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15
On the freeze quantifier in constraint LTL: decidability and complexity
 I & C
, 2005
"... Constraint LTL, a generalization of LTL over Presburger constraints, is often used as a formal language to specify the behavior of operational models with constraints. The freeze quantifier can be part of the language, as in some realtime logics, but this variablebinding mechanism is quite general ..."
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Cited by 28 (9 self)
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Constraint LTL, a generalization of LTL over Presburger constraints, is often used as a formal language to specify the behavior of operational models with constraints. The freeze quantifier can be part of the language, as in some realtime logics, but this variablebinding mechanism is quite general and ubiquitous in many logical languages (firstorder temporal logics, hybrid logics, logics for sequence diagrams, navigation logics, etc.). We show that Constraint LTL over the simple domain =# augmented with the freeze operator is undecidable which is a surprising result regarding the poor language for constraints (only equality tests). Many versions of freezefree Constraint LTL are decidable over domains with qualitative predicates and our undecidability result actually establishes # 1 completeness. On the positive side, we provide complexity results when the domain is finite (EXPSPACEcompleteness) or when the formulae are flat in a sense introduced in the paper. Our undecidability results are quite sharp (i.e. with restrictions on the number of variables) and all our complexity characterizations insure completeness with respect to some complexity class (mainly PSPACE and EXPSPACE).
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
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.
The expressivity of universal timed CCP: undecidability of Monadic FLTL and closure operators for security
 IN PPDP ’08: PROCEEDINGS OF THE 10TH INTERNATIONAL ACM SIGPLAN CONFERENCE ON PRINCIPLES AND PRACTICE OF DECLARATIVE PROGRAMMING
, 2008
"... The timed concurrent constraint programing model (tcc) is a declarative framework, closely related to FirstOrder Linear Temporal Logic (FLTL), for modeling reactive systems. The universal tcc formalism (utcc) is an extension of tcc with the ability to express mobility. Here mobility is understood a ..."
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Cited by 12 (8 self)
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The timed concurrent constraint programing model (tcc) is a declarative framework, closely related to FirstOrder Linear Temporal Logic (FLTL), for modeling reactive systems. The universal tcc formalism (utcc) is an extension of tcc with the ability to express mobility. Here mobility is understood as communication of private names as typically done for mobile systems and security protocols. This paper is devoted to the study of 1) the expressiveness of utcc and 2) its semantic foundations. As applications of this study, we also state 3) a noteworthy decidability result for the wellestablished framework of FLTL and 4) bring new semantic insights into the modeling of security protocols. More precisely, we show that in contrast to tcc, utcc is Turingpowerful by encoding Minsky machines. The encoding uses a monadic constraint system allowing us to prove a new result for a fragment of FLTL: The undecidability of the validity problem for monadic FLTL without equality and function symbols. This result refutes a decidability conjecture for FLTL from a previous paper. It also justifies the restriction imposed in previous decidability results on the quantification of flexiblevariables. We shall also show that as in tcc, utcc processes can be semantically represented as partial closure operators. The representation is fully abstract wrt the inputoutput behavior of processes for a meaningful fragment of the utcc. This shows that mobility can be captured as closure operators over an underlying constraint system. As an application we identify a language for security protocols that can be represented as closure operators over a cryptographic constraint system.
A Complete Quantified Epistemic Logic for Reasoning about Message Passing Systems
 PROCEEDINGS OF THE 8TH INTERNATIONAL WORKSHOP ON COMPUTATIONAL LOGIC IN MULTIAGENT SYSTEMS (CLIMA VIII
, 2008
"... We introduce quantified interpreted systems, a semantics to reason about knowledge in multiagent systems in a firstorder setting. Quantified interpreted systems may be used to interpret a variety of firstorder modal epistemic languages with global and local terms, quantifiers, and individual and ..."
