Analytic Tableaux for Higher-Order Logic with Choice

Backes, Julian; Brown, Chad E.

doi:10.1007/978-3-642-14203-1_7

Cited by 22 publications

(19 citation statements)

References 14 publications

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“…Satallax is a higher-order automated theorem prover with additional model finding capabilities. The system is based on a complete ground tableau calculus for ST T with a choice operator [7]. An initial tableau branch is formed from the axioms of the problem and negation of the conjecture (if any is given).…”

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 higher-order automatic provers LEO-II [7] and Satallax [3,16] have THF0 as their input language. Both attempt to find a refutation from the negated conjecture and the axioms, amounting to a proof of the original conjecture.…”

Section: Leo-ii and Satallaxmentioning

confidence: 99%

“…Until five years ago, there were only two higher-order ATPs, LEO [6] and TPS [1], both based on classical higher-order logic [18]. Since then, a new generation of higher-order ATPs has emerged: LEO-II by Benzmüller et al [7,37] and Satallax by Brown et al [3,17]. This development coincided with the extension of the TPTP (Thousands of Problems for Theorem Provers) infrastructure with a language for encoding problems in higher-order logic (THF0) [8], a collection of benchmark problems [5,36], and a competition category for higher-order provers at CASC [31].…”

Section: Introductionmentioning

confidence: 99%

LEO-II and Satallax on the Sledgehammer test bench

Sultana

Blanchette

Paulson

2013

Journal of Applied Logic

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Sledgehammer is a tool that harnesses external first-order automatic theorem provers (ATPs) to discharge interactive proof obligations arising in Isabelle/HOL. We extended it with LEO-II and Satallax, the two most prominent higher-order ATPs, improving its performance on higher-order problems. To explore their usefulness, these ATPs are measured against first-order ATPs and built-in Isabelle tactics on a variety of benchmarks from Isabelle and the TPTP library. Sledgehammer provides an ideal test bench for individual features of LEO-II and Satallax, revealing areas for improvements.

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“…The use of abstract consistency to prove completeness was first used by Smullyan [29,30] and later used by several authors in various higher-order settings [2,9,14,21]. To prove completeness of the tableau calculus, it is enough to consider branches (finite sets of normal formulas) as in [6]. To obtain a more general result which will imply compactness and the existence of countable models, we also consider sets A of normal formulas which may be infinite.…”

Section: Abstract Consistency and Completenessmentioning

confidence: 99%

“…In Section 7 we extend the calculus to include an if-then-else operator. We discuss related work and conclude in Sections 8 and 9. This article is an expanded version of [6].…”

Section: Introductionmentioning

confidence: 97%

Analytic Tableaux for Higher-Order Logic with Choice

Backes

Brown

2011

J Autom Reasoning

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While many higher-order interactive theorem provers include a choice operator, higher-order automated theorem provers so far have not. In order to support automated reasoning in the presence of a choice operator, we present a cut-free 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.

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Analytic Tableaux for Higher-Order Logic with Choice

Cited by 22 publications

References 14 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

LEO-II and Satallax on the Sledgehammer test bench

Analytic Tableaux for Higher-Order Logic with Choice

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