Invited Talk: Rewrite-Based Deduction and Symbolic Constraints
Building a state-of-the-art theorem prover requires the combination of at least three main ingredients: good theory, clever heuristics, and the necessary engineering skills to implement it all in an efficient way. Progress in each of these ingredients interacts in different ways.
On the one hand, new theoretical insights replace heuristics by more precise and effective techniques. For example, the completeness proof of basic paramod- ulation [NR95,BGLS95] shows why no inferences below Skolem functions are needed, as conjectured by McCune in [McC90]. Regarding implementation tech- niques, ad-hoc algorithms for procedures like demodulation or subsumption are replaced by efficient, re-usable, general-purpose indexing data structures for which the time and space requirements are well-known.
KeywordsTheorem Prove Ground Instance Automate Deduction Empty Clause 14th IEEE Symposium
Unable to display preview. Download preview PDF.
- BG98.Leo Bachmair and Harald Ganzinger. Equational reasoning in saturationbased theorem proving. In W. Bibel and P. Schmitt, editors, Automated Deduction: A Basis for Applications. Kluwer, 1998.Google Scholar
- BGNR99.Miquel Bofill, Guillem Godoy, Robert Nieuwenhuis, and Albert Rubio. Paramodulation with non-monotonic orderings. In 14th IEEE Symposium on Logic in Computer Science (LICS), Trento, Italy, July 2–5, 1999.Google Scholar
- BGW93a.Leo Bachmair, Harald Ganzinger, and Uwe Waldmann. Set constraints are the monadic class. In Eighth Annual IEEE Symposium on Logic in Computer Science, pages 75–83, Montreal, Canada, June 19-23, 1993. IEEE Computer Society Press.Google Scholar
- BGW93b.Leo Bachmair, Harald Ganzinger, and Uwe Waldmann. Superposition with simplification as a decision procedure for the monadic class with equality. In 3rd Kurt Gödel Colloquium: Computational Logic and Proof Theory, LNCS 713, pages 83–96. SpringerVerlag, 1993.Google Scholar
- BS99.Franz Baader and Wayne Snyder. Unification theory. In J.A. Robinson and A. Voronkov, editors, Handbook of Automated Reasoning. Elsevier Science Publishers (to appear), 1999.Google Scholar
- CNNR98.Hubert Comon, Paliath Narendran, Robert Nieuwenhuis, and Michael Rusinowitch. Decision problems in ordered rewriting. In 13th IEEE Symposium on Logic in Computer Science (LICS), pages 410–422, Indianapolis, USA, June 27-30, 1998.Google Scholar
- GdN99.Harald Ganzinger and Hans de Nivelle. A superposition decision procedure for the guarded fragment with equality. In 14th IEEE Symposium on Logic in Computer Science (LICS), Trento, Italy, July 2–5, 1999.Google Scholar
- GMV99.Harald Ganzinger, Christoph Meyer, and Margus Veanes. The two-variable guarded fragment with transitive relations. In 14th IEEE Symposium on Logic in Computer Science (LICS), Trento, Italy, July 2–5, 1999.Google Scholar
- GNN95.Harald Ganzinger, Robert Nieuwenhuis, and Pilar Nivela. The Saturate System, 1995. Software and documentation available at: http://www.mpi-sb.mpg.de/SATURATE/Saturate.html.
- GS92.Harald Ganzinger and Jürgen Stuber. Inductive theorem proving by consistency for first-order clauses (extended abstract). In M[ichaël] Rusinowitch and J[ean-]L[uc] Rémy, editors, The Third InternationalWorkshop on Conditional Term Rewriting Systems, Extended Abstracts, pages 130–135, Pontá-Mousson, France, July 8-10, 1992. Centre de Recherche en Informatique de Nancy and INRIA Lorraine.Google Scholar
- JMW98.Florent Jacquemard, Christoph Meyer, and Christoph Weidenbach. Unification in extensions of shallow equational theories. In Proceedings of the 9th International Conference on Rewriting Techniques and Applications, RTA-9, volume to appear, Tsukuba, Japan, 1998. Springer.Google Scholar
- LS98.C. Lynch and C. Scharff. Basic completion with E-cycle simplification. In Artificial Intelligence and Symbolic Computation, lncs 1476, pages 121–121, 1998.Google Scholar
- McC90.William McCune. Skolem functions and equality in automated deduction. In Tom Dietterich and William Swartout, editors, Proceedings of the 8th National Conference on Artificial Intelligence, pages 246–251, Hynes Convention Centre?, July 29-August 3 1990. MIT Press.Google Scholar
- NR99a.Robert Nieuwenhuis and Jos*#x00E9; Miguel Rivero. Solved forms for path ordering constraints. In P. Narendran and M. Rusinowitch, editors, Tenth International Conference on Rewriting Techniques and Applications (RTA), LNCS, Trento, Italy, July 2-4, 1999. Springer-Verlag.Google Scholar
- NR99b.Robert Nieuwenhuis and Albert Rubio. Paramodulation-based theorem proving. In J.A. Robinson and A. Voronkov, editors, Handbook of Automated Reasoning. Elsevier Science Publishers (to appear), 1999.Google Scholar
- Vig94.Laurent Vigneron. Associative Commutative Deduction with constraints. In Alan Bundy, editor, 12th International Conference on Automated Deduction, LNAI 814, pages 530–544, Nancy, France, June 1994. Springer-Verlag.Google Scholar