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A superposition oriented theorem prover

Laurent Fribourg
1985 Theoretical Computer Science  
The basic-theoretical result is the completeness of a strong restriction of paramodulation for locking resolution procedures.  ...  In addition, term simplification is incorporated in our procedure as well as subsumption.  ...  Gerard Huet and Guy Cousineau for numerous helpful discussions about theory as well as implementation.  ... 
doi:10.1016/0304-3975(85)90011-8 fatcat:gne5ztee4fba5e2aq6dnk4gllq

Using Decision Procedures to Accelerate Domain-Specific Deductive Synthesis Systems [chapter]

Jeffrey Van Baalen, Steven Roach
1999 Lecture Notes in Computer Science  
This paper describes a class of decision procedures that we have found useful for efficient, domain-specific deductive synthesis, and a method for integrating this type of procedure into a general-purpose  ...  We suggest that this is a large and interesting class of procedures and show how to integrate these procedures to accelerate a general-purpose theorem prover doing deductive synthesis.  ...  ACKNOWLEDGEMENTS Tom Pressburger read and helped with useful discussions of several drafts of this paper.  ... 
doi:10.1007/3-540-48958-4_4 fatcat:aczcxfbt6ra3lpitasxcut2tgi

Editorial

Leo Bachmair, Jieh Hsiang
1991 Journal of symbolic computation  
Kounalis & Rusinowitch suggest a notion of saturated set for Horn clauses and give sufficient conditions under which the use of saturated sets as rewrite rules provides a decision procedure for the word  ...  For instance, reduction orderings, a key concept in term rewriting, have been used to develop improved versions, both in terms of efficiency and completeness, of resolution/paramodulation type deduction  ...  Leo Bachmair and Jieh Hsiang  ... 
doi:10.1016/s0747-7171(08)80129-0 fatcat:524cajbdfze73njq3r7nknovmy

Equality Reasoning in Sequent-Based Calculi [chapter]

Anatoli Degtyarev, Andrei Voronkov
2001 Handbook of Automated Reasoning  
We consider the history of handling equality in sequent systems, methods based on rigid E-uni cation, paramodulation-based methods, the equality elimination method and equality reasoning in nonclassical  ...  Acknowledgements We thank Evgeny Dantsin, Thomas Eiter, Georg Gottlob, and Gabriel Kuper.  ...  can be used as a decision procedure for simultaneous rigid E-uni cation.  ... 
doi:10.1016/b978-044450813-3/50012-6 fatcat:fix4fevuazaojn7acaoonwg5du

Maximal Models and Refutation Completeness: Semidecision Procedures in Automatic Theorem Proving [chapter]

L. T. Wos, G. A. Robinson
1983 Automation of Reasoning  
In the example above, the procedure would consist of applying the various rules of II, resolution, factoring, and paramodulation, in some order until a contradiction was found.  ...  and. paramodulation with syllogism (or modus ponens) and substitution, respectively, is intended as motivation for, not as a precise characterization of, resolution and paramodulation.  ...  The following proof is also of example 12 but employing paramodulation as an additional inference rule. Proof. ?-• Rf(ee)e. 2. Rf(xf(yz))f(f(xy)z).  ... 
doi:10.1007/978-3-642-81955-1_33 fatcat:mmo22j33zzbifo6xdx65ym5r2u

Page 271 of Mathematical Reviews Vol. 43, Issue 1 [page]

1972 Mathematical Reviews  
In order to remedy this difficulty | several modifications of the resolution method have been | proposed. Of these the paramodulation strategy seems to | be particularly simple and efficient.  ...  and numerals are treated as constants.  ... 

Decision procedures and model building in equational clause logic

C. Fermuller
1998 Logic Journal of the IGPL  
It is shown that a combination of semantic resolution and ordered paramodulation provides a decision procedure for a large class PVD = g of clause sets with equality.  ...  This algorithm always terminates on clause sets in PVD = g and yields an appropriate model representation.  ...  Acknowledgements We like to thank the referees for their careful reading of preliminary versions of the paper and very helpful comments.  ... 
doi:10.1093/jigpal/6.1.17 fatcat:nnfoucmlmrg2lbjgta57rbussa

Page 1901 of Mathematical Reviews Vol. 57, Issue 5 [page]

1979 Mathematical Reviews  
Basic resolution is in- troduced as a breadth-first proof procedure.  ...  The equality relation with its syntax and *mantics is usually treated in resolution procedures as a built-in tation.  ... 

