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Automatic Theorem Provers
"... • Formal verification techniques can, in theory, prove beyond a doubt that a system is implemented correctly. • In practice, there are still many challenges, but there are ..."
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• Formal verification techniques can, in theory, prove beyond a doubt that a system is implemented correctly. • In practice, there are still many challenges, but there are
My Life with an Automatic Theorem Prover
"... Sledgehammer integrates thirdparty automatic theorem provers in the proof assistant Isabelle/HOL. In the seven years since its first release in 2007, it has grown to become an essential part of most Isabelle users’ workflow. Although a lot of effort has gone into tuning the system, the main reason ..."
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Sledgehammer integrates thirdparty automatic theorem provers in the proof assistant Isabelle/HOL. In the seven years since its first release in 2007, it has grown to become an essential part of most Isabelle users’ workflow. Although a lot of effort has gone into tuning the system, the main
Logical ontology validation using an automatic theorem prover
 In Proceedings of the 19th European Conference on Arti cial Intelligence (ECAI
, 2010
"... Abstract. Ontologies are utilized for a wide range of tasks, like information retrieval/extraction or text generation, and in a multitude of domains, such as biology, medicine or business and commerce. To be actually usable in such realworld scenarios, ontologies usually have to encompass a large ..."
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mechanisms are applied on these ontologies, even minimal inconsistencies oftentimes lead to serious errors and are hard to trace back and find. This paper addresses this issue and describes a method to validate ontologies using an automatic theorem prover and MultiNet axioms. This logicbased approach allows
A new algebraic tool for automatic theorem provers
 Annals of Mathematics and Artificial Intelligence
, 2004
"... The concepts of implicates and implicants are widely used in several fields of "Automated Reasoning". Particularly, our research group has developed several techniques that allow us to reduce efficiently the size of the input, and therefore the complexity of the problem. These techniques ..."
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Cited by 4 (1 self)
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The concepts of implicates and implicants are widely used in several fields of "Automated Reasoning". Particularly, our research group has developed several techniques that allow us to reduce efficiently the size of the input, and therefore the complexity of the problem. These techniques are based on obtaining and using implicit information that is collected in terms of unitary implicates and implicants. Thus, we require efficient algorithms to calculate them. In classical propositional logic it is easy to obtain efficient algorithms to calculate the set of unitary implicants and implicates of a formula. In temporal logics, contrary to what we see in classical propositional logic, these sets may contain infinitely many members. Thus, in order to calculate them in an efficient way, we have to base the calculation on the theoretical study of how these sets behave. Such a study reveals the need to make a generalization of Lattice Theory, which is very important in "Computational Algebra". In this paper we introduce the multisemilattice structure as a generalization of the semilattice structure. Such a structure is proposed as a particular type of poset. Subsequently, we offer an equivalent algebraic characterization based on nondeterministic operators and with a weakly associative property. We also show that from the structure of multisemilattice we can obtain an algebraic characterization of the multilattice structure. This paper concludes by showing the relevance of the multisemilattice structure in the design of algorithms aimed at calculating unitary implicates and implicants in temporal logics. Concretely, we show that it is possible to design efficient algorithms to calculate the unitary implicants/implicates only if the unitary formulae set has the multisemilattice structure.
Case Splitting in an Automatic Theorem Prover for RealValued Special Functions
, 2012
"... Case splitting, with and without backtracking, is compared with straightforward ordered resolution. Both forms of splitting have been implemented for MetiTarski, an automatic theorem prover for realvalued special functions such as exp, ln, sin, cos and tan −1. The experimental findings confirm the ..."
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Case splitting, with and without backtracking, is compared with straightforward ordered resolution. Both forms of splitting have been implemented for MetiTarski, an automatic theorem prover for realvalued special functions such as exp, ln, sin, cos and tan −1. The experimental findings confirm
System Description: aRa  An Automatic Theorem Prover for Relation Algebras
 Automated Deduction CADE17, LNAI 1831
, 2000
"... Abstract. aRa is an automatic theorem prover for various kinds of relation algebras. It is based on Gordeev’s Reduction Predicate Calculi for nvariable logic (RPCn) which allow firstorder finite variable proofs. Employing results from Tarski/Givant and Maddux we can prove validity in the theories ..."
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Abstract. aRa is an automatic theorem prover for various kinds of relation algebras. It is based on Gordeev’s Reduction Predicate Calculi for nvariable logic (RPCn) which allow firstorder finite variable proofs. Employing results from Tarski/Givant and Maddux we can prove validity in the theories
A LEMMA DRIVEN AUTOMATIC THEOREM PROVER FOR RECURSIVE FUNCTION THEORY
"... We describe work in progress on an automatic theorem prover for recursive function theory that we intend to apply in the analysis (including verification and transformation) of useful computer programs. The mathematical theory of our theorem prover is extendible by the user and serves as a logical b ..."
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We describe work in progress on an automatic theorem prover for recursive function theory that we intend to apply in the analysis (including verification and transformation) of useful computer programs. The mathematical theory of our theorem prover is extendible by the user and serves as a logical
LEOII — A cooperative automatic theorem prover for higherorder logic
 In Fourth International Joint Conference on Automated Reasoning (IJCAR’08), volume 5195 of LNAI
, 2008
"... Abstract. LEOII is a standalone, resolutionbased higherorder theorem prover designed for effective cooperation with specialist provers for natural fragments of higherorder logic. At present LEOII can cooperate with the firstorder automated theorem provers E, SPASS, and Vampire. The improved pe ..."
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Cited by 58 (26 self)
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Abstract. LEOII is a standalone, resolutionbased higherorder theorem prover designed for effective cooperation with specialist provers for natural fragments of higherorder logic. At present LEOII can cooperate with the firstorder automated theorem provers E, SPASS, and Vampire. The improved
MetiTarski: An Automatic Theorem Prover for RealValued Special Functions
"... Abstract Many theorems involving special functions such as ln, exp and sin can be proved automatically by MetiTarski: a resolution theorem prover modified to call a decision procedure for the theory of real closed fields. Special functions are approximated by upper and lower bounds, which are typica ..."
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Cited by 42 (6 self)
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Abstract Many theorems involving special functions such as ln, exp and sin can be proved automatically by MetiTarski: a resolution theorem prover modified to call a decision procedure for the theory of real closed fields. Special functions are approximated by upper and lower bounds, which
Results 1  10
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