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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
Automated reasoning in higherorder logic using the TPTP THF infrastructure
 J. of Formalized Reasoning
, 2010
"... Articulate Software The Thousands of Problems for Theorem Provers (TPTP) problem library is the basis of a well known and well established infrastructure that supports research, development, and deployment of Automated Theorem Proving (ATP) systems. The extension of the TPTP from firstorder form (F ..."
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Cited by 34 (14 self)
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Articulate Software The Thousands of Problems for Theorem Provers (TPTP) problem library is the basis of a well known and well established infrastructure that supports research, development, and deployment of Automated Theorem Proving (ATP) systems. The extension of the TPTP from firstorder form (FOF) logic to typed higherorder form (THF) logic has provided a basis for new development and application of ATP systems for higherorder logic. Key developments have been the specification of the THF language, the addition of higherorder problems to the TPTP, the development of the TPTP THF infrastructure, several ATP systems for higherorder logic, and the use of higherorder ATP in a range of domains. This paper surveys these developments. 1.
2001b, ‘The CADE17 ATP System Competition
 Journal of Automated Reasoning
"... Abstract. The results of the IJCAR ATP System Competition are presented. ..."
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Cited by 31 (7 self)
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Abstract. The results of the IJCAR ATP System Competition are presented.
Quantified multimodal logics in simple type theory
, 2009
"... We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple experiments, using existing higherorder theorem provers, to demonstr ..."
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Cited by 27 (16 self)
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We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple experiments, using existing higherorder theorem provers, to demonstrate that the embedding allows automated proofs of statements in these logics, as well as meta properties of them.
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 theory with choice. The tableau calculus is designed with automated search in mind. In particular, the rules only operate on the top level structure of formulas. Additionally, we restrict the instantiation terms for quantifiers to a universe that depends on the current branch. At base types the universe of instantiations is finite. Both of these restrictions are intended to minimize the number of rules a corresponding search procedure is obligated to consider. We prove completeness of the tableau calculus relative to Henkin models. 1
Multimodal and Intuitionistic Logics in Simple Type Theory
"... We study straightforward embeddings of propositional normal multimodal logic and propositional intuitionistic logic in simple type theory. The correctness of these embeddings is easily shown. We give examples to demonstrate that these embeddings provide an effective framework for computational inve ..."
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Cited by 14 (12 self)
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We study straightforward embeddings of propositional normal multimodal logic and propositional intuitionistic logic in simple type theory. The correctness of these embeddings is easily shown. We give examples to demonstrate that these embeddings provide an effective framework for computational investigations of various nonclassical logics. We report some experiments using the higherorder automated theorem prover LEOII.
Automating access control logics in simple type theory with LEOII
 FB Informatik, U. des Saarlandes
, 2008
"... Abstract Garg and Abadi recently proved that prominent access control logics can be translated in a sound and complete way into modal logic S4. We have previously outlined how normal multimodal logics, including monomodal logics K and S4, can be embedded in simple type theory and we have demonstrate ..."
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Cited by 13 (11 self)
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Abstract Garg and Abadi recently proved that prominent access control logics can be translated in a sound and complete way into modal logic S4. We have previously outlined how normal multimodal logics, including monomodal logics K and S4, can be embedded in simple type theory and we have demonstrated that the higherorder theorem prover LEOII can automate reasoning in and about them. In this paper we combine these results and describe a sound (and complete) embedding of different access control logics in simple type theory. Employing this framework we show that the off the shelf theorem prover LEOII can be applied to automate reasoning in and about prominent access control logics. 1
Knowledge Representation and Classical Logic
, 2007
"... Mathematical logicians had developed the art of formalizing declarative knowledge long before the advent of the computer age. But they were interested primarily in formalizing mathematics. Because of the important role of nonmathematical knowledge in AI, their emphasis was too narrow from the perspe ..."
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Cited by 11 (5 self)
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Mathematical logicians had developed the art of formalizing declarative knowledge long before the advent of the computer age. But they were interested primarily in formalizing mathematics. Because of the important role of nonmathematical knowledge in AI, their emphasis was too narrow from the perspective of knowledge representation, their formal languages were not sufficiently expressive. On the other hand, most logicians were not concerned about the possibility of automated reasoning; from the perspective of knowledge representation, they were often too generous in the choice of syntactic constructs. In spite of these differences, classical mathematical logic has exerted significant influence on knowledge representation research, and it is appropriate to begin this handbook with a discussion of the relationship between these fields. The language of classical logic that is most widely used in the theory of knowledge representation is the language of firstorder (predicate) formulas. These are the formulas that John McCarthy proposed to use for representing declarative knowledge in his advice taker paper [176], and Alan Robinson proposed to prove automatically using resolution [236]. Propositional logic is, of course, the most important subset of firstorder logic; recent
Reducing HigherOrder Theorem Proving to a Sequence of SAT Problems
, 2011
"... Abstract. We describe a complete theorem proving procedure for higherorder logic that uses SATsolving to do much of the heavy lifting. The theoretical basis for the procedure is a complete, cutfree, ground refutation calculus that incorporates a restriction on instantiations. The refined nature o ..."
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Cited by 10 (0 self)
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Abstract. We describe a complete theorem proving procedure for higherorder logic that uses SATsolving to do much of the heavy lifting. The theoretical basis for the procedure is a complete, cutfree, ground refutation calculus that incorporates a restriction on instantiations. The refined nature of the calculus makes it conceivable that one can search in the ground calculus itself, obtaining a complete procedure without resorting to metavariables and a higherorder lifting lemma. Once one commits to searching in a ground calculus, a natural next step is to consider ground formulas as propositional literals and the rules of the calculus as propositional clauses relating the literals. With this view in mind, we describe a theorem proving procedure that primarily generates relevant formulas along with their corresponding propositional clauses. The procedure terminates when the set of propositional clauses is unsatisfiable. We prove soundness and completeness of the procedure. The procedure has been implemented in a new higherorder theorem prover, Satallax, which makes use of the SATsolver MiniSat. We also describe the implementation and give some experimental results.
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.