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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*.
Some philosophical problems from the standpoint of artificial intelligence
 AI, IN MACHINE INTELLIGENCE 4, MELTZER AND MICHIE (EDS
, 1969
"... ..."
A Propositional Modal Logic of Time Intervals
 Journal of the ACM
, 1996
"... : In certain areas of artificial intelligence there is need to represent continuous change and to make statements that are interpreted with respect to time intervals rather than time points. To this end we develop a modal temporal logic based on time intervals, a logic which can be viewed as a gener ..."
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Cited by 119 (2 self)
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: In certain areas of artificial intelligence there is need to represent continuous change and to make statements that are interpreted with respect to time intervals rather than time points. To this end we develop a modal temporal logic based on time intervals, a logic which can be viewed as a generalization of pointbased modal temporal logic. We discuss related logics, give an intuitive presentation of the new logic, and define its formal syntax and semantics. We make no assumption about the underlying nature of time, allowing it to be discrete (such as the natural numbers) or continuous (such as the rationals or the reals), linear or branching, complete (such as the reals) or not (such as the rationals). We show, however, that there are formulas in the logic that allow us to distinguish all these situations. We also give a translation of our logic into firstorder logic, which allows us to apply some results on firstorder logic to our modal one. Finally, we consider the difficulty o...
Hybrid Logics: Characterization, Interpolation and Complexity
 Journal of Symbolic Logic
, 1999
"... Hybrid languages are expansions of propositional modal languages which can refer to (or even quantify over) worlds. The use of strong hybrid languages dates back to at least [Pri67], but recent work (for example [BS98, BT98a, BT99]) has focussed on a more constrained system called H(#; @). We sho ..."
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Cited by 100 (35 self)
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Hybrid languages are expansions of propositional modal languages which can refer to (or even quantify over) worlds. The use of strong hybrid languages dates back to at least [Pri67], but recent work (for example [BS98, BT98a, BT99]) has focussed on a more constrained system called H(#; @). We show in detail that H(#; @) is modally natural. We begin by studying its expressivity, and provide model theoretic characterizations (via a restricted notion of EhrenfeuchtFrasse game, and an enriched notion of bisimulation) and a syntactic characterization (in terms of bounded formulas). The key result to emerge is that H(#; @) corresponds to the fragment of rstorder logic which is invariant for generated submodels. We then show that H(#; @) enjoys (strong) interpolation, provide counterexamples for its nite variable fragments, and show that weak interpolation holds for the sublanguage H(@). Finally, we provide complexity results for H(@) and other fragments and variants, and sh...
Strategies for Temporal Resolution
, 1995
"... Verifying that a temporal logic specification satisfies a temporal property requires some form of theorem proving. However, although proof procedures exist for such logics, many are either unsuitable for automatic implementation or only deal with small fragments of the logic. In this thesis the algo ..."
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Cited by 93 (42 self)
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Verifying that a temporal logic specification satisfies a temporal property requires some form of theorem proving. However, although proof procedures exist for such logics, many are either unsuitable for automatic implementation or only deal with small fragments of the logic. In this thesis the algorithms for, and strategies to guide, a fully automated temporal resolution theorem prover are given, proved correct and evaluated. An approach to applying resolution, a proof method for classical logics suited to mechanisation, to temporal logics has been developed by Fisher. The method involves translation to a normal form, classical style resolution within states and temporal resolution over states. It has only one temporal resolution rule and is therefore particularly suitable as the basis of an automated temporal resolution theorem prover. As the application of the temporal resolution rule is the most costly part of the method, involving search amongst graphs, different algorithms on w...
Internalizing Labelled Deduction
 Journal of Logic and Computation
, 2000
"... This paper shows how to internalize the Kripke satisfaction denition using the basic hybrid language, and explores the proof theoretic consequences of doing so. As we shall see, the basic hybrid language enables us to transfer classic Gabbaystyle labelled deduction methods from the metalanguage to ..."
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Cited by 74 (20 self)
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This paper shows how to internalize the Kripke satisfaction denition using the basic hybrid language, and explores the proof theoretic consequences of doing so. As we shall see, the basic hybrid language enables us to transfer classic Gabbaystyle labelled deduction methods from the metalanguage to the object language, and to handle labelling discipline logically. This internalized approach to labelled deduction links neatly with the Gabbaystyle rules now widely used in modal Hilbertsystems, enables completeness results for a wide range of rstorder denable frame classes to be obtained automatically, and extends to many richer languages. The paper discusses related work by Jerry Seligman and Miroslava Tzakova and concludes with some reections on the status of labelling in modal logic. 1 Introduction Modern modal logic revolves around the Kripke satisfaction relation: M;w ': This says that the model M satises (or forces, or supports) the modal formula ' at the state w in M....
