraic Modal Logic
"... In recent years, a tight connection has emerged between modal logic on the one hand and coalgebras, understood as generic transition systems, on the other hand. Here, we prove that (finitary) coalgebraic modal logic has the finite model property. This fact not only reproves known completeness result ..."
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Cited by 24 (16 self)
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In recent years, a tight connection has emerged between modal logic on the one hand and coalgebras, understood as generic transition systems, on the other hand. Here, we prove that (finitary) coalgebraic modal logic has the finite model property. This fact not only reproves known completeness results for coalgebraic modal logic, which we push further by establishing that every coalgebraic modal logic admits a complete axiomatization of rank 1; it also enables us to establish a generic decidability result and a first complexity bound. Examples covered by these general results include, besides standard HennessyMilner logic, graded modal logic and probabilistic modal logic.
A Sahlqvist theorem for distributive modal logic
 Annals of Pure and Applied Logic 131, Issues
, 2002
"... Dedicated to Bjarni Jónsson In this paper we consider distributive modal logic, a setting in which we may add modalities, such as classical types of modalities as well as weak forms of negation, to the fragment of classical propositional logic given by conjunction, disjunction, true, and false. For ..."
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Cited by 23 (9 self)
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Dedicated to Bjarni Jónsson In this paper we consider distributive modal logic, a setting in which we may add modalities, such as classical types of modalities as well as weak forms of negation, to the fragment of classical propositional logic given by conjunction, disjunction, true, and false. For these logics we define both algebraic semantics, in the form of distributive modal algebras, and relational semantics, in the form of ordered Kripke structures. The main contributions of this paper lie in extending the notion of Sahlqvist axioms to our generalized setting and proving both a correspondence and a canonicity result for distributive modal logics axiomatized by Sahlqvist axioms. Our proof of the correspondence result relies on a reduction to the classical case, but our canonicity proof departs from the traditional style and uses the newly extended algebraic theory of canonical extensions.
A Computationally Grounded Logic of Visibility, Perception, and Knowledge
, 2001
"... VSK logic is a family of multimodal logics for reasoning about the information properties of computational agents situated in some environment. Using VSK logic, we can represent what is objectively true of the environment, the information that is visible,orknowable about the environment, informat ..."
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Cited by 17 (1 self)
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VSK logic is a family of multimodal logics for reasoning about the information properties of computational agents situated in some environment. Using VSK logic, we can represent what is objectively true of the environment, the information that is visible,orknowable about the environment, information the agent perceives of the environment, and finally, information the agent actually knows about the environment. The semantics of VSK logic are given in terms of a general, automatalike model of agents. In this paper, we prove completeness for an axiomatisation of VSK logic, and present correspondence results for a number of VSK interaction axioms in terms of the architectural properties of the agent that they represent. The completeness proof is novel in that we are able to prove completeness with respect to the automatalike semantics. In this sense, VSK logic is said to be computationally grounded. We give an example to illustrate the formalism, and present conclusions and issues for further work.
A Logic for Reasoning about Upper Probabilities
, 2002
"... We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization for the logic, and show that the satisfiability problem is ..."
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Cited by 16 (4 self)
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We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization for the logic, and show that the satisfiability problem is NPcomplete, no harder than satisfiability for propositional logic.
A Logical and Computational Theory of Located Resource
, 2008
"... Experience of practical systems modelling suggests that the key conceptual components of a model of a system are processes, resources, locations, and environment. In recent work, we have given a processtheoretic account of this view in which resources as well as processes are firstclass citizens. ..."
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Cited by 13 (9 self)
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Experience of practical systems modelling suggests that the key conceptual components of a model of a system are processes, resources, locations, and environment. In recent work, we have given a processtheoretic account of this view in which resources as well as processes are firstclass citizens. This process calculus, SCRP, captures the structural aspects of the semantics of the Demos2k modelling tool. Demos2k represents environment stochastically using a wide range of probability distributions and queuelike data structures. Associated with SCRP is a (bunched) modal logic, MBI, which combines the usual additive connectives of HennessyMilner logic with their multiplicative counterparts. In this paper, we complete our conceptual framework by adding to SCRP and MBI an account of a notion of location that is simple, yet sufficiently expressive to capture naturally a wide range of forms of location, both spatial and logical. We also provide a description of an extension of the Demos2k tool to incorporate this notion of location. 1
Counterfactuals and Updates as Inverse Modalities
 Journal of Logic, Language and Information
, 1997
"... . We point out a simple but hitherto ignored link between the theory of updates and counterfactuals and classical modal logic: update is a classical existential modality, counterfactual is a classical universal modality, and the accessibility relations corresponding to these modalities are inverses. ..."
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Cited by 13 (1 self)
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. We point out a simple but hitherto ignored link between the theory of updates and counterfactuals and classical modal logic: update is a classical existential modality, counterfactual is a classical universal modality, and the accessibility relations corresponding to these modalities are inverses. The Ramsey Rule (often thought esoteric) is simply an axiomatisation of this inverse relationship. We use this fact to translate between postulates for updates and postulates for counterfactuals. Thus, Katsuno/Mendelzon's postulates U1U8 are translated into counterfactual postulates C1C8 (table VII), and many of the familiar counterfactual postulates are translated into postulates for updates (table VIII). Our conclusions are summarised in table V. We also present a syntactic condition which is sufficient to guarantee that a translation from update to counterfactual (or vice versa) is possible. 1. Introduction Background. An intuitive connection between theory change and counterfactuals...