A. Nonnengart. Resolution-Based Calculi for Modal and Temporal Logics. In M. A. McRobbie and J. K. Slaney, editors, Proceedings of the Thirteenth International Conference on Automated Deduction (CADE), volume 1104 of Lecture Notes in Artificial Intelligence, pages 598--612, New Brunswick, New Jersey, July/August 1996. Springer-Verlag.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....information that satisfies the conditions for the Breadth First Search algorithm but even if it forms part of a loop resolvents from it will not provide any new information. 6 Related Work Resolution systems based on translations from modal logics into first order classical logics are given in [AE89, Cha87, Non96, Ohl88]. Auffray and Enjalbert [AE89] translate modal formulae into a first order classical logic known as Path Logic and different properties of the accessibility relation are captured by sets of equations. The system described by Ohlbach [Ohl88] translates modal formulae into a first order classical ....

....translates modal formulae into a first order classical logic known as P logic. Here different properties of the modal accessibility relation are captured by special unification algorithms. The system described in [Cha87] is similar but deals with only the propositional S4 system. Nonnengart [Non96] uses a semi functional translation into first order logic where modal formulae are translated into first order formulae and a background theory is added dependent on which logic is being considered. Although both modal and temporal logics are considered, the approach cannot deal with temporal ....

A. Nonnengart. Resolution-Based Calculi for Modal and Temporal Logics. In M. A. McRobbie and J. K. Slaney, editors, Proceedings of the Thirteenth International Conference on Automated Deduction (CADE), volume 1104 of Lecture Notes in Artificial Intelligence, pages 598--612, New Brunswick, New Jersey, July/August 1996. Springer-Verlag.

....between tableaux calculi and known cut free Gentzen systems for these logics. An alternative approach is to translate propositional modal logics into classical first order logic since this allows us to use the wealth of knowledge in firstorder theorem proving to mechanize modal deduction (see e.g. [Mor76, Ohl88, Her89, dMP95, Non96, Ohl98]) Let FO n be the fragment of classical first order logic using at most n individual variables and no function symbols. Any modal logic characterized by a first order definable class of modal frames can be translated into FO n for some fixed n 2. The decidable modal logic K4, for example, is ....

A. Nonnengart. Resolution-based calculi for modal and temporal logics. In M. McRobbie and J. Slaney, editors, CADE-13, pages 599--612. LNAI 1104, Springer-Verlag, 1996.

.... [15] have been proposed [1, 5, 23] Temporal logics have been used for the specification and verification of properties of concurrent systems, see for example [2, 12, 14, 18] Proof methods have also been developed for these logics based on tableau [11, 24] automata [22, 25] and translation [17]. Resolution based methods have the advantage that they are not limited to finite state problems and, as for resolution in classical logics, strategies can be used to reduce the search space. The complexity of such logics is a barrier to efficient proof, for example the complexity of ....

A. Nonnengart. Resolution-Based Calculi for Modal and Temporal Logics. In M. A. McRobbie and J. K. Slaney, editors, Proceedings of the Thirteenth International Conference on Automated Deduction (CADE), volume 1104 of Lecture Notes in Artificial Intelligence, pages 598-- 612, New Brunswick, New Jersey, July/August 1996. Springer-Verlag.

....45: true ) y [24; 44 MRES1] 46: x ) h false [19; 45 SRES2] 47: true ) x [46 SRES3] 48: start ) false [18; 47 IRES1] 8 Related Work The work we have presented is a resolution method for a temporal logic of knowledge. Although resolution methods have been described for both modal logics [2, 3, 9, 6, 13, 16, 29, 30, 31] and temporal logics [1, 5, 39] the only method for logics with both dimensions we know about is that in [20] This work has the same mechanism for the temporal dimension as presented here but differs elsewhere. The normal form in [20] allows both temporal and modal operators in the same rules ....

.... efficient algorithms to apply the complex temporal resolution rule [10] developing strategies to guide the search [11] as well as extending the approach to other logics [4] Other resolution approaches for temporal logics can be found in [1, 5, 39] Resolution for modal systems are given in [2, 3, 9, 6, 13, 16, 29, 30, 31]. These fall into two main groups, those that work in the modal logic directly [2, 29] or those that use a translation into predicate logic for example [30, 31] Our system follows the former route and is based on that for propositional S5 modal logic given by Mints [29] The use of new variables ....

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A. Nonnengart. Resolution-Based Calculi for Modal and Temporal Logics. In M. A. McRobbie and J. K. Slaney, editors, Proceedings of the Thirteenth International Conference on Automated Deduction (CADE), volume 1104 of Lecture Notes in Artificial Intelligence, pages 598--612, New Brunswick, New Jersey, July/August 1996. Springer-Verlag.

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