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HigherOrder Automated Theorem Proving
, 1998
"... Consistency Class) Let Ñ S be a class of sets of propositions, then Ñ S is called an abstract consistency class, iff each Ñ S is closed under subsets, and satisfies conditions (1) to (8) for all sets F 2 Ñ S . If it also satisfies (9), then we call it extensional. 1. If A is atomic, then A = 2 F or ..."
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Cited by 7 (2 self)
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Consistency Class) Let Ñ S be a class of sets of propositions, then Ñ S is called an abstract consistency class, iff each Ñ S is closed under subsets, and satisfies conditions (1) to (8) for all sets F 2 Ñ S . If it also satisfies (9), then we call it extensional. 1. If A is atomic, then A = 2 F or :A = 2 F. 2. If A 2 F and if B is the bhnormal form of A, then B F 2 Ñ S 2 . 3. If ::A 2 F, then A F 2 Ñ S . 4. If AB2F, then F A 2 Ñ S or F B 2 Ñ S . 5. If :(AB) 2 F, then F :A :B2 Ñ S . 6. If P a A 2 F, then F AB 2 Ñ S for each closed formula B 2 wff a (S). 7. If :P a A 2 F, then F :(Aw a ) 2 Ñ S for any witness constant w a 2 W that does not occur in F. 8. If :(A = a!b B) 2 F, then F :(Aw a = Bw) 2 Ñ S for any witness constant w a 2 W that does not occur in F. 9. If :(A = o B) 2 F, then F[fA;:Bg 2 Ñ S or F[f:A;Bg 2 Ñ S . Here, we treat equality as an abbreviation for Leibniz definition. We call an abstract consistency class saturated, iff for all F 2 Ñ S and all...
HigherOrder Automated Theorem Proving for Natural Language Semantics
, 1998
"... This paper describes a tableaubased higherorder theorem prover Hot and an application to natural language semantics. In this application, Hot is used to prove equivalences using world knowledge during higherorder unification (HOU). This extended form of HOU is used to compute the licensing condit ..."
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Cited by 6 (3 self)
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This paper describes a tableaubased higherorder theorem prover Hot and an application to natural language semantics. In this application, Hot is used to prove equivalences using world knowledge during higherorder unification (HOU). This extended form of HOU is used to compute the licensing
Automating Gödel’s ontological proof of god’s existence with higherorder automated theorem prover
 In 21st European Conference on Artificial Intelligence (ECAI
, 2014
"... Abstract. Kurt Gödel’s ontological argument for God’s existence has been formalized and automated on a computer with higherorder automated theorem provers. From Gödel’s premises, the computer proved: necessarily, there exists God. On the other hand, the theorem provers have also confirmed promine ..."
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Cited by 4 (2 self)
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Abstract. Kurt Gödel’s ontological argument for God’s existence has been formalized and automated on a computer with higherorder automated theorem provers. From Gödel’s premises, the computer proved: necessarily, there exists God. On the other hand, the theorem provers have also confirmed
Embedding and automating conditional logics in classical higherorder logic
 Annals of Mathematics and Artificial Intelligence. In Print. DOI
, 2012
"... Abstract. A sound and complete embedding of conditional logics into classical higherorder logic is presented. This embedding enables the application of offtheshelf higherorder automated theorem provers and model finders for reasoning within and about conditional logics. 1 ..."
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Cited by 7 (7 self)
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Abstract. A sound and complete embedding of conditional logics into classical higherorder logic is presented. This embedding enables the application of offtheshelf higherorder automated theorem provers and model finders for reasoning within and about conditional logics. 1
Progress in automating higherorder ontology reasoning
 in Proceedings of the Second International Workshop on Practical Aspects of Automated Reasoning
"... We report on the application of higherorder automated theorem proving in ontology reasoning. Concretely, we have integrated the Sigma knowledge engineering environment and the Suggested UpperLevel Ontology (SUMO) with the higherorder theorem prover LEOII. The basis for this integration is a tran ..."
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Cited by 3 (3 self)
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We report on the application of higherorder automated theorem proving in ontology reasoning. Concretely, we have integrated the Sigma knowledge engineering environment and the Suggested UpperLevel Ontology (SUMO) with the higherorder theorem prover LEOII. The basis for this integration is a
HOL Provers for Firstorder Modal Logics — Experiments∗
"... Higherorder automated theorem provers have been employed to automate firstorder modal logics. Extending previous work, an experiment has been carried out to evaluate their collaborative and individual performances. 1 ..."
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Higherorder automated theorem provers have been employed to automate firstorder modal logics. Extending previous work, an experiment has been carried out to evaluate their collaborative and individual performances. 1
Higherorder aspects and context in SUMO
 Journal of Web Semantics (Special Issue on Reasoning with context in the Semantic Web
, 2012
"... This article addresses the automation of higherorder aspects in expressive ontologies such as the Suggested Upper Merged Ontology SUMO. Evidence is provided that modern higherorder automated theorem provers like LEOII can be fruitfully employed for the task. A particular focus is on embedded for ..."
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Cited by 5 (3 self)
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This article addresses the automation of higherorder aspects in expressive ontologies such as the Suggested Upper Merged Ontology SUMO. Evidence is provided that modern higherorder automated theorem provers like LEOII can be fruitfully employed for the task. A particular focus is on embedded
Analytic tableaux for higherorder logic with choice.
 Automated Reasoning: 5th International Joint Conference, IJCAR 2010, Proceedings,
, 2010
"... Abstract While many higherorder interactive theorem provers include a choice operator, higherorder automated theorem provers so far have not. In order to support automated reasoning in the presence of a choice operator, we present a cutfree ground tableau calculus for Church's simple type t ..."
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Cited by 25 (1 self)
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Abstract While many higherorder interactive theorem provers include a choice operator, higherorder automated theorem provers so far have not. In order to support automated reasoning in the presence of a choice operator, we present a cutfree ground tableau calculus for Church's simple type
Combining and Automating Classical and NonClassical Logics in Classical HigherOrder Logics
 ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE (PREFINAL VERSION)
"... Numerous classical and nonclassical logics can be elegantly embedded in Church’s simple type theory, also known as classical higherorder logic. Examples include propositional and quantified multimodal logics, intuitionistic logics, logics for security, and logics for spatial reasoning. Furthermor ..."
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Cited by 5 (5 self)
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. In this article we focus on combinations of (quantified) epistemic and doxastic logics and study their application for modeling and automating the reasoning of rational agents. We present illustrating example problems and report on experiments with offtheshelf higherorder automated theorem provers.
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