Cancellative abelian monoids and related structures in refutational theorem proving (Part I)

Authors:
Uwe Waldmann
Affiliations:
MPI für Informatik, Stuhlsatzenhausweg 85, 66123 Saarbrücken, Germany
Venue:
Journal of Symbolic Computation
Year:
2002

Citing 23
Cited 2

Termination of rewriting systems by polynomial interpretations and its implementation

Science of Computer Programming
Integrating decision procedures into heuristic theorem provers: a case study of linear arithmetic

Machine intelligence 11
Using forcing to prove completeness of resolution and paramodulation

Journal of Symbolic Computation
Theorem-proving with resolution and superposition

Journal of Symbolic Computation
Rewrite systems

Handbook of theoretical computer science (vol. B)
Proving refutational completeness of theorem-proving strategies: the transfinite semantic tree method

Journal of the ACM (JACM)
Termination and completion modulo associativity, commutativity and identity

Theoretical Computer Science - Selected papers on theoretical issues of design and implementation of symbolic computation systems
A general refutational completeness result for an inference procedure based on associative-commutative unification

Journal of Symbolic Computation
Complexity of unification problems with associative-commutative operators

Journal of Automated Reasoning
First-order logic and automated theorem proving (2nd ed.)

First-order logic and automated theorem proving (2nd ed.)
Normalized rewriting: an alternative to rewriting modulo a set of equations

Journal of Symbolic Computation
Automated Theorem-Proving for Theories with Simplifiers Commutativity, and Associativity

Journal of the ACM (JACM)
A Practical Decision Procedure for Arithmetic with Function Symbols

Journal of the ACM (JACM)
Complete Sets of Reductions for Some Equational Theories

Journal of the ACM (JACM)
Cancellative abelian monoids and related structures in refutational theorem proving (part II)

Journal of Symbolic Computation
Superposition Theorem Proving for Albelian Groups Represented as Integer Modules

RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
AC-Complete Unification and its Application to Theorem Proving

RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
First-Order Theorem Proving Using Conditional Rewrite Rules

Proceedings of the 9th International Conference on Automated Deduction
AC-Superposition with Constraints: No AC-Unifiers Needed

CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Associative-Commutative Deduction with Constraints

CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Theorem Proving in Cancellative Abelian Monoids (Extended Abstract)

CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Associative-Commutative Superposition

CTRS '94 Proceedings of the 4th International Workshop on Conditional and Typed Rewriting Systems
Paramodulation with Built-In Abelian Groups

LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science

Cancellative abelian monoids and related structures in refutational theorem proving (part II)

Journal of Symbolic Computation
Combinable Extensions of Abelian Groups

CADE-22 Proceedings of the 22nd International Conference on Automated Deduction

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present superposition calculi in which the axioms of cancellative Abelian monoids and, optionally, the torsion-freeness axiom are integrated. Cancellative Abelian monoids comprise Abelian groups, but also such ubiquitous structures as the natural numbers or multisets. Our calculi require neither extended clauses nor explicit inferences with the theory axioms. Compared with AC-superposition calculi, the number of variable overlaps is significantly reduced by strong ordering restrictions.