An application of many-valued logic to decide propositional S5 formulae: a strategy designed for a parameterized tableaux-based Theorem Prover

Caferra, Ricardo; Zabel, Nicolas

doi:10.1016/b978-0-444-88771-9.50009-x

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Interaction With Other Non-classical Logics1

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2007

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Cited by 4 publications

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“…Any modal logic with set of possible worlds N and accessibility relation R ~ N x N can be trivially re-interpreted as a 2 N -valued logic by encoding a possible world interpretation r : ~ x N -t {O, I} as a manyvalued interpretation I : ~ -t 2 N • For modal logics with the finite model property this construction yields finite-valued proof systems characterizing those modallogics [Caferra and Zabel, 1990]. Any modal logic with set of possible worlds N and accessibility relation R ~ N x N can be trivially re-interpreted as a 2 N -valued logic by encoding a possible world interpretation r : ~ x N -t {O, I} as a manyvalued interpretation I : ~ -t 2 N • For modal logics with the finite model property this construction yields finite-valued proof systems characterizing those modallogics [Caferra and Zabel, 1990].…”

Section: Interaction With Other Non-classical Logicsmentioning

confidence: 99%

Handbook of Philosophical Logic

2001

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Section: Interaction With Other Non-classical Logicsmentioning

confidence: 99%

Handbook of Philosophical Logic

2001

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“…For instance, Caferra and Zabel[18] give a translation from the propositional modal logic S5, viewed as an infinite-valued logic, into finite-valued logics.…”

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Automated theorem proving by resolution in non-classical logics

Sofronie-Stokkermans

2007

Ann Math Artif Intell

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This paper is an overview of a variety of results, all centered around a common theme, namely embedding of non-classical logics into first order logic and resolution theorem proving. We present several classes of non-classical logics, many of which are of great practical relevance in knowledge representation, which can be translated into tractable and relatively simple fragments of classical logic. In this context, we show that refinements of resolution can often be used successfully for automated theorem proving, and in many interesting cases yield optimal decision procedures

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