A Maximal-Literal Unit Strategy for Horn Clauses

A new positive-unit theorem-proving procedure for equational Horn clauses is presented. It uses a term ordering to restrict paramodulation to potentially maximal sides of equations. Completeness is shown using proof orderings.

[1]  L. Bachmair.  Canonical Equational Proofs , 1991, Progress in Theoretical Computer Science.

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

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

[4]  Nachum Dershowitz.  Orderings for Term-Rewriting Systems , 1979, FOCS.

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

[6]  Lawrence J. Henschen,et al.  Unit Refutations and Horn Sets , 1974, JACM.

[7]  Michaël Rusinowitch,et al.  On Word Problems in Equational Theories , 1987, ICALP.

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

[9]  G. Sivakumar,et al.  Proofs and computations in conditional equational theories , 1990 .

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

[11]  Nachum Dershowitz,et al.  Completion Without Failure11This research was supported in part by the National Science Foundation under grants DCR 85–13417 and DCR 85–16243. , 1989 .

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

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

[14]  Ulrich Furbach.  Oldy but Goody Paramodulation Revisited , 1987, GWAI.

[15]  Nachum Dershowitz,et al.  Proof-theoretic techniques for term rewriting theory , 1988, [1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science.

[16]  Stéphane Kaplan,et al.  Simplifying Conditional Term Rewriting Systems: Unification, Termination and Confluence , 1987, J. Symb. Comput..

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

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

[19]  E. Paul.  On Solving the Equality Problem in Theories Defined by Horn Clauses , 1986, Theor. Comput. Sci..

[20]  Hubert Comon-Lundh.  Solving Inequations in Term Algebras (Extended Abstract) , 1990, LICS.

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

[22]  Harald Ganzinger,et al.  On Restrictions of Ordered Paramodulation with Simplification , 1990, CADE.

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

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

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

[26]  Nachum Dershowitz,et al.  A Rationale for Conditional Equational Programming , 1990, Theor. Comput. Sci..

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

[28]  Maurice Nivat,et al.  Resolution of Equations in Algebraic Structures , 1989 .