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

Robinson, G.; Wos, L.

doi:10.1142/9789812813411_0008

Cited by 25 publications

(29 citation statements)

References 5 publications

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“…The paramodulation rule for equality is defined as follows:

\frac{\begin{matrix} C ([], t), r = s \lor D, r and t are unifiable, \\ t is not normala variable, Unify (() r, t) is θ \end{matrix}}{Cθ [italicsθ] \lor Dθ} .

…”

Section: Equalitymentioning

confidence: 99%

Automated theorem proving

Plaisted

2014

WIRES Cognitive Science

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Automated theorem proving is the use of computers to prove or disprove mathematical or logical statements. Such statements can express properties of hardware or software systems, or facts about the world that are relevant for applications such as natural language processing and planning. A brief introduction to propositional and first-order logic is given, along with some of the main methods of automated theorem proving in these logics. These methods of theorem proving include resolution, Davis and Putnam-style approaches, and others. Methods for handling the equality axioms are also presented. Methods of theorem proving in propositional logic are presented first, and then methods for first-order logic. WIREs Cogn Sci 2014, 5:115-128. doi: 10.1002/wcs.1269 CONFLICT OF INTEREST: The authors has declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website.

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“…The paramodulation rule for equality is defined as follows:

\frac{\begin{matrix} C ([], t), r = s \lor D, r and t are unifiable, \\ t is not normala variable, Unify (() r, t) is θ \end{matrix}}{Cθ [italicsθ] \lor Dθ} .

…”

Section: Equalitymentioning

confidence: 99%

Automated theorem proving

Plaisted

2014

WIRES Cognitive Science

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“…Many problems are computationally inefficient to solve by relying on a single inference rule such as resolution. However resolution has led to the development of inference rules that are effective in these situations, such as hyper-resolution (Robinson, 1965a), unit resolution (Henschen and Wos, 1974) and paramodulation (Robinson and Wos, 1981). In the future it would be interesting to construct a connectionist inference system using distributed representations to perform these inference rules.…”

Section: ( Insert Figure 13 Here )mentioning

confidence: 99%

Connectionist inference models

Browne

Sun

2001

Neural Networks

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The performance of symbolic inference tasks has long been a challenge to connectionists. In this paper, we present an extended survey of this area. Existing connectionist inference systems are reviewed, with particular reference to how they perform variable binding and rule-based reasoning and whether they involve distributed or localist representations. The benefits and disadvantages of different representations and systems are outlined, and conclusions drawn regarding the capabilities of connectionist inference systems when compared with symbolic inference systems or when used for cognitive modelling.

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“…At Argonne, Larry Wos and George Robinson continued theoretical work on proof procedures, for example, combining unification (see sidebar on page 10) with an inference rule for equality to yield the powerful rules of "demodulation" 83 and "paramodulation." 84 To these theoretical advances were added continuous practical improvements (focusing on matters such as indexing and the storage and retrieval of clauses), notably by Ross Overbeek and Ewing Lusk.…”

Section: Automated Theorem Proving After Resolutionmentioning

confidence: 99%