LEO-II - A Cooperative Automatic Theorem Prover for Classical Higher-Order Logic (System Description)

Benzmüller, Christoph; Paulson, Lawrence C.; Theiss, Frank; Fietzke, Arnaud

doi:10.1007/978-3-540-71070-7_14

Cited by 77 publications

(95 citation statements)

References 15 publications

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“…10 Future work includes the combination of temporal, epistemic and doxastic contexts as discussed in this article with further kinds of contexts and other challenge aspects in SUMO. This line of research will adapt, extend and exploit our recent embeddings of intuitionistic logics [74], logics for spatial reasoning [75], conditional logics [87,90] and logics for security [86] in HOL.…”

Section: Resultsmentioning

confidence: 99%

“…10 http://en.wikipedia.org/wiki/CycL; the website says that CycL considers 5 different truth values, but a document with a clear semantics of CycL and in particular with a precise semantics of embedded formulas could not be found by the authors.…”

Section: Resultsmentioning

confidence: 99%

“…We briefly describe these THF0 reasoners in more detail (their descriptions are adapted from [9]): LEO-II. LEO-II [10], the successor of LEO [52], is an automated theorem prover for HOL which is based on extensional higher-order resolution [43]. More precisely, LEO-II employs a refinement of extensional higher-order RUE resolution [44].…”

Section: Higher-order Logic and Higher-order Theorem Provingmentioning

confidence: 99%

“…These experiments, which are reported in Section 5, provide first evidence that higher-order automated reasoning in SUMO is useful and feasible in practice. In particular the prover LEO-II [10], which now also supports relevance filtering, appears suited for the task. In Section 6 we present a solution for SUMO's conflict with Boolean extensionality, which we revealed in Section 3.…”

Section: Introductionmentioning

confidence: 99%

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Higher-order aspects and context in SUMO

Benzmüller

Pease

2012

Journal of Web Semantics

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This article addresses the automation of higher-order aspects in expressive ontologies such as the Suggested Upper Merged Ontology SUMO. Evidence is provided that modern higher-order automated theorem provers like LEO-II 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 higher-order logic. This way automated higher-order 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.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Higher-order Logic and Higher-order Theorem Provingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Higher-order aspects and context in SUMO

Benzmüller

Pease

2012

Journal of Web Semantics

Self Cite

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show abstract

“…The paper thus provides useful and relevant information for evaluations of competitor systems based on the direct approach. Moreover, some light is shed on the collective and individual performances of the higher-order automated theorem provers LEO-II [5], Satallax [7], Isabelle [10], agsyHOL [9] and Nitpick [6].…”

Section: Introductionmentioning

confidence: 99%