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  Resolution-Based Decision Procedures for Subclasses of First-Order Logic

Hustadt, U. (1999). Resolution-Based Decision Procedures for Subclasses of First-Order Logic. PhD Thesis, Universität des Saarlandes, Saarbrücken.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-3545-0 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0024-AD10-3
Genre: Thesis

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 Creators:
Hustadt, Ullrich1, Author           
Affiliations:
1Programming Logics, MPI for Informatics, Max Planck Society, ou_40045              

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 Abstract: This thesis studies decidable fragments of first-order logic which are relevant to the field of non-classical logic and knowledge representation. We show that refinements of resolution based on suitable liftable orderings provide decision procedures for the subclasses $\CE^+$, $\overline{\mathrm{K}}$, and $\overline{\mathrm{DK}}$ of first-order logic. By the use of semantics-based translation methods we can embed the description logic $\mathcal{ALCR}$ and extensions of the basic modal logic $\mathsf{K}$ into fragments of first-order logic. We describe various decision procedures based on ordering refinements and selection functions for these fragments and show that a polynomial simulation of tableaux-based decision procedures for these logics is possible. In the final part of the thesis we develop a benchmark suite and perform an empirical analysis of various modal theorem provers.

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Language(s): eng - English
 Dates: 2010-03-121999-11-081999
 Publication Status: Issued
 Pages: -
 Publishing info: Saarbrücken : Universität des Saarlandes
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 519730
Other: Local-ID: C1256104005ECAFC-3C4F8D74A0A484FFC125675A005CF7E5-Hustadt1999
 Degree: PhD

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