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# Publications Master Template :: Thesis :: Hustadt, Ullrich

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## Thesis - Doctoral dissertation | @PhdThesis | Doktorarbeit

Title*: Resolution-Based Decision Procedures for Subclasses of First-Order Logic Universität des Saarlandes Doctoral dissertation March 1999

LaTeX 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.

1. Referee: Harald Ganzinger Hans Jürgen Ohlbach Harald Ganzinger Completed 8 November 1999

MPG Unit: Max-Planck-Institut für Informatik Programming Logics Group experts only MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat

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