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Thesis - Doctoral dissertation | @PhdThesis | Doktorarbeit

Author(s)*:Stuber, Jürgen
BibTeX citekey*:Stuber1999

Title, School
Title*:Superposition Theorem Proving for Commutative Algebraic Theories
School:Universität des Saarlandes
Type of Thesis*:Doctoral dissertation

Note, Abstract, Copyright
LaTeX Abstract:We develop special superposition calculi for first-order

theorem proving in the theories of abelian groups,
commutative rings, and modules and commutative algebras
over fields or over the ring of integers,
in order to make automated theorem proving in these theories more effective.
The calculi are refutationally complete
on arbitrary sets of ground clauses,
which in particular may contain additional function symbols.

The calculi are derived systematically from a representation
of the theory as a convergent term rewriting system.
Compared to standard superposition they have stronger ordering restrictions
so that inferences are applied only to maximal summands,
and they contain macro inference rules
that use theory axioms in a goal directed fashion.
In general we need additional inferences to handle critical peaks
between extended clauses.
We show that these are not needed for abelian groups and modules,
and that for commutative rings and commutative algebras
one such inference suffices for any pair of ground clauses.
To facilitate the construction of term orderings for such calculi
we introduce theory path orderings.

Keywords:Theorem Proving, Superposition
HyperLinks / References / URLs:
Download Access Level:Public
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Referees, Status, Dates
1. Referee:Harald Ganzinger
2. Referee:Christopher Lynch
Supervisor:Harald Ganzinger
Location of Lecture:MPI Saarbrücken
Date Kolloquium:25 May 2000
Chair Kolloquium:Gert Smolka

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

BibTeX Entry:
AUTHOR = {Stuber, J{\"u}rgen},
TITLE = {Superposition Theorem Proving for Commutative Algebraic Theories},
SCHOOL = {Universit{\"a}t des Saarlandes},
YEAR = {1999},
TYPE = {Doctoral dissertation}
MONTH = {December},

Entry last modified by Anja Becker, 07/08/2011
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Jürgen Stuber
09/05/2000 12:01:50 PM
Anja Becker
Uwe Brahm
Uwe Brahm
Uwe Brahm
Uwe Brahm
Edit Dates
08.07.2011 13:47:11
2007-07-02 11:09:53
2007-07-02 11:09:13
2007-07-02 10:57:54
2007-07-02 10:57:34