Progress in Automating Higher-Order Ontology Reasoning

Benzmüller, Christoph; Pease, Adam

doi:10.29007/dtnz

“…This article combines and extends previous results [88,89]. A main extension is that relevance filtering and scalability to large knowledge bases, which was still mentioned as future work before, has been included in the studies in this article.…”

Section: Related Worksupporting

confidence: 71%

Higher-Order Aspects and Context in SUMO

Benzmüller

¹

,

Pease

²

2011

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…On the practical side there are now several automated higher-order reasoning systems available in our approach that can be uniformly applied to (intuitively sound) formalizations of context. This article combines and extends previous results [88,89]. A main extension is that relevance filtering and scalability to large knowledge bases, which was still mentioned as future work before, has been included in the studies in this article.…”

Section: Related Worksupporting

confidence: 52%

Higher-order aspects and context in SUMO

Benzmüller

¹

,

Pease

²

2012

Journal of Web Semantics

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…This research, amongst others, is currently continued in the DFG project ONTOLEO (BE 2501/6-1). In ONTOLEO we study whether our approach can be applied to automate modalities in ontology reasoning [18,19]. However, our work is obviously relevant also for many other application directions.…”

Section: Resultsmentioning

confidence: 99%

Combining and automating classical and non-classical logics in classical higher-order logics

Benzmüller

¹

2011

Ann Math Artif Intell

Self Cite

View full text Add to dashboard Cite

Numerous classical and non-classical logics can be elegantly embedded in Church's simple type theory, also known as classical higher-order logic. Examples include propositional and quantified multimodal logics, intuitionistic logics, logics for security, and logics for spatial reasoning. Furthermore, simple type theory is sufficiently expressive to model combinations of embedded logics and it has a well understood semantics. Off-the-shelf reasoning systems for simple type theory exist that can be uniformly employed for reasoning within and about embedded logics and logics combinations. In this article we focus on combinations of (quantified) epistemic and doxastic logics and study their application for modeling and automating the reasoning of rational agents. We present illustrating example problems and report on experiments with off-the-shelf higher-order automated theorem provers.

show abstract

Progress in Automating Higher-Order Ontology Reasoning

Cited by 5 publications

References 10 publications

Higher-Order Aspects and Context in SUMO

Higher-Order Aspects and Context in SUMO

Higher-order aspects and context in SUMO

Combining and automating classical and non-classical logics in classical higher-order logics

Contact Info

Product

Resources

About