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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 performance of LEOII, especially in comparison to its predecessor LEO, is due to several novel features including the exploitation of term sharing and term indexing techniques, support for primitive equality reasoning, and improved heuristics at the calculus level. LEOII is implemented in Objective Caml and its problem representation language is the new TPTP THF language. 1
THF0 – The Core TPTP Language for Classical HigherOrder Logic
"... Abstract. There is a well established infrastructure that supports research, development, and deployment of firstorder Automated Theorem Proving (ATP) systems, stemming from the Thousands of Problems for Theorem Provers (TPTP) problem library. One of the keys to the success of the TPTP and related ..."
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Cited by 16 (12 self)
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Abstract. There is a well established infrastructure that supports research, development, and deployment of firstorder Automated Theorem Proving (ATP) systems, stemming from the Thousands of Problems for Theorem Provers (TPTP) problem library. One of the keys to the success of the TPTP and related infrastructure is the consistent use of the TPTP language. This paper introduces the core TPTP language for classical higherorder logic (Church’s simple type theory) – THF0. THF0 is a conservative extension of the existing firstorder TPTP language. The use of THF0 in building higherorder analogs of some of the existing firstorder TPTP infrastructure is explained. 1
THF0 – the core of the TPTP language for higherorder logic
 Automated Reasoning, 4th International Joint Conference, IJCAR 2008
"... Abstract. One of the keys to the success of the Thousands of Problems for Theorem Provers (TPTP) problem library and related infrastructure is the consistent use of the TPTP language. This paper introduces the core of the TPTP language for higherorder logic – THF0, based on Church’s simple type the ..."
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Cited by 14 (1 self)
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Abstract. One of the keys to the success of the Thousands of Problems for Theorem Provers (TPTP) problem library and related infrastructure is the consistent use of the TPTP language. This paper introduces the core of the TPTP language for higherorder logic – THF0, based on Church’s simple type theory. THF0 is a syntactically conservative extension of the untyped firstorder TPTP language. 1
Progress report on LEOII, an automatic theorem prover for higherorder logic
, 2007
"... Abstract. LeoII, a resolution based theorem prover for classical higherorder logic, is currently being developed in a one year research project at the University of Cambridge, UK, with support from Saarland University, Germany. We report on the current stage of development of LeoII. In particular, ..."
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Cited by 12 (8 self)
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Abstract. LeoII, a resolution based theorem prover for classical higherorder logic, is currently being developed in a one year research project at the University of Cambridge, UK, with support from Saarland University, Germany. We report on the current stage of development of LeoII. In particular, we sketch some main aspects of LeoII’s automated proof search procedure, discuss its cooperation with firstorder specialist provers, show that LeoII is also an interactive proof assistant, and explain its shared term data structure and its term indexing mechanism. 1
Progress in the Development of Automated Theorem Proving for Higherorder Logic
"... The Thousands of Problems for Theorem Provers (TPTP) problem library is the basis of a well established infrastructure supporting research, development, and deployment of firstorder Automated Theorem Proving (ATP) systems. Recently, the TPTP has been extended to include problems in higherorder log ..."
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Cited by 9 (4 self)
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The Thousands of Problems for Theorem Provers (TPTP) problem library is the basis of a well established infrastructure supporting research, development, and deployment of firstorder Automated Theorem Proving (ATP) systems. Recently, the TPTP has been extended to include problems in higherorder logic, with corresponding infrastructure and resources. This paper describes the practical progress that has been made towards the goal of TPTP support for higherorder ATP systems.
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 formulas (formulas as terms), which are used in SUMO, for example, for modeling temporal, epistemic, or doxastic contexts. This modeling is partly in conflict with SUMO’s assumption of a bivalent, classical semantics and it may hence lead to counterintuitive reasoning results with automated theorem provers in practice. A solution is proposed that maps SUMO to quantified multimodal logic which is in turn modeled as a fragment of classical higherorder logic. This way automated higherorder theorem provers can be safely applied for reasoning about modal contexts in SUMO. Our findings are of wider relevance as they analogously apply to other expressive ontologies and knowledge representation formalisms.
The HigherOrder Prover LEOII
 J AUTOM REASONING
, 2015
"... LeoII is an automated theorem prover for classical higherorder logic. The prover has pioneered cooperative higherorder–firstorder proof automation, it has influenced the development of the TPTP THF infrastructure for higherorder logic, and it has been applied in a wide array of problems. Leo ..."
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Cited by 1 (0 self)
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LeoII is an automated theorem prover for classical higherorder logic. The prover has pioneered cooperative higherorder–firstorder proof automation, it has influenced the development of the TPTP THF infrastructure for higherorder logic, and it has been applied in a wide array of problems. LeoII may also be called in proof assistants as an external aid tool to save user effort. For this it is crucial that LeoII returns proof information in a standardised syntax, so that these proofs can eventually be transformed and verified within proof assistants. Recent progress in this direction is reported for the Isabelle/HOL system.
Classical HigherOrder Logic
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Automated Higherorder Reasoning about
"... Originally developed as an algebraic characterisation for quantum mechanics, the algebraic structure of quantales nowadays finds widespread applications ranging from (noncommutative) logics to hybrid systems. We present an approach to bring reasoning about quantales into the realm of (fully) automat ..."
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Originally developed as an algebraic characterisation for quantum mechanics, the algebraic structure of quantales nowadays finds widespread applications ranging from (noncommutative) logics to hybrid systems. We present an approach to bring reasoning about quantales into the realm of (fully) automated theorem proving. This will yield automation in various (new) fields of applications in the future. To achieve this goal and to receive a general approach (independent of any particular theorem prover), we use the TPTP Problem Library for higherorder logic. In particular, we give an encoding of quantales in the typed higherorder form (THF) and present some theorems about quantales which can be proved fully automatically. We further present prospective applications for our approach and discuss practical experiences using THF. 1
Abstract
, 2010
"... Originally developed as an algebraic characterisation for quantum mechanics, the algebraic structure of quantales nowadays finds widespread applications ranging from (noncommutative) logics to hybrid systems. We present an approach to bring reasoning in quantales into the realm of (fully) automated ..."
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Originally developed as an algebraic characterisation for quantum mechanics, the algebraic structure of quantales nowadays finds widespread applications ranging from (noncommutative) logics to hybrid systems. We present an approach to bring reasoning in quantales into the realm of (fully) automated theorem proving. Hence the paper paves the way for automatisation in various (new) fields of applications. To achieve this goal and to receive a general approach (independent of any particular theorem prover), we use the TPTP Problem Library for higherorder logic. In particular, we give an encoding of quantales in the typed higherorder form (THF) and present some theorems about quantales which can be proved fully automatically. We further present prospective applications for our approach and discuss practical experiences using THF. 1