leanCoP: lean connection-based theorem proving

Otten, Jens; Bibel, Wolfgang

doi:10.1016/s0747-7171(03)00037-3

Cited by 66 publications

(61 citation statements)

References 11 publications

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“…The clausal connection calculus is successfully used for theorem proving in classical logic (see, e.g., [12]). A basic version of the connection calculus for first-order classical logic is presented in [19]. The calculus uses a connection-driven search strategy, i.e.…”

Section: A Prefixed Connection Calculusmentioning

confidence: 99%

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Clausal Connection-Based Theorem Proving in Intuitionistic First-Order Logic

Otten

2005

Lecture Notes in Computer Science

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Abstract. We present a clausal connection calculus for first-order intuitionistic logic. It extends the classical connection calculus by adding prefixes that encode the characteristics of intuitionistic logic. Our calculus is based on a clausal matrix characterisation for intuitionistic logic, which we prove correct and complete. The calculus was implemented by extending the classical prover leanCoP. We present some details of the implementation, called ileanCoP, and experimental results.

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Section: A Prefixed Connection Calculusmentioning

confidence: 99%

“…leanCoP is an implementation of the clausal connection calculus presented in Section 3 for classical first-order logic [19]. The reduction rule is applied before extension rules are applied and open branches are selected in a depth-first way.…”

Section: The Codementioning

confidence: 99%

Clausal Connection-Based Theorem Proving in Intuitionistic First-Order Logic

Otten

2005

Lecture Notes in Computer Science

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“…This however does not mean that such a compression is worthless. On the contrary, our experience shows that the performance may increase dramatically as we demonstrated through a comparison of leanTAP with leanCoP in [OB03]. In fact, the intuitionistic version of leanCoP, called ileanCoP, is now by a wide margin the fastest theorem prover in existence for intuitionistic rst-order logic [Ott05].…”

Section: Formal Systemsmentioning

confidence: 92%

Research Perspectives for Logic and Deduction

Bibel

2006

Reasoning, Action and Interaction in AI Theories and Systems

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The article is meant to be kind of the author's manifesto for the role of logic and deduction within Intellectics. Based on a brief analysis of this role the paper presents a number of proposals for future scienti c research along the various dimensions in the space of logical explorations. These dimensions include the range of possible applications including modelling intelligent behavior, the grounding of logic in some semantic context, the choice of an appropriate logic from the great variety of alternatives, then the choice of an appropriate formal system for representing the chosen logic, and nally the issue of developing the most e cient search strategies. Among the proposals is a conjecture concerning the treatment of cuts in proof search.

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“…The usage of signed formulae allows an elegant and uniform representation of the rules of the tableau calculus. The α-rules add formulae to a branch of a derivation, and the β-rules split a branch of the derivation [14] [12,24])). cnf(26,plain,(~big_q(X1)),inference(csr,[], [9,21])).…”

Section: Representing Derivations In the Tableau Calculusmentioning

confidence: 99%

Using the TPTP Language for Representing Derivations in Tableau and Connection Calculi

Otten

Sutcliffe

EPiC Series in Computing

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The TPTP language, developed within the framework of the TPTP library, allows the representation of problems and solutions in first-order and higher-order logic. Whereas the writing of solutions in resolution calculi is well documented and used, an appropriate representation of solutions in tableau or connection calculi using the TPTP syntax has not yet been specified. This paper describes how the TPTP language can be used to represent derivations and solutions in standard tableau, sequent and connection calculi for classical first-order logic.

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leanCoP: lean connection-based theorem proving

Cited by 66 publications

References 11 publications

Clausal Connection-Based Theorem Proving in Intuitionistic First-Order Logic

Clausal Connection-Based Theorem Proving in Intuitionistic First-Order Logic

Research Perspectives for Logic and Deduction

Using the TPTP Language for Representing Derivations in Tableau and Connection Calculi

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