Results 1 - 10 of 12

First-order resolution for CTL

by Lan Zhang, Ullrich Hustadt, Clare Dixon
"... In this paper, we describe an approach to theorem proving in Computational Tree Logic (CTL) which utilises classical first-order resolution techniques. Since there already exist a lot of well-developed first-order logic theorem provers, reusing those techniques provides great benefit for solving oth ..."
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In this paper, we describe an approach to theorem proving in Computational Tree Logic (CTL) which utilises classical first-order resolution techniques. Since there already exist a lot of well-developed first-order logic theorem provers, reusing those techniques provides great benefit for solving

First Order Logic in Semantic Tableau and VAMPIRE

by Rania Mahmoud, Ismail Amr Ismail, Ahmed Fahim
"... Semantic tableau is a proof system used to prove the validity of a formula using Prolog, it can also be used to prove if a formula is a logic consequence of a set of formulas. Semantic tableau is used in both propositional and predicate logic. Tableau is a disjunction normal form. VAMPIRE is a high ..."
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high-performance theorem prover for first-order logic with or without equality. In this paper, a modified version of semantic tableau is presented, experimental results proved the validity of modified tableau. Also, it is shown how Tableau proof system and VAMPIRE can be used in predicate logic.

Breeding Theorem Proving Heuristics with Genetic Algorithms

by Stephan Schulz
"... First-order theorem provers have to search for proofs in an infinite space of possible derivations. Proof search heuristics play a vital role for the practical performance of these systems. In the current generation of saturation-based theorem provers like SPASS, E, Vampire or Prover 9, one of the m ..."
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First-order theorem provers have to search for proofs in an infinite space of possible derivations. Proof search heuristics play a vital role for the practical performance of these systems. In the current generation of saturation-based theorem provers like SPASS, E, Vampire or Prover 9, one

Using Vampire in Soundness Proofs of Type Systems

by Sylvia Grewe, Sebastian Erdweg, Mira Mezini, Tu Darmstadt
"... Type systems for programming languages shall detect type errors in programs before runtime. To ensure that a type system meets this requirement, its soundness must be formally verified. We aim at automating soundness proofs of type systems to facilitate the development of sound type systems for doma ..."
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provers such as Vampire with automated proof strategies specific to type systems. In this paper, we describe how we encode type soundness proofs in first-order logic using TPTP. We show how we use Vampire to prove the soundness of type systems for the simply-typed lambda calculus and for parts of a typed

An Ordered Theory Resolution Calculus for Hybrid Reasoning in First-order Extensions of Description Logic

by Scott Sanner, Sheila Mcilraith
"... Systems for hybrid reasoning with first-order logic (FOL) extensions of description logic (DL) date back at least 20 years and are enjoying a renewed interest in the context of recent FOL extensions of OWL DL for the Semantic Web. However, current systems for reasoning with such languages can only h ..."
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Systems for hybrid reasoning with first-order logic (FOL) extensions of description logic (DL) date back at least 20 years and are enjoying a renewed interest in the context of recent FOL extensions of OWL DL for the Semantic Web. However, current systems for reasoning with such languages can only

An Ordered Theory Resolution Calculus for Hybrid Reasoning in First-order Extensions of Description Logic

by unknown authors
"... Systems for hybrid reasoning with first-order logic (FOL) extensions of description logic (DL) date back at least 20 years and are enjoying a renewed interest in the context of recent FOL extensions of OWL DL for the Semantic Web. However, current systems for reasoning with such languages can only h ..."
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Systems for hybrid reasoning with first-order logic (FOL) extensions of description logic (DL) date back at least 20 years and are enjoying a renewed interest in the context of recent FOL extensions of OWL DL for the Semantic Web. However, current systems for reasoning with such languages can only

Sledgehammer: Judgement Day

by Sascha Böhme , Tobias Nipkow - In Giesl and Hähnle [62
"... Abstract. Sledgehammer, a component of the interactive theorem prover Isabelle, finds proofs in higher-order logic by calling the automated provers for first-order logic E, SPASS and Vampire. This paper is the largest and most detailed empirical evaluation of such a link to date. Our test data cons ..."
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Abstract. Sledgehammer, a component of the interactive theorem prover Isabelle, finds proofs in higher-order logic by calling the automated provers for first-order logic E, SPASS and Vampire. This paper is the largest and most detailed empirical evaluation of such a link to date. Our test data

Automated Reasoning: Past Story and New Trends*

by Andrei Voronkov
"... We overview the development of first-order automated reasoning systems starting from their early years. Based on the analysis of current and potential applications of such systems, we also try to predict new trends in first-order automated reasoning. Our presentation will be centered around two main ..."
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of the theorem prover Vampire, see [Riazanov and Voronkov, 2002a]. It reflects our recent experience with applications of Vampire in verification, proof assistants, theorem proving, and semantic Web, as well as the analysis of future potential applications. 1 Theorem Proving in First-Order Logic The idea

A Survey of Some Recent Trends in Rewrite-Based and Paramodulation-Based Deduction

by Robert Nieuwenhuis
"... Introduction Deduction with equality is fundamental in mathematics, logics and many applications of formal methods in computer science. During the last two decades this field has importantly progressed through new Knuth-Bendix-like completion techniques and their extensions to ordered paramodulatio ..."
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paramodulation for first-order clauses. These techniques have lead to important results on deduction in firstorder logic with equality, like [HR91,BDH86,BD94,BG94,BG98,NR01], results that have been applied to state-of-the-art theorem provers like Spass [Wei97] and Vampire [RV01]. These techniques have also led

System Description: E.T. 0.1

by Cezary Kaliszyk, Stephan Schulz, Josef Urban, Jiří Vyskočil
"... Abstract. E.T. 0.1 is a meta-system specialized for theorem proving over large first-order theories containing thousands of axioms. Its design is motivated by the recent theorem proving experiments over the Mizar, Flyspeck and Isabelle data-sets. Unlike other approaches, E.T. does not learn from rel ..."
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Abstract. E.T. 0.1 is a meta-system specialized for theorem proving over large first-order theories containing thousands of axioms. Its design is motivated by the recent theorem proving experiments over the Mizar, Flyspeck and Isabelle data-sets. Unlike other approaches, E.T. does not learn from
Results 1 - 10 of 12