Paramodulation with Built-In Abelian Groups

Authors:
Guillem Godoy;Robert Nieuwenhuis
Affiliations:
-;-
Venue:
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Year:
2000

Citing 18
Cited 4

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

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

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Superposition with completely built-in Abelian groups

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Constraint Solving for Term Orderings Compatible with Abelian Semigroups, Monoids and Groups

Constraints

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Abstract

A new technique is presented for superposition with first-order clauses with built-in abelian groups (AG). Compared with previous approaches, it is simpler, and no inferences with the AG axioms or abstraction rules are needed. Furthermore, AG-unification is used instead of the computationally more expensive unification modulo associativity and commutativity. Due to the simplicity and restrictiveness of our inference system, its compatibility with redundancy notions and constraints, and the fact that standard term orderings like RPO can be used, we believe that our technique will become the method of choice for practice, as well as a basis for new theoretical developments like logic-based complexity and decidability analysis.