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21
Monodic fragments of firstorder temporal logics: 20002001 A.D.
"... The aim of this paper is to summarize and analyze some results obtained in 20002001 about decidable and undecidable fragments of various firstorder temporal logics, give some applications in the field of knowledge representation and reasoning, and attract the attention of the `temporal community' ..."
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Cited by 48 (8 self)
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The aim of this paper is to summarize and analyze some results obtained in 20002001 about decidable and undecidable fragments of various firstorder temporal logics, give some applications in the field of knowledge representation and reasoning, and attract the attention of the `temporal community' to a number of interesting open problems.
Monodic temporal resolution
 ACM Transactions on Computational Logic
, 2003
"... Until recently, FirstOrder Temporal Logic (FOTL) has been only partially understood. While it is well known that the full logic has no finite axiomatisation, a more detailed analysis of fragments of the logic was not previously available. However, a breakthrough by Hodkinson et al., identifying a f ..."
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Cited by 27 (15 self)
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Until recently, FirstOrder Temporal Logic (FOTL) has been only partially understood. While it is well known that the full logic has no finite axiomatisation, a more detailed analysis of fragments of the logic was not previously available. However, a breakthrough by Hodkinson et al., identifying a finitely axiomatisable fragment, termed the monodic fragment, has led to improved understanding of FOTL. Yet, in order to utilise these theoretical advances, it is important to have appropriate proof techniques for this monodic fragment. In this paper, we modify and extend the clausal temporal resolution technique, originally developed for propositional temporal logics, to enable its use in such monodic fragments. We develop a specific normal form for monodic formulae in FOTL, and provide a complete resolution calculus for formulae in this form. Not only is this clausal resolution technique useful as a practical proof technique for certain monodic classes, but the use of this approach provides us with increased understanding of the monodic fragment. In particular, we here show how several features of monodic FOTL can be established as corollaries of the completeness result for the clausal temporal resolution method. These include definitions of new decidable monodic classes, simplification of existing monodic classes by reductions, and completeness of clausal temporal resolution in the case of
On the Computational Complexity of SpatioTemporal Logics
 Proceedings of the 16th AAAI International FLAIRS Conference
, 2003
"... Recently, a hierarchy of spatiotemporal languages based on the propositional temporal logic PTL and the spatial languages RCC8, BRCC8 and S4u has been introduced. Although a number of results on their computational properties were obtained, the most important questions were left open. ..."
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Cited by 21 (0 self)
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Recently, a hierarchy of spatiotemporal languages based on the propositional temporal logic PTL and the spatial languages RCC8, BRCC8 and S4u has been introduced. Although a number of results on their computational properties were obtained, the most important questions were left open.
TeMP: A Temporal Monodic Prover
 In Proc. IJCAR04, LNAI
, 2004
"... We present TeMPthe first experimental system for testing validity of monodic temporal logic formulae. The prover implements finegrained temporal resolution. The core operations required by the procedure are performed by an efficient resolutionbased prover for classical firstorder logic. ..."
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Cited by 20 (11 self)
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We present TeMPthe first experimental system for testing validity of monodic temporal logic formulae. The prover implements finegrained temporal resolution. The core operations required by the procedure are performed by an efficient resolutionbased prover for classical firstorder logic.
Temporalising Tableaux
 STUDIA LOGICA
, 2004
"... As a remedy for the bad computational behaviour of firstorder temporal logic (FOTL), it has recently been proposed to restrict the application of temporal operators to formulas with at most one free variable thereby obtaining socalled monodic fragments of FOTL. In this paper, we are concerned with ..."
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Cited by 17 (5 self)
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As a remedy for the bad computational behaviour of firstorder temporal logic (FOTL), it has recently been proposed to restrict the application of temporal operators to formulas with at most one free variable thereby obtaining socalled monodic fragments of FOTL. In this paper, we are concerned with constructing tableau algorithms for monodic fragments based on decidable fragments of firstorder logic like the twovariable fragment or the guarded fragment. We present a general framework that shows how existing decision procedures for firstorder fragments can be used for constructing a tableau algorithm for the corresponding monodic fragment of FOTL.
A Simplified Clausal Resolution Procedure for Propositional LinearTime Temporal Logic
 In Tableaux 2002, Proceedings
, 2002
"... The clausal resolution method for propositional lineartime temporal logics is well known and provides the basis for a number of temporal provers. The method is based on an intuitive clausal form, called SNF, comprising three main clause types and a small number of resolution rules. In this paper ..."
