The Set of Support strategy in temporal resolution

Dixon, Clare; Fisher, Michael

doi:10.1109/time.1998.674140

Cited by 4 publications

(2 citation statements)

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“…Goal-resolution and next-resolution are two particular forms of the well-known setof-support restriction of resolution 6 (see, e.g., Section 2.6 in Schöning [1989] and Dixon and Fisher [1998]). In particular, they can be seen as N-restrictions of resolution.…”

Section: Operational Semanticsmentioning

confidence: 99%

Logical foundations for more expressive declarative temporal logic programming languages

Gaintzarain

Lucio

2013

ACM Trans. Comput. Logic

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In this article, we present a declarative propositional temporal logic programming language called TeDiLog that is a combination of the temporal and disjunctive paradigms in logic programming. TeDiLog is, syntactically, a sublanguage of the well-known Propositional Linear-time Temporal Logic (PLTL). TeDiLog allows both eventualities and always-formulas to occur in clause heads and also in clause bodies. To the best of our knowledge, TeDiLog is the first declarative temporal logic programming language that achieves this high degree of expressiveness. We establish the logical foundations of our proposal by formally defining operational and logical semantics for TeDiLog and by proving their equivalence. The operational semantics of TeDiLog relies on a restriction of the invariant-free temporal resolution procedure for PLTL that was introduced by Gaintzarain et al. in [2013]. We define a fixpoint semantics that captures the reverse (bottom-up) operational mechanism and prove its equivalence with the logical semantics. We also provide illustrative examples and comparison with other proposals. ACM Reference Format:Gaintzarain, J. and Lucio, P. 2013. Logical foundations for more expressive declarative temporal logic programming languages.

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Section: Operational Semanticsmentioning

confidence: 99%

Logical foundations for more expressive declarative temporal logic programming languages

Gaintzarain

Lucio

2013

ACM Trans. Comput. Logic

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“…In particular, we are interested in the most efficient way to apply the resolution operations in order to reduce the number of resolution inferences that are made that do not contribute towards finding a proof. The work described in [DF98] outlines preliminary steps in the definition of a temporal set of support. The set of support strategy for classical resolution restricts the number of resolution inferences that can be made.…”

Section: Future Workmentioning

confidence: 99%

Clausal temporal resolution

Fisher

Dixon

Peim

2001

ACM Trans. Comput. Logic

137

158

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In this article, we examine how clausal resolution can be applied to a specific, but widely used, non-classical logic, namely discrete linear temporal logic. Thus, we first define a normal form for temporal formulae and show how arbitrary temporal formulae can be translated into the normal form, while preserving satisfiability. We then introduce novel resolution rules that can be applied to formulae in this normal form, provide a range of examples and examine the correctness and complexity of this approach. Finally, we describe related work and future developments concerning this work.

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