(LIA) - Model Evolution with Linear Integer Arithmetic Constraints

Authors:
Peter Baumgartner;Alexander Fuchs;Cesare Tinelli
Affiliations:
National ICT Australia (NICTA),;The University of Iowa, USA;The University of Iowa, USA
Venue:
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Year:
2008

Citing 7
Cited 7

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Abstract

Many applications of automated deduction require reasoning modulo some form of integer arithmetic. Unfortunately, theory reasoning support for the integers in current theorem provers is sometimes too weak for practical purposes. In this paper we propose a novel calculus for a large fragment of first-order logic modulo Linear Integer Arithmetic (LIA) that overcomes several limitations of existing theory reasoning approaches. The new calculus -- based on the Model Evolution calculus, a first-order logic version of the propositional DPLL procedure -- supports restricted quantifiers, requires only a decision procedure for LIA-validity instead of a complete LIA-unification procedure, and is amenable to strong redundancy criteria. We present a basic version of the calculus and prove it sound and (refutationally) complete.