Proof Normalization for Resolution and Paramodulation

We prove the refutation completeness of restricted versions of resolution and paramodulation for first-order predicate logic with equality. Furthermore, we show that these inference rules can be combined with various deletion and simplification rules, such as rewriting, without compromising refutation completeness. The techniques employed in the completeness proofs are based on proof normalization and proof orderings.

[1]  L. Wos,et al.  Maximal Models and Refutation Completeness: Semidecision Procedures in Automatic Theorem Proving* , 1983 .

[2]  Deepak Kapur,et al.  First-Order Theorem Proving Using Conditional Rewrite Rules , 1988, CADE.

[3]  J. A. Robinson,et al.  A Machine-Oriented Logic Based on the Resolution Principle , 1965, JACM.

[4]  T. C. Brown.  A structured design-method for specialized proof procedures , 1975 .

[5]  William H. Joyner.  Resolution Strategies as Decision Procedures , 1976, JACM.

[6]  Richard C. T. Lee,et al.  Symbolic logic and mechanical theorem proving , 1973, Computer science classics.

[7]  James R. Slagle,et al.  Automated Theorem-Proving for Theories with Simplifiers Commutativity, and Associativity , 1974, JACM.

[8]  Larry Wos,et al.  The Concept of Demodulation in Theorem Proving , 1967, JACM.

[9]  Nachum Dershowitz,et al.  Termination of Rewriting , 1987, J. Symb. Comput..

[10]  Donald Michie,et al.  Machine Intelligence 4 , 1970 .

[11]  Michaël Rusinowitch.  Theorem-Proving with Resolution and Superposition: An Extension of the Knuth and Bendic Procedure to a Complete Set of Inference Rules , 1988, FGCS.

[12]  Harald Ganzinger.  A Completion Procedure for Conditional Equations , 1987, CTRS.

[13]  Nachum Dershowitz,et al.  Orderings for Equational Proofs , 1986, LICS.

[14]  D. Knuth,et al.  Simple Word Problems in Universal Algebras , 1983 .

[15]  Zohar Manna,et al.  Proving termination with multiset orderings , 1979, CACM.

[16]  Daniel Brand,et al.  Proving Theorems with the Modification Method , 1975, SIAM J. Comput..

[17]  Harald Ganzinger,et al.  A Completion Procedure for Conditional Equations , 1988, J. Symb. Comput..

[18]  H. Brown,et al.  Computational Problems in Abstract Algebra , 1971 .

[19]  Gerald E. Peterson,et al.  A Technique for Establishing Completeness Results in Theorem Proving with Equality , 1980, SIAM J. Comput..

[20]  Nachum Dershowitz,et al.  Orderings for term-rewriting systems , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[21]  Michaël Rusinowitch,et al.  A New Method for Establishing Refutational Completeness in Theorem Proving , 1986, CADE.

[22]  Leo Bachmair.  Proof methods for equational theories , 1987 .

[23]  L. Wos,et al.  Paramodulation and Theorem-Proving in First-Order Theories with Equality , 1983 .