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Tableau Methods for Modal and Temporal Logics
, 1995
"... This document is a complete draft of a chapter by Rajeev Gor'e on "Tableau Methods for Modal and Temporal Logics" which is part of the "Handbook of Tableau Methods", edited by M. D'Agostino, D. Gabbay, R. Hahnle and J. Posegga, to be published in 1998 by Kluwer, Dordrec ..."
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Cited by 127 (20 self)
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This document is a complete draft of a chapter by Rajeev Gor'e on "Tableau Methods for Modal and Temporal Logics" which is part of the "Handbook of Tableau Methods", edited by M. D'Agostino, D. Gabbay, R. Hahnle and J. Posegga, to be published in 1998 by Kluwer, Dordrecht. Any comments and corrections are highly welcome. Please email me at rpg@arp.anu.edu.au The latest version of this document can be obtained via my WWW home page: http://arp.anu.edu.au/ Tableau Methods for Modal and Temporal Logics Rajeev Gor'e Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1 Syntax and Notational Conventions . . . . . . . . . . . . 3 2.2 Axiomatics of Modal Logics . . . . . . . . . . . . . . . . 4 2.3 Kripke Semantics For Modal Logics . . . . . . . . . . . . 5 2.4 Known Correspondence and Completeness Results . . . . 6 2.5 Logical Consequence . . . . . . . . . . . . . . . . . . . . 8 2....
The Complexity of Propositional Linear Temporal Logics in Simple Cases
 Information and Computation
, 1998
"... this paper we investigate this issue and consider model checking and satisfiability for all fragments of PLTL obtainable by restricting (1) the temporal connectives allowed, (2) the number of atomic propositions, and (3) the temporal height. Key Words: logic in computer science, computational comple ..."
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Cited by 51 (1 self)
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this paper we investigate this issue and consider model checking and satisfiability for all fragments of PLTL obtainable by restricting (1) the temporal connectives allowed, (2) the number of atomic propositions, and (3) the temporal height. Key Words: logic in computer science, computational complexity, verification, temporal logic, model checking 1.
Cutfree Sequent and Tableau Systems for Propositional Diodorean Modal Logics
"... We present sound, (weakly) complete and cutfree tableau systems for the propositional normal modal logics S4:3, S4:3:1 and S4:14. When the modality 2 is given a temporal interpretation, these logics respectively model time as a linear dense sequence of points; as a linear discrete sequence of po ..."
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Cited by 20 (3 self)
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We present sound, (weakly) complete and cutfree tableau systems for the propositional normal modal logics S4:3, S4:3:1 and S4:14. When the modality 2 is given a temporal interpretation, these logics respectively model time as a linear dense sequence of points; as a linear discrete sequence of points; and as a branching tree where each branch is a linear discrete sequence of points. Although cutfree, the last two systems do not possess the subformula property. But for any given finite set of formulae X the "superformulae" involved are always bounded by a finite set of formulae X L depending only on X and the logic L. Thus each system gives a nondeterministic decision procedure for the logic in question. The completeness proofs yield deterministic decision procedures for each logic because each proof is constructive. Each tableau system has a cutfree sequent analogue proving that Gentzen's cutelimination theorem holds for these latter systems. The techniques are due to Hi...
epage MATHEMATICAL MODAL LOGIC: A VIEW OF ITS EVOLUTION
"... ... there is no one fundamental logical notion of necessity, nor consequently of possibility. If this conclusion is valid, the subject of modality ought to be banished from logic, since propositions are simply true or false... [Russell, 1905] 1 ..."
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... there is no one fundamental logical notion of necessity, nor consequently of possibility. If this conclusion is valid, the subject of modality ought to be banished from logic, since propositions are simply true or false... [Russell, 1905] 1
unknown title
"... The theory θ presented here is the smallest theory in the temporal logic TLB [10] that all distributed systems, according to our definition of a distributed system, must satisfy. θ is an instance of the classical modal logic S4.2. The central theorems of θ are stated here without proof. Proofs will ..."
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The theory θ presented here is the smallest theory in the temporal logic TLB [10] that all distributed systems, according to our definition of a distributed system, must satisfy. θ is an instance of the classical modal logic S4.2. The central theorems of θ are stated here without proof. Proofs will appear in [10]. Logics like TLA [14] and TLRCS [18] are used for specifying computer programs and reasoning about their behaviors. Their usefulness for large distributed systems has yet to be proven. Systems with multithousand node networks exhibit inherently asynchronous concurrency. Logics like TLA and TLRCS only provide a sequential (interleaved) concurrent execution model. Hence TLA and the futuretense part of TLRCS should be instances of the modal logic S4.3.1 [11, p. 179], but we are unaware if this has been proven. Not having a fully asynchronous concurrent execution model makes proofs about distributed systems within these logics suspect. Like quantum systems, distributed systems have pairs of observables that are not simultaneously measurable which leads to inherent uncertainty in their behaviors. θ has an asynchronous concurrent execution model and accounts for this inherent uncertainty. Unlike S4.2, TLB has a second primitive modal operator called the “everywhere sometime ” operator that mixes space and time. The reduction formulas of θ allow us to reduce distributed correctness proofs to finitely many program proofs running on single computers. For distributed systems with the peer process architecture, θ allow us to reduce distributed correctness proofs to a single program proof running on a single computer. 1.