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Cited by 12 (8 self)
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The clausal resolution method for propositional lineartime temporal logics is well known and provides the basis for a number of temporal provers. The method is based on an intuitive clausal form, called SNF, comprising three main clause types and a small number of resolution rules. In this paper, we show how the normal form can be radically simplified and, consequently, how a simplified clausal resolution method can be defined for this important variety of logic.
TRP ++ : A temporal resolution prover
 In Collegium Logicum
, 2002
"... this paper. 2 Basics of PLTL Let P be a set of propositional variables. The set of formulae of propositional linear time logic PLTL (over P) is inductively defined as follows: (i) ? is a formula of PLTL, (ii) every propositional variable of P is a formula of PLTL, (iii) if ' and / are formulae of ..."
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Cited by 11 (5 self)
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this paper. 2 Basics of PLTL Let P be a set of propositional variables. The set of formulae of propositional linear time logic PLTL (over P) is inductively defined as follows: (i) ? is a formula of PLTL, (ii) every propositional variable of P is a formula of PLTL, (iii) if ' and / are formulae of PLTL, then :' and (' /) are formulae of PLTL, and (iv) if ' and / are formulae of PLTL, then #' (in the next moment of time ' is true), 3' (sometimes in the future ' is true), 2' (always in the future ' is true), (' U /) (' is true until / is true), and (' W /) (' is true unless / is true) are formulae of PLTL. Other Boolean connectives including ?, , !, and $ are defined using ?, :, and
Towards the Implementation of FirstOrder Temporal Resolution: the Expanding Domain Case
"... Firstorder temporal logic is a concise and powerful notation, with many potential applications in both Computer Science and Artificial Intelligence. While the full logic is highly complex, recent work on monodic firstorder temporal logics has identified important enumerable and even decidable frag ..."
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Cited by 11 (7 self)
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Firstorder temporal logic is a concise and powerful notation, with many potential applications in both Computer Science and Artificial Intelligence. While the full logic is highly complex, recent work on monodic firstorder temporal logics has identified important enumerable and even decidable fragments. In this paper, we develop a clausal resolution method for the monodic fragment of firstorder temporal logic over expanding domains. We first define a normal form for monodic formulae and show how arbitrary monodic formulae can be translated into the normal form, while preserving satisfiability. We then introduce novel resolution calculi that can be applied to formulae in this normal form and state correctness and completeness results for the method. We illustrate the method on a comprehensive example. The method is based on classical firstorder resolution and can, thus, be efficiently implemented.
Is There a Future for Deductive Temporal Verification
 In Proc. TIME06. IEEE Computer
, 2006
"... complexity; clausal temporal resolution. In this paper, we consider a tractable subclass of propositional linear time temporal logic, and provide a complete clausal resolution calculus for it. The fragment is important as it captures simple Büchi automata. We also show that, just as the emptiness c ..."
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Cited by 9 (7 self)
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complexity; clausal temporal resolution. In this paper, we consider a tractable subclass of propositional linear time temporal logic, and provide a complete clausal resolution calculus for it. The fragment is important as it captures simple Büchi automata. We also show that, just as the emptiness check for a Büchi automaton is tractable, the complexity of deciding unsatisfiability, via resolution, of our logic is polynomial (rather than exponential). Consequently, a Büchi automaton can be represented within our logic, and its emptiness can be tractably decided via deductive methods. This may have a significant impact upon approaches to verification, since techniques such as model checking inherently depend on the ability to check emptiness of an appropriate Büchi automaton. Thus, we also discuss how such a logic might form the basis for practical deductive temporal verification. 1
Mechanising FirstOrder Temporal Resolution
, 2003
"... Firstorder temporal logic is a concise and powerful notation, with many potential applications in both Computer Science and Artificial Intelligence. While the full logic is highly complex, recent work on monodic firstorder temporal logics has identified important enumerable and even decidable frag ..."
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Cited by 7 (5 self)
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Firstorder temporal logic is a concise and powerful notation, with many potential applications in both Computer Science and Artificial Intelligence. While the full logic is highly complex, recent work on monodic firstorder temporal logics has identified important enumerable and even decidable fragments. Although a complete and correct resolutionstyle calculus has already been suggested for this specific fragment, this calculus involves constructions too complex to be of a practical value. In this paper, we develop a machineoriented clausal resolution method which features radically simplified proof search. We first define a normal form for monodic formulae and then introduce a novel resolution calculus that can be applied to formulae in this normal form. The calculus is based on classical firstorder resolution and can, thus, be efficiently implemented. We prove correctness and completeness results for the calculus and illustrate it on a comprehensive example. An implementation of the method is briefly discussed.