Paramodulation and Theorem-Proving in First-Order Theories with Equality

Robinson, George; Wos, Larry

doi:10.1007/978-3-642-81955-1_19

Cited by 102 publications

(41 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Of course, many theorems of object theory do explicitly involve equality reasoning. For such problems, we have used (in addition to hyperresolution) paramodulation (Robinson and Wos 1969) and demodulation (Wos et al . 1967), which are mechanical rules for first-order equality reasoning that have been efficiently implemented in otter and prover9.…”

Section: Implementing Object Theory In Prover9mentioning

confidence: 99%

Steps Toward a Computational Metaphysics

Fitelson

Zalta

2007

J Philos Logic

View full text Add to dashboard Cite

In this paper, the authors describe their initial investigations in computational metaphysics. Our method is to implement axiomatic metaphysics in an automated reasoning system. In this paper, we describe what we have discovered when the theory of abstract objects is implemented in prover9 (a first-order automated reasoning system which is the successor to otter). After reviewing the second-order, axiomatic theory of abstract objects, we show (1) how to represent a fragment of that theory in prover9's firstorder syntax, and (2) how prover9 then finds proofs of interesting theorems of metaphysics, such as that every possible world is maximal. We conclude the paper by discussing some issues for further research.

show abstract

Section: Implementing Object Theory In Prover9mentioning

confidence: 99%

Steps Toward a Computational Metaphysics

Fitelson

Zalta

2007

J Philos Logic

View full text Add to dashboard Cite

show abstract

“…It is well-known that in first order logic the combination of resolution and paramodulation is complete, see [9]. This means that a formula is unsatisfiable if and only if the empty clause can be derived.…”

Section: Er Rulementioning

confidence: 99%

“…It is well-known that by the combination of paramodulation and resolution the empty clause can be deduced from unsatisfiable set of clauses [9]. However, earlier resolution-based proof systems for logics with equality can either generate numerous useless resolvents or generate clauses containing new literals.…”

Section: Introductionmentioning

confidence: 99%

A Proof System and a Decision Procedure for Equality Logic

Tveretina

Zantema

2004

LATIN 2004: Theoretical Informatics

View full text Add to dashboard Cite

Abstract. We give an approach for deciding satisfiability of equality logic formulas (E-SAT) in conjunctive normal form. Central in our approach is a single proof rule called equality resolution (ER). For this single rule we prove soundness and completeness. Based on this rule we propose a complete procedure for E-SAT and prove its correctness. Applying our procedure on a variation of the pigeon hole formula yields a polynomial complexity contrary to earlier approaches to E-SAT. Parts of the theory we developed for proving completeness of the proof rule and the algorithm are of interest in itself: we give techniques for removing clauses preserving unsatisfiability, and we give a general theorem globalizing a local commutation criterion for different proof systems.

show abstract

“…Simultaneous paramodulation is a re nement o f paramodulation | the main rule for handling equality introduced by Robinson & Wos 1969]. Paramodulation is de ned on clauses with free variables, and uses most general uni ers.…”

Section: More On Equational Logicmentioning

confidence: 99%