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A Normal Form for Temporal Logic and its Application in TheoremProving and Execution
 Journal of Logic and Computation
, 1997
"... In this paper a normal form, called Separated Normal Form (SNF), for temporal logic formulae is described. A simple propositional temporal logic, based on a discrete linear model structure, is introduced and a procedure for transforming an arbitrary formula of this logic into SNF is described. It is ..."
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Cited by 44 (26 self)
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In this paper a normal form, called Separated Normal Form (SNF), for temporal logic formulae is described. A simple propositional temporal logic, based on a discrete linear model structure, is introduced and a procedure for transforming an arbitrary formula of this logic into SNF is described. It is shown that the transformation process preserves satisfiability and ensures that any model of the transformed formula is a model of the original one. This normal form not only provides a simple and concise representation for temporal formulae, but is also used as the basis for both a resolution proof method and an execution mechanism for this type of temporal logic. In addition to outlining these applications, we show how the normal form can be extended to deal with firstorder temporal logic. 1
Resolution for Temporal Logics of Knowledge
 Journal of Logic and Computation
, 1998
"... A resolution based proof system for a temporal logic of knowledge is presented and shown to be correct. Such logics are useful for proving properties of distributed and multiagent systems. Examples are given to illustrate the proof system. An extension of the basic system to the multimodal case is ..."
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Cited by 35 (18 self)
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A resolution based proof system for a temporal logic of knowledge is presented and shown to be correct. Such logics are useful for proving properties of distributed and multiagent systems. Examples are given to illustrate the proof system. An extension of the basic system to the multimodal case is given and illustrated using the `muddy children problem'. 1 Introduction Temporal logics have been shown to have many applications in computer science and artificial intelligence. For example, they are used in the specification and verification of reactive systems [28], in temporal query languages [8], executable logics [18] and for reasoning about action [36]. For some applications, however, logics containing connectives that operate over just the one modal dimension of time do not provide sufficient expressive power. For such applications, it is necessary to provide connectives that allow us to represent the properties of different modal dimensions in the same logic. In this paper, we co...
Deciding regular grammar logics with converse through firstorder logic
 JOURNAL OF LOGIC, LANGUAGE AND INFORMATION
, 2005
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Constructing the Least Models for Positive Modal Logic Programs
, 2000
"... We give algorithms to construct the least Lmodel for a given positive modal logic program P , where L can be one of the modal logics KD, T , KDB, B, KD4, S4, KD5, KD45, and S5. If L 2 fKD5;KD45;S5g, or L 2 fKD;T ; KDB;Bg and the modal depth of P is finitely bounded, then the least Lmodel of P can ..."
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Cited by 18 (16 self)
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We give algorithms to construct the least Lmodel for a given positive modal logic program P , where L can be one of the modal logics KD, T , KDB, B, KD4, S4, KD5, KD45, and S5. If L 2 fKD5;KD45;S5g, or L 2 fKD;T ; KDB;Bg and the modal depth of P is finitely bounded, then the least Lmodel of P can be constructed in PTIME and coded in polynomial space. We also show that if P has no flat models then it has the least models in KB, K5, K45, and KB5. As a consequence, the problem of checking the satisfiability of a set of modal Horn formulae with finitely bounded modal depth in KD, T , KB, KDB, or B is decidable in PTIME. The known result that the problem of checking the satisfiability of a set of Horn formulae in K5, KD5, K45, KD45, KB5, or S5 is decidable in PTIME is also studied in this work via a different method. 1.
Using temporal logics of knowledge in the formal verification of security protocols
, 2004
"... Temporal logics of knowledge are useful for reasoning about situations where the knowledge of an agent or component is important, and where change may occur in this knowledge over time. Here we use temporal logics of knowledge to reason about security protocols. We show how to specify the NeedhamSc ..."
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Cited by 12 (1 self)
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Temporal logics of knowledge are useful for reasoning about situations where the knowledge of an agent or component is important, and where change may occur in this knowledge over time. Here we use temporal logics of knowledge to reason about security protocols. We show how to specify the NeedhamSchroeder protocol using temporal logics of knowledge and prove various properties using a resolution calculus for this logic. 1
Clausal Resolution for Logics of Time and Knowledge with Synchrony and Perfect Recall
 In Proceedings of ICTL 2000
, 2000
"... Temporal logics of knowledge are widely used in the specification and analysis of distributed and multiagent systems where the behaviour of a component is captured by its set of possible executions. In spite of this, proof methods for these logics are rare, particularly in cases where the temporal ..."
