TPS: A hybrid automatic-interactive system for developing proofs

Andrews, Peter B.; Brown, Chad E.

doi:10.1016/j.jal.2005.10.002

Cited by 32 publications

(14 citation statements)

References 35 publications

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“…TPS (version 3.080227G1d). TPS is a fully automated version of the higher-order theorem proving system TPS [5,6]. TPS can be used to prove theorems of ST T automatically, interactively, or semi-automatically.…”

Section: Methodsmentioning

confidence: 99%

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

Benzmüller

2011

Ann Math Artif Intell

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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.

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Section: Methodsmentioning

confidence: 99%

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

Benzmüller

2011

Ann Math Artif Intell

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“…The revised system was then called TPS. The TPS proof assistant (Miller et al, 1982;Andrews et al, 1996Andrews et al, , 2000Andrews and Brown, 2006), was, in fact, not based on resolution but on matrix-style theorem proving. Both λProlog (Nadathur and Miller, 1988) and the Isabelle theorem prover (Paulson, 1989) were early systems that implemented sizable fragments of the intuitionistic variants of ETT: they were tractable systems because they either removed or greatly restricted predicate quantification.…”

Section: Early Systemsmentioning

confidence: 99%

Automation of Higher-Order Logic

Benzmüller¹,

Miller²

2014

Handbook of the History of Logic

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“…More recently extensionality and equality reasoning in HOL has been studied [43,44,45,46]. The TPS system [47,48], which is based on a higher-order mating calculus, is a pioneering ATP system for HOL.…”

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

confidence: 99%

“…TPS is a pioneering higher-order theorem proving system [47,48]. It can be used to prove theorems of HOL automatically, interactively, or semi-automatically.…”

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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TPS: A hybrid automatic-interactive system for developing proofs

Cited by 32 publications

References 35 publications

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

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

Automation of Higher-Order Logic

Higher-order aspects and context in SUMO

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