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106
Logics for Hybrid Systems
 Proceedings of the IEEE
, 2000
"... This paper offers a synthetic overview of, and original contributions to, the use of logics and formal methods in the analysis of hybrid systems ..."
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Cited by 93 (7 self)
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This paper offers a synthetic overview of, and original contributions to, the use of logics and formal methods in the analysis of hybrid systems
Combining Deduction and Model Checking into Tableaux and Algorithms for ConversePDL
 Information and Computation
, 1998
"... . This paper presents a prefixed tableaux calculus for Propositional Dynamic Logic with Converse based on a combination of different techniques such as prefixed tableaux for modal logics and model checkers for ¯calculus. We prove the correctness and completeness of the calculus and illustrate its f ..."
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Cited by 57 (7 self)
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. This paper presents a prefixed tableaux calculus for Propositional Dynamic Logic with Converse based on a combination of different techniques such as prefixed tableaux for modal logics and model checkers for ¯calculus. We prove the correctness and completeness of the calculus and illustrate its features. We also discuss the transformation of the tableaux method (naively NEXPTIME) into an EXPTIME algorithm. 1 Introduction Propositional Dynamic Logics (PDLs) are modal logics introduced in [10] to model the evolution of the computation process by describing the properties of states reached by programs during their execution [15, 24, 27]. Over the years, PDLs have been proved to be a valuable formal tool in Computer Science, Logic, Computational Linguistics, and Artificial Intelligence far beyond their original use for program verification (e.g. [4, 12, 14, 15, 24, 23]). In this paper we focus on ConversePDL (CPDL) [10], obtained from the basic logic PDL by adding the converse operat...
EXPTIME tableaux for ALC
 ARTIFICIAL INTELLIGENCE
, 2000
"... The last years have seen two major advances in Knowledge Representation and Reasoning. First, many interesting problems (ranging from Semistructured Data to Linguistics) were shown to be expressible in logics whose main deductive problems are EXPTIMEcomplete. Second, experiments in automated reaso ..."
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Cited by 51 (3 self)
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The last years have seen two major advances in Knowledge Representation and Reasoning. First, many interesting problems (ranging from Semistructured Data to Linguistics) were shown to be expressible in logics whose main deductive problems are EXPTIMEcomplete. Second, experiments in automated reasoning have substantially broadened the meaning of “practical tractability”. Instances of realistic size for PSPACEcomplete problems are now within reach for implemented systems. Still, there is a gap between the reasoning services needed by the expressive logics mentioned above and those provided by the current systems. Indeed, the algorithms based on treeautomata, which are used to prove EXPTIMEcompleteness, require exponential time and space even in simple cases. On the other hand, current algorithms based on tableau methods can take advantage of such cases, but require double exponential time in the worst case. We propose a tableau calculus for the description logic ALC for checking the satisfiability of a concept with respect to a TBox with general axioms, and transform it into the first simple tableaubased decision procedure working in single exponential time. To guarantee the ease of implementation, we also discuss the effects that optimizations (propositional backjumping, simplification, semantic branching, etc.) might have on our complexity result, and introduce a few optimizations ourselves.
Free Variable Tableaux for Propositional Modal Logics
 TABLEAUX97, LNCS 1227
, 1997
"... We present a sound, complete, modular and lean labelled tableau calculus for many propositional modal logics where the labels contain "free" and "universal" variables. Our "lean" Prolog implementation is not only surprisingly short, but compares favourably with other considerably more complex implem ..."
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Cited by 41 (5 self)
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We present a sound, complete, modular and lean labelled tableau calculus for many propositional modal logics where the labels contain "free" and "universal" variables. Our "lean" Prolog implementation is not only surprisingly short, but compares favourably with other considerably more complex implementations for modal deduction.
Efficient LoopCheck for Backward Proof Search in Some NonClassical Propositional Logics
, 1996
"... . We consider the modal logics KT and S4, the tense logic K t , and the fragment IPC (^;!) of intuitionistic logic. For these logics backward proof search in the standard sequent or tableau calculi does not terminate in general. In terms of the respective Kripke semantics, there are several kinds of ..."
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Cited by 33 (1 self)
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. We consider the modal logics KT and S4, the tense logic K t , and the fragment IPC (^;!) of intuitionistic logic. For these logics backward proof search in the standard sequent or tableau calculi does not terminate in general. In terms of the respective Kripke semantics, there are several kinds of nontermination: loops inside a world (KT), innite resp. looping branches (S4, IPC (^;!) ), and innite branching degree (K t ). We give uniform sequentbased calculi that contain specically tailored loopchecks such that the eciency of proof search is not deteriorated. Moreover all these loopchecks are easy to implement and can be combined with optimizations. Note that our calculus for S4 is not a pure contractionfree sequent calculus, but this (theoretical) defect does not hinder its application in practice. 1 Introduction For many nonclassical propositional logics, backward proof search in the usual sequent calculi does not terminate in general. For all the logics we consider in th...
