Automated theorem proving

Plaisted, David A.

doi:10.1002/wcs.1269

Cited by 5 publications

(3 citation statements)

References 68 publications

(58 reference statements)

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“…Superposition dates back to the late 1960's [112,82]; inference systems of this kind appear in many papers (e.g., [72,113,10,34]); several general treatments or surveys with additional references and historic background are available (e.g., [54,106,19,55,104,22,87,107,21]). Superposition-based strategies yield decision procedures for several fragments of first-order logic (e.g., [63,59] and [58] for a survey), and are implemented in many theorem-provers including, in alphabetical order, E [114], Spass [124], Vampire [84], Waldmeister [70], and Zipperposition [48].…”

Section: Superposition-based Decision Proceduresmentioning

confidence: 99%

Theory Combination: Beyond Equality Sharing

Bonacina

Fontaine

Ringeissen

et al. 2019

Lecture Notes in Computer Science

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Satisfiability is the problem of deciding whether a formula has a model. Although it is not even semidecidable in first-order logic, it is decidable in some first-order theories or fragments thereof (e.g., the quantifier-free fragment). Satisfiability modulo a theory is the problem of determining whether a quantifier-free formula admits a model that is a model of a given theory. If the formula mixes theories, the considered theory is their union, and combination of theories is the problem of combining decision procedures for the individual theories to get one for their union. A standard solution is the equality-sharing method by Nelson and Oppen, which requires the theories to be disjoint and stably infinite. This paper surveys selected approaches to the problem of reasoning in the union of disjoint theories, that aim at going beyond equality sharing, including: asymmetric extensions of equality sharing, where some theories are unrestricted, while others must satisfy stronger requirements than stable infiniteness; superposition-based decision procedures; and current work on conflict-driven satisfiability (CDSAT).

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Section: Superposition-based Decision Proceduresmentioning

confidence: 99%

Theory Combination: Beyond Equality Sharing

Bonacina

Fontaine

Ringeissen

et al. 2019

Lecture Notes in Computer Science

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“…Chou, Gao and Zhang [6] developed 'area method' which is able to produce short and readable proofs of geometric theorems. In his paper, David A. Plaisted [7] reviewed different techniques of ATP. Among these techniques are: propositional proof procedures [8,9], first order logic [10], clause linking [11], instance-based procedures [12], model evolution [13], modulo theories [14], unification and resolution [15] and combined systems [16,17].…”

Section: Introductionmentioning

confidence: 99%

GraATP: A graph theoretic approach for Automated Theorem Proving in plane geometry

Mahmud

Shatabda

Huda

2014

The 8th International Conference on Software, Knowledge, Information Management and Applications (SKIMA 2014)

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Automated Theorem Proving (ATP) is an established branch of Artificial Intelligence. The purpose of ATP is to design a system which can automatically figure out an algorithm either to prove or disprove a mathematical claim, on the basis of a set of given premises, using a set of fundamental postulates and following the method of logical inference. In this paper, we propose GraATP, a generalized framework for automated theorem proving in plane geometry. Our proposed method translates the geometric entities into nodes of a graph and the relations between them as edges of that graph. The automated system searches for different ways to reach the conclusion for a claim via graph traversal by which the validity of the geometric theorem is examined.

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“…All methods are described in expository style, and the interested reader may find the technical details in the references. Background material is available in previous surveys, such as [67,68,18,59,69] for theorem-proving strategies, [19] for decision procedures based on theorem-proving strategies or their integration with SMT-solvers, and books such as [70,17,76].…”

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confidence: 99%

On First-Order Model-Based Reasoning

Bonacina

Furbach

Sofronie-Stokkermans

2015

Lecture Notes in Computer Science

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Reasoning semantically in first-order logic is notoriously a challenge. This paper surveys a selection of semantically-guided or model-based methods that aim at meeting aspects of this challenge. For first-order logic we touch upon resolution-based methods, tableaux-based methods, DPLL-inspired methods, and we give a preview of a new method called SGGS, for Semantically-Guided Goal-Sensitive reasoning. For first-order theories we highlight hierarchical and locality-based methods, concluding with the recent Model-Constructing satisfiability calculus.Comment: In Narciso Marti-Oliet, Peter Olveczky, and Carolyn Talcott (Eds.), "Logic, Rewriting, and Concurrency: Essays in Honor of Jose Meseguer" Springer, Lecture Notes in Computer Science 9200, September 2015, 24 page

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Automated theorem proving

Cited by 5 publications

References 68 publications

Theory Combination: Beyond Equality Sharing

Theory Combination: Beyond Equality Sharing

GraATP: A graph theoretic approach for Automated Theorem Proving in plane geometry

On First-Order Model-Based Reasoning

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