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# Publications Master Template :: Thesis :: Schmidt, Renate A.

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## Thesis - Doctoral dissertation | @PhdThesis | Doktorarbeit

Author(s)*: Schmidt, Renate A. Schmidt97d English

Title*: Optimised Modal Translation and Resolution Universität des Saarlandes Doctoral dissertation November 1997

LaTeX Abstract: This thesis studies the optimised functional translation of propositional modal logics to first-order logic, and first-order resolution as a means for realising modal reasoning. The optimised functional translation maps modal logics to a lattice of clausal logics, called path logics. The general apparatus of inference for path logics is theory resolution. We show that satisfiability in basic path logic and certain extensions can be decided by resolution and condensing without requiring additional refinement strategies. We propose an improved theory unification algorithm for \textit{S4}, and we present a calculus of ordered $E$-resolution with normalisation. We show also that some essentially second-order modal logics convert to path logics, which can be exploited for accomodating inference for modal logics with numerical quantifiers in a calculus of resolution and simple arithmetic. automated theorem proving, correspondence problem, E-resolution, graded modal logic, modal logics, optimised functional translation, ordered resolution, quantifier elimination, resolution decision procedures, theorem proving for non-classical logics, theory resolution, translation methods, E-unification http://www.mpi-sb.mpg.de/~schmidt/publications/PhD.ps.gz

1. Referee: Ohlbach, Hans Jürgen Ganzinger, Harald Ohlbach, Hans Jürgen Completed 11 March 1997 Wilhelm, Reinhard

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

BibTeX Entry:

@PHDTHESIS{Schmidt97d,
AUTHOR = {Schmidt, Renate A.},
TITLE = {Optimised Modal Translation and Resolution},
SCHOOL = {Universit{\"a}t des Saarlandes},
YEAR = {1997},
TYPE = {Doctoral dissertation}
MONTH = {November},
}