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MPI-INF RG1 Publications :: Thesis :: Waldmann, Uwe

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Thesis - Doctoral dissertation | @PhdThesis | Doktorarbeit

Author(s)*:Waldmann, Uwe
BibTeX citekey*:Waldmann1997

Title, School
Title*:Cancellative Abelian Monoids in Refutational Theorem Proving
School:Universität des Saarlandes
Type of Thesis*:Doctoral dissertation

Note, Abstract, Copyright
LaTeX Abstract:We present a constraint superposition calculus in which the axioms of cancellative abelian monoids and, optionally, further axioms (e.g., torsion-freeness) are integrated. Cancellative abelian monoids comprise abelian groups, but also such ubiquitous structures as the natural numbers or multisets. Our calculus requires neither extended clauses nor explicit inferences with the theory axioms. The number of variable overlaps is significantly reduced by strong ordering restrictions and powerful variable elimination techniques; in divisible torsion-free abelian groups, variable overlaps can even be avoided completely. Thanks to the equivalence of torsion-free cancellative and totally ordered abelian monoids, our calculus allows us to solve equational problems in totally ordered abelian monoids without requiring a detour via ordering literals.
Keywords:first-order theorem proving, paramodulation, superposition, algebra
HyperLinks / References / URLs:

Referees, Status, Dates
1. Referee:Harald Ganzinger
2. Referee:Michaël Rusinowitch
Supervisor:Harald Ganzinger
Date Kolloquium:28 July 1997
Chair Kolloquium:Jörg Siekmann

Audience:experts only
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BibTeX Entry:

AUTHOR = {Waldmann, Uwe},
TITLE = {Cancellative Abelian Monoids in Refutational Theorem Proving},
SCHOOL = {Universit{\"a}t des Saarlandes},
YEAR = {1997},
TYPE = {Doctoral dissertation}
MONTH = {July},

Entry last modified by Uwe Waldmann, 11/07/2006
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Uwe Waldmann
11/07/2006 11:46:09 AM

Uwe Waldmann
Uwe Waldmann

Edit Date
27/07/98 23:12:53
07/01/98 15:43:39