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Cited by 9 (6 self)
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We introduce quantified interpreted systems, a semantics to reason about knowledge in multiagent systems in a firstorder setting. Quantified interpreted systems may be used to interpret a variety of firstorder modal epistemic languages with global and local terms, quantifiers, and individual and distributed knowledge operators for the agents in the system. We define firstorder modal axiomatisations for different settings, and show that they are sound and complete with respect to the corresponding semantical classes. The expressibility potential of the formalism is explored by analysing two MAS scenarios: an infinite version of the muddy children problem, a typical epistemic puzzle, and a version of the battlefield game. Furthermore, we apply the theoretical results here presented to the analysis of message passing systems [17,41], and compare the results obtained to their propositional counterparts. By doing so we find that key known metatheorems of the propositional case can be expressed as validities on the corresponding class of quantified interpreted systems.
Monodic ASMs and temporal verification
 PROCEEDINGS ASM 2004
, 2004
"... In this paper, we pursue the goal of automatic deductive verification for certain classes of ASM. In particular, we base our work on a translation of general ASMs to full firstorder temporal logic. While such a logic is, in general, not finitely axiomatisable, recent work has identified a fragment ..."
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Cited by 2 (0 self)
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In this paper, we pursue the goal of automatic deductive verification for certain classes of ASM. In particular, we base our work on a translation of general ASMs to full firstorder temporal logic. While such a logic is, in general, not finitely axiomatisable, recent work has identified a fragment, termed the monodic fragment, that is finitely axiomatisable and many of its subfragments are decidable. Thus, in this paper, we define a class of monodic ASMs whose semantics in terms of temporal logic fits within the monodic fragment. This, together with recent work on clausal resolution methods for monodic fragments, allows us to carry out temporal verification of monodic ASMs. The approach is illustrated by the deductive verification of FloodSet algorithm for Consensus problem, and Synapse N+1 cache coherence protocol; both are specified by monodic ASMs.
Searching for Invariants using Temporal Resolution
 Proceedings of LPAR 2002
, 2002
"... Abstract. In this paper, we show how the clausal temporal resolution technique developed for temporal logic provides an effective method for searching for invariants, and so is suitable for mechanising a wide class of temporal problems. We demonstrate that this scheme of searching for invariants can ..."
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Cited by 2 (2 self)
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Abstract. In this paper, we show how the clausal temporal resolution technique developed for temporal logic provides an effective method for searching for invariants, and so is suitable for mechanising a wide class of temporal problems. We demonstrate that this scheme of searching for invariants can be also applied to a class of multipredicate induction problems represented by mutually recursive definitions. Completeness of the approach, examples of the application of the scheme, and overview of the implementation are described. 1
Exploring the Monodic Fragment of FirstOrder Temporal Logic using Clausal Temporal Resolution
, 2003
"... Until recently, firstorder temporal logic has been little understood. ..."
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Until recently, firstorder temporal logic has been little understood.
Practical firstorder temporal reasoning
 Proceedings of 15th International Symposium on Temporal Representation and Reasoning (TIME), IEEE
, 2008
"... In this paper we consider the specification and verification of infinitestate systems using temporal logic. In particular, we describe parameterised systems using a new variety of firstorder temporal logic that is both powerful enough for this form of specification and tractable enough for practic ..."
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Cited by 2 (1 self)
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In this paper we consider the specification and verification of infinitestate systems using temporal logic. In particular, we describe parameterised systems using a new variety of firstorder temporal logic that is both powerful enough for this form of specification and tractable enough for practical deductive verification. Importantly, the power of the temporal language allows us to describe (and verify) asynchronous systems, communication delays and more complex liveness and fairness properties. These aspects appear difficult for many other approaches to infinitestate verification. 1.
Interactions between Knowledge and Time in a FirstOrder Logic for MultiAgent Systems: Completeness Results
"... We investigate a class of firstorder temporalepistemic logics for reasoning about multiagent systems. We encode typical properties of systems including perfect recall, synchronicity, no learning, and having a unique initial state in terms of variants of quantified interpreted systems, a firstorde ..."
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We investigate a class of firstorder temporalepistemic logics for reasoning about multiagent systems. We encode typical properties of systems including perfect recall, synchronicity, no learning, and having a unique initial state in terms of variants of quantified interpreted systems, a firstorder extension of interpreted systems. We identify several monodic fragments of firstorder temporalepistemic logic and show their completeness with respect to their corresponding classes of quantified interpreted systems. 1.