ME(LIA) — model evolution with linear integer arithmetic constraints
Authors
NICTA
The University of Iowa
USA
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 \emph{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.
BibTeX Entry
@inproceedings{Baumgartner_FT_08, month = nov, paperurl = {https://ts.data61.csiro.au/publications/nicta_full_text/1102.pdf}, publisher = {Springer}, booktitle = {Proceedings of the 15thInternational Conference on Logic for Programming, Artificial Intelligence and Reasoning}, editor = {{Iliano Cervesato, Helmut Veith, Andrei Voronkov}}, author = {Baumgartner, Peter and Fuchs, Alexander and Tinelli, Cesare}, year = {2008}, pages = {258--273}, title = {{ME}({LIA}) --- Model Evolution With Linear Integer Arithmetic Constraints}, address = {Doha, Qatar} }