Preface

Nederpelt, RP Rob; Geuvers, Herman; Vrijer, Roel de

doi:10.1016/s0049-237x(08)70195-2

Cited by 20 publications

(20 citation statements)

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“…Prominent interactive provers for classical higher logic include HOL [26], HOL Light [27], PVS [28], Isabelle/HOL [29], and OMEGA [30]. Prominent interactive type theory provers include the pioneering Automath system [31], Nuprl [32], Lego [33], Matita [34], and Coq [35]. The latter three are based on the calculus of constructions [36].…”

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

confidence: 99%

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: Higher-order Logic and Higher-order Theorem Provingmentioning

confidence: 99%

Higher-order aspects and context in SUMO

Benzmüller

Pease

2012

Journal of Web Semantics

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“…Completely indispensable is a thorough reading of the Automath papers [11,27]-some recent MKM work just "rediscovers" some of de Bruijn's early insights. Similarly, the QED Manifesto [5] has helped frame the discussion around formalized mathematics for a very long time (see [32] as an enlightening and readable example).…”

Section: Historymentioning

confidence: 99%

A Review of Mathematical Knowledge Management

Carette

Farmer

2009

Lecture Notes in Computer Science

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Abstract. Mathematical Knowledge Management (MKM), as a field, has seen tremendous growth in the last few years. This period was one where many research threads were started, and the field was defining itself. We believe that we are now in a position to use the MKM body of knowledge as a means to define what MKM is, what it worries about, etc. In this paper, we review the literature of MKM and gather various metadata from these papers. After offering some definitions surrounding MKM, we analyse the metadata we have gathered from these papers, in an effort to cast more light on the field of MKM and its evolution.

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“…The ratio between the proof script describing (or rather generating) the formal proof and the original text in informal mathematics is usually called the De Bruijn factor (after N.G. de Bruijn, see [14]). In the early days of formalization the De Bruijn factor was around ten.…”

Section: The Complete Proof By Cronheimmentioning

confidence: 99%

On the Mechanization of the Proof of Hessenberg’s Theorem in Coherent Logic

Bezem

Hendriks

2007

J Autom Reasoning

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We propose to combine interactive proof construction with proof automation for a fragment of first-order logic called Coherent Logic (CL). CL allows enough existential quantification to make Skolemization unnecessary. Moreover, CL has a constructive proof system based on forward reasoning, which is easy to automate and where standardized proof objects can easily be obtained. We have implemented in Prolog a CL prover which generates Coq proof scripts. We test our approach with a case study: Hessenberg's theorem, which states that in elementary projective plane geometry Pappus' axiom implies Desargues' axiom. Our CL prover makes it possible to automate large parts of the proof, in particular taking care of the large number of degenerate cases.

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Preface

Cited by 20 publications

References 0 publications

Higher-order aspects and context in SUMO

Higher-order aspects and context in SUMO

A Review of Mathematical Knowledge Management

On the Mechanization of the Proof of Hessenberg’s Theorem in Coherent Logic

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