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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.
Embedding deduction modulo into a prover
 CSL. Lecture Notes in Computer Science
, 2010
"... Abstract. Deduction modulo consists in presenting a theory through rewrite rules to support automatic and interactive proof search. It induces proof search methods based on narrowing, such as the polarized resolution modulo. We show how to combine this method with more traditional ordering restric ..."
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Cited by 6 (1 self)
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Abstract. Deduction modulo consists in presenting a theory through rewrite rules to support automatic and interactive proof search. It induces proof search methods based on narrowing, such as the polarized resolution modulo. We show how to combine this method with more traditional ordering restrictions. Interestingly, no compatibility between the rewriting and the ordering is requested to ensure completeness. We also show that some simplification rules, such as strict subsumption eliminations and demodulations, preserve completeness. For this purpose, we use a new framework based on a proof ordering. These results show that polarized resolution modulo can be integrated into existing provers, where these restrictions and simplifications are present. We also discuss how this integration can actually be done by diverting the main algorithm of stateoftheart provers. Whatever their applications, proofs are rarely searched for without context: mathematical proofs rely on set theory, or Euclidean geometry, or arithmetic,
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.
Representing Story plans in SUMO
 In Proceedings of the NAACL HLT 2010 Second Workshop on Computational Approaches to Linguistic Creativity. Association for Computational Linguistics
, 2010
"... Automatic story generation systems require a body of commonsense knowledge about the basic relationships between concepts we find everyday in our world in order to produce interesting narratives that describe human actions and world events. This paper presents an ongoing work that investigates the u ..."
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Cited by 3 (0 self)
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Automatic story generation systems require a body of commonsense knowledge about the basic relationships between concepts we find everyday in our world in order to produce interesting narratives that describe human actions and world events. This paper presents an ongoing work that investigates the use of Suggested Upper Merged Ontology (SUMO) to represent storytelling knowledge and its inference engine Sigma to query actions and events that may take place in the story to be generated. The resulting story plan (fabula) is also represented in SUMO, allowing for a single story representation to be realized in various human languages. 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 translation from SUMO’s SUOKIF representations into the new typed higherorder form representation language TPTP THF. We illustrate the benefits of our integration with examples, report on experiments and analyze open challenges. 1
LEOII and Satallax on the Sledgehammer Test Bench
, 2012
"... Sledgehammer is a tool that harnesses external firstorder automatic theorem provers (ATPs) to discharge interactive proof obligations arising in Isabelle/HOL. We extended it with LEOII and Satallax, the two most prominent higherorder ATPs, improving its performance on higherorder problems. To ex ..."
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Cited by 3 (1 self)
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Sledgehammer is a tool that harnesses external firstorder automatic theorem provers (ATPs) to discharge interactive proof obligations arising in Isabelle/HOL. We extended it with LEOII and Satallax, the two most prominent higherorder ATPs, improving its performance on higherorder problems. To explore their usefulness, these ATPs are measured against firstorder ATPs and builtin Isabelle tactics on a variety of benchmarks from Isabelle and the TPTP library. Sledgehammer provides an ideal test bench for individual features of LEOII and Satallax, revealing areas for improvements.