A Resolution Decision Procedure for Fluted Logic

Schmidt, Renate A.; Hustadt, Ullrich

doi:10.1007/10721959_34

Cited by 34 publications

(12 citation statements)

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“…It is still the case that the clausal form of some relational correspondence properties including transitivity and Euclideanness do not belong to either GC or DL * . The clausal classes associated with fluted logic [84] or Maslov's class DK [51] are no help here either.…”

Section: Respect To a Set Of Non-logical Axioms Of A Formula ϕ Is Linmentioning

confidence: 99%

First-Order Resolution Methods for Modal Logics

Schmidt

Hustadt

2013

Programming Logics

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Abstract. In this paper we give an overview of results for modal logic which can be shown using techniques and methods from first-order logic and resolution. Because of the breadth of the area and the many applications we focus on the use of first-order resolution methods for modal logics. In addition to traditional propositional modal logics we consider more expressive PDL-like dynamic modal logics which are closely related to description logics. Without going into too much detail, we survey different ways of translating modal logics into first-order logic, we explore different ways of using first-order resolution theorem provers, and we discuss a variety of results which have been obtained in the setting of first-order resolution.

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Section: Respect To a Set Of Non-logical Axioms Of A Formula ϕ Is Linmentioning

confidence: 99%

First-Order Resolution Methods for Modal Logics

Schmidt

Hustadt

2013

Programming Logics

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“…The splitting rule is don't know non-deterministic and usually requires backtracking. However, in the resolution framework an alternative to explicit splitting is splitting through new propositional variables [9,39] implemented in the theorem prover VAMPIRE [40] or the generalisation called separation in [44].…”

Section: Theorem 1 There Is a Linear Reduction Cls Of Any First-ordermentioning

confidence: 99%

A new methodology for developing deduction methods

Schmidt

2009

Ann Math Artif Intell

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This paper explores the use of resolution as a meta-framework for developing various, different deduction calculi. In this work the focus is on developing deduction calculi for modal dynamic logics. Dynamic modal logics are PDL-like extended modal logics which are closely related to description logics. We show how tableau systems, modal resolution systems and Rasiowa-Sikorski systems can be developed and studied by using standard principles and methods of first-order theorem proving. The approach is based on the translation of reasoning problems in modal logic to first-order clausal form and using a suitable refinement of resolution to construct and mimic derivations of the desired proof method. The inference rules of the calculus can then be read off from the clausal form. We show how this approach can be used to generate new proof calculi and prove soundness, completeness and decidability results. This slightly unusual approach allows us to gain new insights and results for familiar and less familiar logics, for different proof methods, and compare them not only theoretically but also empirically in a uniform framework.

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“…However, starting with [123], a large number of fragments of first-order logic have been shown to be decidable by resolution or refinements of resolution [48,65,76,82,117,179].…”

Section: Local Satisfiability In Multi Modal K Nmentioning

confidence: 99%

“…In general, the formulae we obtain in this way from the relational translation of modal formulae (as well as the corresponding sets of clauses) belong to quite a number of decidable fragments of first-order logic, for example, the two-variable fragment, the guarded fragment [3], Maslov's class K [135], and fluted logic [165,166]. Resolution decision procedures have been developed for the guarded fragment [48,76], for Maslov's class K [111,117], for fluted logic [179] and various other classes related to modal logics, see e.g. [65,82,83,111].…”

Section: Resolutionmentioning

confidence: 99%

“…An alternative to explicit splitting is splitting through new propositional variables [168] implemented in the theorem prover VAMPIRE [169] or the generalisation called separation in [179]. In the splitting through propositional variables approach, a clause C ∨ D with variable-disjoint components C and D is replaced with two clauses C ∨ p and D ∨ ¬p, where p is a new propositional variable called a split propositional variable.…”

Section: Implementation and Optimisationmentioning

confidence: 99%

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