Combining Hilbert Style and Semantic Reasoning in a Resolution Framework

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Combining Hilbert Style and Semantic Reasoning in a Resolution Framework (1998)

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by Hans Jürgen Ohlbach

Venue:	In Proc. CADE-15, LNAI 1421
Citations:	15 - 0 self

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@INPROCEEDINGS{Ohlbach98combininghilbert,
    author = {Hans Jürgen Ohlbach},
    title = {Combining Hilbert Style and Semantic Reasoning in a Resolution Framework},
    booktitle = {In Proc. CADE-15, LNAI 1421},
    year = {1998},
    pages = {205--219},
    publisher = {Springer}
}

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Abstract

Many non-classical logics can be axiomatized by means of Hilbert Systems. Reasoning in Hilbert Systems, however, is extremely inefficient. Most inference methods therefore use the semantics of a logic in one kind or another to get more efficiency. In this paper a combination of Hilbert style and semantic reasoning is proposed. It is particularly tailored for cases where either the semantics of some operators is not known, or it is second-order, or it is just too complicated to handle, or flexibility in experimenting with different versions of a logic is required. First-order predicate logic is used as a meta-logic for combining the Hilbert part with the semantics part. Reasoning is done in a (theory) resolution framework. The basic method is applicable to many different (monotonic propositional) non-classical logics. It can, however, be improved by treating particular formulae in a special way, as rewrite rules, as theory unification or t...

Keyphrases

resolution framework hilbert style semantic reasoning hilbert system inference method hilbert part rewrite rule first-order predicate logic basic method monotonic propositional theory unification semantics part non-classical logic different version many non-classical logic special way particular formula

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