The Logical Modelling of Computational MultiAgent Systems
, 1992
"... THE aim of this thesis is to investigate logical formalisms for describing, reasoning about, specifying, and perhaps ultimately verifying the properties of systems composed of multiple intelligent computational agents. There are two obvious resources available for this task. The first is the (largel ..."
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Cited by 60 (17 self)
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THE aim of this thesis is to investigate logical formalisms for describing, reasoning about, specifying, and perhaps ultimately verifying the properties of systems composed of multiple intelligent computational agents. There are two obvious resources available for this task. The first is the (largely AI) tradition of reasoning about the intentional notions (belief, desire, etc.). The second is the (mainstream computer science) tradition of temporal logics for reasoning about reactive systems. Unfortunately, neither resource is ideally suited to the task: most intentional logics have little to say on the subject of agent architecture, and tend to assume that agents are perfect reasoners, whereas models of concurrent systems from mainstream computer science typically deal with the execution of individual program instructions. This thesis proposes a solution which draws upon both resources. It defines a model of agents and multiagent systems, and then defines two execution models, which ...
The Computational Complexity of Hybrid Temporal Logics
 Logic Journal of the IGPL
, 2000
"... In their simplest form, hybrid languages are propositional modal languages which can refer to states. They were introduced by Arthur Prior, the inventor of tense logic, and played an important role in his work: because they make reference to specic times possible, they remove the most serious obstac ..."
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Cited by 55 (11 self)
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In their simplest form, hybrid languages are propositional modal languages which can refer to states. They were introduced by Arthur Prior, the inventor of tense logic, and played an important role in his work: because they make reference to specic times possible, they remove the most serious obstacle to developing modal approaches to temporal representation and reasoning. However very little is known about the computational complexity of hybrid temporal logics. In this paper we analyze the complexity of the satisability problem of a number of hybrid temporal logics: the basic hybrid language over transitive frames; nominal tense logic over transitive frames, strict total orders, and transitive trees; nominal Until logic; and referential interval logic. We discuss the eects of including nominals, the @ operator, the somewhere modality E, and the dierence operator D. Adding nominals to tense logic leads for several frame{classes to an increase in complexity of the satisability pro...
A Modal Perspective on the Computational Complexity of Attribute Value Grammar
 Journal of Logic, Language and Information
, 1992
"... Many of the formalisms used in Attribute Value grammar are notational variants of languages of propositional modal logic, and testing whether two Attribute Value descriptions unify amounts to testing for modal satisfiablity. In this paper we put this observation to work. We study the complexity of t ..."
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Cited by 44 (7 self)
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Many of the formalisms used in Attribute Value grammar are notational variants of languages of propositional modal logic, and testing whether two Attribute Value descriptions unify amounts to testing for modal satisfiablity. In this paper we put this observation to work. We study the complexity of the satisfiability problem for nine modal languages which mirror different aspects of AVS description formalisms, including the ability to express reentrancy, the ability to express generalisations, and the ability to express recursive constraints. Two main techniques are used: either Kripke models with desirable properties are constructed, or modalities are used to simulate fragments of Propositional Dynamic Logic. Further possibilities for the application of modal logic in computational linguistics are noted. Attribute Value Structures (AVSs) are probably the most widely used means of representing linguistic structure in current computational linguistics, and the process of unifying...
Hybrid languages and temporal logic
 Logic J. IGPL
, 1999
"... Hybridization is a method invented by Arthur Prior for extending the expressive power of modal languages. Although developed in interesting ways by Robert Bull, and by the So a school (notably, George Gargov, Valentin Goranko, Solomon Passy and Tinko Tinchev), the method remains little known. In our ..."
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Cited by 36 (15 self)
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Hybridization is a method invented by Arthur Prior for extending the expressive power of modal languages. Although developed in interesting ways by Robert Bull, and by the So a school (notably, George Gargov, Valentin Goranko, Solomon Passy and Tinko Tinchev), the method remains little known. In our view this has deprived temporal logic of a valuable tool. The aim of the paper is to explain why hybridization is useful in temporal logic. We make two major points, the rst technical, the second conceptual. First, we showthathybridization gives rise to wellbehaved logics that exhibit an interesting synergy between modal and classical ideas. This synergy, obvious for hybrid languages with full rstorder expressive strength, is demonstrated for a weaker local language capable of de ning the Until operator � we provide a minimal axiomatization, and show that in a wide range of temporally interesting cases extended completeness results can be obtained automatically. Second, we argue that the idea of sorted atomic symbols which underpins the hybrid enterprise can be developed further. To illustrate this, we discuss the advantages and disadvantages of a simple hybrid language which can quantify over paths. 1