On theorem-proving in Horn theories with built-in algebras
We present a semi-decision procedure to prove ground theorems in Horn theories with built-in algebras. This is a maximal-unit-strategy based method, i.e in all our inference rules at least one of the premises clauses is an unit one. As in , constraint formalism is used as well; but more general specifications are studied. To limit the search space, an rpo-like ordering is used. Neither unification nor matching modulo the predefined algebra is needed. As a result, thanks to available constraint solvers on finite domains, naturals, integers, finite sets,... our method is easy to implement and it is actually efficient to prove ground theorems.
Unable to display preview. Download preview PDF.
- 1.Anantharaman, S., Andrianarivelo, N.: A semi-decision procedure in Horn Theories. technical report, Laboratoire d'Informatique Fondamentale d'Orléans-Laboratoire de Recherche en Informatique d'Orsay, (1991)Google Scholar
- 2.Bousdira, W., Andrianarivelo, N.: A rewrite-based strategy for theorem proving in first order logic with equality and ordering constraints. technical report, Laboratoire d'Informatique Fondamentale d'Orléans, (1994), 94-4Google Scholar
- 3.Avenhaus, J., Becker, K.: Conditional Rewriting modulo a Built-in Algebra. technical report Number 11, Universitat Kaiserslautern, West Germany, (1992)Google Scholar
- 4.Avenhaus, J., Becker, K.: Operational Specifications with Built-Ins. 7th Symposium on Theoretical Aspects of Computer Science, Caen, France, (1994), 263–274Google Scholar
- 5.Dershowitz, N.: Corrigendum to Termination of Rewriting. In Journal of Symbolic Computation, Vol. 4, 409–410Google Scholar
- 6.Dershowitz, N.: A maximal-literal strategy for Horn Clauses. 2nd International Workshop on Conditional Term Rewriting Systems, Montreal, Canada, (1990), 143–154Google Scholar
- 7.Ganzinger, H.: Ground Term Confluence in Parametric Conditional Equational Specifications. 4th annual Sympoisum on Theoretical Aspects of Computer Science, Passau, RFA, (1987), Vol. 247, 286–298Google Scholar
- 8.Kirchner, C. and Kirchner, H. and Rusinowitch, M.: Deduction with Symbolic Constraints. Revue Française d'Intelligence Artificielle, (1990), Vol. 4, Number. 3, 9–52Google Scholar
- 9.Kounalis, E., Rusinowitch, M.: Mechanizing Inductive Reasoning. EATCS Bulletin, Vol. 41, (1990), 216–226Google Scholar
- 10.Smolka, G.: Logic Programming over Polymorphically Order-Sorted Types. PHD Thesis, Universitat Kaiserslautern, West Germany, (1989)Google Scholar
- 11.Vorobyov, S.G.: Conditional Rewrite Rules Systems with Built-in Arithmetic and Induction. 3rd International Conference on Rewriting Techniques and Applications, Chapel Hill, North California, (1989), 492–512Google Scholar