A ResolutionBased Proof Method for Temporal Logics of Knowledge and Belief
 Journal of Applied NonClassical Logics
, 1996
"... In this paper we define two logics, KL n and BL n , and present resolutionbased proof methods for both. KL n is a temporal logic of knowledge. Thus, in addition to the usual connectives of linear discrete temporal logic, it contains a set of unary modal connectives for representing the knowledge pos ..."
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Cited by 30 (15 self)
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In this paper we define two logics, KL n and BL n , and present resolutionbased proof methods for both. KL n is a temporal logic of knowledge. Thus, in addition to the usual connectives of linear discrete temporal logic, it contains a set of unary modal connectives for representing the knowledge possessed by agents. The logic BL n is somewhat similar: it is a temporal logic that contains connectives for representing the beliefs of agents. The proof methods we present for these logics involve two key steps. First, a formula to be tested for unsatisfiability is translated into a normal form. Secondly, a family of resolution rules are used, to deal with the interactions between the various operators of the logics. In addition to a description of the normal form and the proof methods, we present some short worked examples and proposals for future work. 1
Deciding regular grammar logics with converse through firstorder logic
 JOURNAL OF LOGIC, LANGUAGE AND INFORMATION
, 2005
"... ..."
A Tableau Calculus for Multimodal Logics and Some (Un)Decidability Results
 IN PROC. OF TABLEAUX98
, 1998
"... In this paper we present a prefixed analytic tableau calculus for a class of normal multimodal logics and we present some results about decidability and undecidability of this class. The class is characterized by axioms of the form [t 1 ] : : : [t n ]' oe [s1 ] : : : [sm ]', called inclusion axio ..."
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Cited by 24 (8 self)
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In this paper we present a prefixed analytic tableau calculus for a class of normal multimodal logics and we present some results about decidability and undecidability of this class. The class is characterized by axioms of the form [t 1 ] : : : [t n ]' oe [s1 ] : : : [sm ]', called inclusion axioms, where the t i 's and s j 's are constants. This class of logics, called grammar logics, was introduced for the first time by Farinas del Cerro and Penttonen to simulate the behaviour of grammars in modal logics, and includes some wellknown modal systems. The prefixed tableau method is used to prove the undecidability of modal systems based on unrestricted, context sensitive, and context free grammars. Moreover, we show that the class of modal logics, based on rightregular grammars, are decidable by means of the filtration methods, by defining an extension of the FischerLadner closure.
Using Resolution for Testing Modal Satisfiability and Building Models
, 2000
"... . This paper presents a translationbased resolution decision procedure for the multimodal logic K (m) (\; [; ^) dened over families of relations closed under intersection, union and converse. The relations may satisfy certain additional frame properties. Dierent from previous resolution decision p ..."
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Cited by 23 (11 self)
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. This paper presents a translationbased resolution decision procedure for the multimodal logic K (m) (\; [; ^) dened over families of relations closed under intersection, union and converse. The relations may satisfy certain additional frame properties. Dierent from previous resolution decision procedures which are based on ordering renements our procedure is based on a selection renement, the derivations of which correspond to derivations of tableaux or sequent proof systems. This procedure has the advantage that it can be used both as a satisability checker and a model builder. We show that tableaux and sequentstyle proof systems can be polynomially simulated with our procedure. Furthermore, the nite model property follows for a number of extended modal logics. Keywords: modal logic, automated theorem proving, resolution decision procedures, tableaux proof systems, satisability testing, model generation, simulation, relative proof complexity, relative search space complex...
EXPTime tableaux with global caching for description logics with transitive roles, inverse roles and role hierarchies
 IN PROC. TABLEAUX 2007, AIX EN PROVENCE
, 2007
"... The description logic SHI extends the basic description logic ALC with transitive roles, role hierarchies and inverse roles. The known tableaubased decision procedure [9] for SHI exhibit (at least) NEXPTIME behaviour even though SHI is known to be EXPTIMEcomplete. The automatabased algorithms fo ..."
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Cited by 21 (11 self)
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The description logic SHI extends the basic description logic ALC with transitive roles, role hierarchies and inverse roles. The known tableaubased decision procedure [9] for SHI exhibit (at least) NEXPTIME behaviour even though SHI is known to be EXPTIMEcomplete. The automatabased algorithms for SHI often yield optimal worstcase complexity results, but do not behave well in practice since good optimisations for them have yet to be found. We extend our method for global caching in ALC to SHI by adding analytic cut rules, thereby giving the first EXPTIME tableaubased decision procedure for SHI, and showing one way to incorporate global caching and inverse roles.