On Interpolation in Automated Theorem Proving

Maria Paola Bonacina, Moa Johansson
2014 Journal of automated reasoning  
We show by examples that the color-based approach cannot handle non-ground refutations by resolution and paramodulation/superposition.  ...  Interpolation finds application in program analysis, verification, and synthesis, for example, towards invariant generation.  ...  ,T n , and the T -decision procedure is obtained by combining by equality sharing [54] (cf. Chapter 10 of [14] for a more recent presentation) T i -decision procedures for 1 ≤ i ≤ n.  ... 
doi:10.1007/s10817-014-9314-0 fatcat:p4l7gjyafbbxrg3fbe6npjbwqm

On solving the equality problem in theories defined by Horn clauses

E. Paul
1986 Theoretical Computer Science  
Experimental results, and comparisons with other resolution/paramodulation-based methods, in particular the methods proposed by Lankford (1975) and Peterson (1983) , are included in the paper.  ...  Another application of the Knuth and Bendix procedure is the proof by induction (Musser, 1980; Huet-Hullot, 1982 and others).  ...  A classical inference rule in first-order predicate calculus with equality is 'paramodulation' which is defined as follows. Definition 1.7 (paramodulation).  ... 
doi:10.1016/0304-3975(86)90114-3 fatcat:5klyzsqzf5h4vi4pamasubukjy

On Deciding Satisfiability by Theorem Proving with Speculative Inferences

Maria Paola Bonacina, Christopher A. Lynch, Leonardo de Moura
2010 Journal of automated reasoning  
Inference systems with resolution and superposition are strong at reasoning with equalities, universally quantified variables, and Horn clauses.  ...  Termination is enforced by introducing additional axioms as hypotheses. The system detects any unsoundness introduced by these speculative inferences and recovers from it.  ...  The first-order engine alone was used as decision procedure, with no integration with an SMT-solver.  ... 
doi:10.1007/s10817-010-9213-y fatcat:lamj72ivrja4nni5yppx6wes6e

Modal Theorem Proving: An Equational Viewpoint

YVES AUFFRAY, PATRICE ENJALBERT
1992 Journal of Logic and Computation  
Different methods can be investigated and in this paper we consider Resolution. We may use Resolution with Paramodulation, or a combination of Resolution and Rewriting techniques.  ...  We propose a new method for automated theorem proving in first order modal logic.  ...  Or we can use a combination of Resolution and Rewriting techniques,j and this is what we present now. semi-decision procedure for the modal systems under consideration.  ... 
doi:10.1093/logcom/2.3.247 fatcat:ma7epmwvd5ec5bzz4xtlq7xzpa

Page 1911 of Mathematical Reviews Vol. , Issue 81E [page]

1981 Mathematical Reviews  
using input resolution and paramodulation in such a set of clauses will require, in the worst case, exponential time.  ...  Such a resignation is not taken as an error and is always strictly preferred to a wrong decision.  ... 

Integration of Equality Reasoning into the Disconnection Calculus [chapter]

Reinhold Letz, Gernot Stenz
2002 Lecture Notes in Computer Science  
We consider both saturation based and goal-oriented methods for equality handling.  ...  The disconnection tableau calculus represents a new confluent framework well suited for the integration of a large class of different methods for equality handling, as we demonstrate in this paper.  ...  We would like to thank Peter Baumgartner for his unrelenting questions and some fruitful discussions which helped to eliminate a number of errors that could be found in earlier versions of this paper.  ... 
doi:10.1007/3-540-45616-3_13 fatcat:ucm4vazjdfaghncx5cup5u3qhq

Automated theorem proving: mapping logic into AI

D W Loveland
1986 Proceedings of the ACM SIGART international symposium on Methodologies for intelligent systems -  
The A T P field, via resolution, has even provided the foundation for an exciting AI and database programming language, PROLOG.  ...  Logic can be defined as the formal study of reasoning; if we replace "formal" by "mechanical" we can place almost the entire set of methodologies used in the field of automated theorem proving (ATP) within  ...  Other decision procedures are augmentation of Pr.A. to include array functions, a decision procedure for part of set theory, and a very powerful and interesting new decision procedure for part of elementary  ... 
doi:10.1145/12808.12833 fatcat:badcsorb25gufhgobxumlws7me
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