Uniform Derivation of Decision Procedures by Superposition

We show how a well-known superposition-based inference system for first-order equational logic can be used almost directly as a decision procedure for various theories including lists, arrays, extensional arrays and combinations of them. We also give a superposition-based decision procedure for homomorphism.

[1]  Ricardo Caferra,et al.  Decision Procedures Using Model Building Techniques , 1995, CSL.

[2]  Herbert B. Enderton,et al.  A mathematical introduction to logic , 1972 .

[3]  Ashish Tiwari,et al.  Abstract Congruence Closure and Specializations , 2000, CADE.

[4]  Michaël Rusinowitch.  Theorem-Proving with Resolution and Superposition , 1991, J. Symb. Comput..

[5]  Charles Gregory Nelson,et al.  Techniques for program verification , 1979 .

[6]  Donald E. Knuth,et al.  Simple Word Problems in Universal Algebras††The work reported in this paper was supported in part by the U.S. Office of Naval Research. , 1970 .

[7]  I. V. Ramakrishnan,et al.  Congruence Closure Modulo Associativity and Commutativity , 2000, FroCoS.

[8]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[9]  Harald Ganzinger,et al.  Rewrite-Based Equational Theorem Proving with Selection and Simplification , 1994, J. Log. Comput..

[10]  Greg Nelson,et al.  Simplification by Cooperating Decision Procedures , 1979, TOPL.

[11]  Claude Marché.  The Word Problem of ACD-Ground Theories is Undecidable , 1992, Int. J. Found. Comput. Sci..

[12]  Alexander Leitsch.  Deciding Horn Classes by Hyperresolution , 1989, CSL.

[13]  Greg Nelson,et al.  Fast Decision Procedures Based on Congruence Closure , 1980, JACM.

[14]  Michaël Rusinowitch,et al.  On Word Problems in Horn Theories , 1988, J. Symb. Comput..

[15]  David L. Dill,et al.  A decision procedure for an extensional theory of arrays , 2001, Proceedings 16th Annual IEEE Symposium on Logic in Computer Science.

[16]  Alessandro Armando,et al.  A Practical Extension Mechanism for Decision Procedures: the Case Study of Universal Presburger Arithmetic , 2001, J. Univers. Comput. Sci..

[17]  Albert Rubio,et al.  Paramodulation-Based Theorem Proving , 2001, Handbook of Automated Reasoning.

[18]  Jean-Pierre Jouannaud,et al.  Rewrite Systems , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.