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Cited by 10 (7 self)
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Temporal logics of knowledge are widely used in the specification and analysis of distributed and multiagent systems where the behaviour of a component is captured by its set of possible executions. In spite of this, proof methods for these logics are rare, particularly in cases where the temporal and epistemic dimensions can interact. In this paper, we present a clausal resolution system for a temporal logic of knowledge admitting such interactions. The particular interaction we consider captures synchronous systems with perfect recall. A system is said to have perfect recall if the set of executions an agent considers possible stays the same or decreases over time. Soundness, termination and completeness results for the resolution system are discussed. Keywords: nonclassical resolution, temporal logics of knowledge, synchrony and perfect recall, agentbased systems. 1 Introduction Temporal logics of knowledge are widely used for analysing distributed and multiagent systems [7, 9...
ResolutionBased Proof for MultiModal Temporal Logics of Knowledge
 Proceedings of TIME00 the Seventh International Workshop on Temporal Representation and Reasoning, Cape Breton, Nova
, 2000
"... Temporal logics of knowledge are useful in order to specify complex systems in which agents are both dynamic and have information about their surroundings. We present a resolution method for propositional temporal logic combined with multimodal S5 and illustrate its use on examples. This paper corr ..."
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Cited by 9 (6 self)
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Temporal logics of knowledge are useful in order to specify complex systems in which agents are both dynamic and have information about their surroundings. We present a resolution method for propositional temporal logic combined with multimodal S5 and illustrate its use on examples. This paper corrects a previous proposal for resolution in multimodal temporal logics of knowledge. Keywords: temporal and modal logics, nonclassical resolution, theoremproving 1 Introduction Combinations of logics have been useful for specifying and reasoning about complex situations, for example multiagent systems [21, 24], accident analysis [15], and security protocols [18]. For example, logics to formalise multiagent systems often incorporate a dynamic component representing change of over time; an informational component to capture the agent's knowledge or beliefs; and a motivational component for notions such as goals, wishes, desires or intentions. Often temporal or dynamic logic is used for...
Clausal tableau systems and space bounds for the modal logics
 KD, T, KB, KDB, and B. Submitted to Journal of Logic and Computation
, 1999
"... Abstract. We propose so called clausal tableau systems for the common modal logics K, KD, T, KB, KDB and B. There is a measure such that for each tableau rule of these systems the measure of all its denominators is smaller than the measure of its numerator. Basing on these systems, we give a decisio ..."
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Cited by 7 (5 self)
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Abstract. We propose so called clausal tableau systems for the common modal logics K, KD, T, KB, KDB and B. There is a measure such that for each tableau rule of these systems the measure of all its denominators is smaller than the measure of its numerator. Basing on these systems, we give a decision procedure for the logics, which uses O(n 2)space for the logics T, KB, KDB and B, and O(n. log n)space for the logics K and KD. We also show that the problem of checking satisfiability in T, KB, KDB, or B for formulae with finitely bounded modaldepth is decidable in O(n. log n)space. We are the first who explicitly establish space requirements for the logics KB, KDB and B. 1
Foundations of Modal Logic Programming: The Direct Approach (release 2.0)”, manuscript (provided as a technical report), available at http://www.mimuw.edu. pl/~nguyen/papers.html
"... 1.1 Classical Logic Programming............................ 5 1.2 Previous Works on Modal Logic Programming.................. 7 ..."
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Cited by 5 (5 self)
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1.1 Classical Logic Programming............................ 5 1.2 Previous Works on Modal Logic Programming.................. 7
A GraphBased Approach To Resolution In Temporal Logic
 In Temporal Logic, First International Conference, ICTL '94, Proceedings
, 1994
"... . In this paper, we present algorithms developed in order to implement a clausal resolution method for discrete, linear temporal logics, presented in [Fis91]. As part of this method, temporal formulae are rewritten into a normal form and both `nontemporal' and `temporal' inference rules are applied ..."
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Cited by 4 (3 self)
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. In this paper, we present algorithms developed in order to implement a clausal resolution method for discrete, linear temporal logics, presented in [Fis91]. As part of this method, temporal formulae are rewritten into a normal form and both `nontemporal' and `temporal' inference rules are applied. Through the use of a graphbased representation for the normal form, "efficient" search algorithms can be applied to detect sets of formulae for which temporal resolution is applicable. Further, rather than constructing the full graph structure, our algorithms only explore and construct as little of the graph as possible. These algorithms have been implemented and have been combined with subprograms performing translation to normal form and nontemporal resolution to produce an integrated resolution based temporal theoremprover. 1 Introduction Although resolution has been widely used as a decision procedure in classical logics, decision procedures in temporal logic have usually been tab...