A Principle for Incorporating Axioms into the First-Order Translation of Modal Formulae

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A Principle for Incorporating Axioms into the First-Order Translation of Modal Formulae (2003)

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by Renate A. Schmidt , Ullrich Hustadt

Venue:	Automated Deduction—CADE-19, volume 2741 of Lecture Notes in Artificial Intelligence
Citations:	20 - 7 self

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@INPROCEEDINGS{Schmidt03aprinciple,
    author = {Renate A. Schmidt and Ullrich Hustadt},
    title = {A Principle for Incorporating Axioms into the First-Order Translation of Modal Formulae},
    booktitle = {Automated Deduction—CADE-19, volume 2741 of Lecture Notes in Artificial Intelligence},
    year = {2003},
    pages = {412--426},
    publisher = {Springer}
}

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Abstract

In this paper we present a translation principle, called the axiomatic translation, for reducing propositional modal logics with background theories, including triangular properties such as transitivity, Euclideanness and functionality, to decidable logics. The goal of the axiomatic translation principle is to find simplified theories, which capture the inference problems in the original theory, but in a way that is more amenable to automation and easier to deal with by existing theorem provers. The principle of the axiomatic translation is conceptually very simple and can be largely automated. Soundness is automatic under reasonable assumptions, and termination of ordered resolution is easily achieved, but the non-trivial part of the approach is proving completeness.

Keyphrases

modal formula first-order translation axiomatic translation reasonable assumption propositional modal logic non-trivial part inference problem translation principle simplified theory background theory theorem provers axiomatic translation principle triangular property ordered resolution original theory

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