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Automation of Higher-Order Logic
[chapter]
2014
Handbook of the History of Logic
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Besides the readers of this chapter, we thank Zakaria Chihani, Julian Röder, Leon Weber, and Max Wisnieswki for proofreading the document. ...
., 2003) , a first-order presentation of (intensional) higher-order logic can be exploited to automate higher-order reasoning . ...
In the last century, much of the work on the automation of higher-order logic focused on the automation of the elementary type theory. ...
doi:10.1016/b978-0-444-51624-4.50005-8
fatcat:jfcztdvymjfujg3bzb2rq2qyzy
Evaluation of Systems for Higher-order Logic (ESHOL)
2008
Conference on Automated Deduction
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-The development of automated reasoning systems for higher-order logic (or fragments of it). -Promising application areas for automated higher-order reasoning systems. ...
The notion of higher-order included, but was not limited to, ramified type theory, simple type theory, intuitionistic and constructive type theory, and logical frameworks. ...
dblp:conf/cade/BenzmullerRSS08
fatcat:dxtlbrmbvng3zadrqbhojnpelm
Self-Formalisation of Higher-Order Logic
2016
Journal of automated reasoning
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We present a mechanised semantics for higher-order logic (HOL), and a proof of soundness for the inference system, including the rules for making definitions, implemented by the kernel of the HOL Light ...
Soundness of the logic extends to soundness of a theorem prover, because we also show that a synthesised implementation of the kernel in CakeML refines the inference system. ...
Acknowledgements We thank Mike Gordon for helpful comments on drafts of this paper. We are grateful to John Harrison and Freek Wiedijk for providing inspiration for this project. ...
doi:10.1007/s10817-015-9357-x
fatcat:3dcm7pdklzcrhc37yryjzm3f7u
Analytic Tableaux for Higher-Order Logic with Choice
2011
Journal of automated 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. ...
Introduction Interactive theorem provers based on classical higher-order logic ( e.g., Isabelle-HOL [26], HOL88 [17], HOL-light [18], ProofPower [22] and HOL4 [28]) build in the axiom of choice by including ...
doi:10.1007/s10817-011-9233-2
fatcat:3k5t7oreonhgdmcsepqbb5krv4
Partial and Nested Recursive Function Definitions in Higher-order Logic
2009
Journal of automated reasoning
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Based on inductive definitions, we develop a tool that automates the definition of partial recursive functions in higher-order logic (HOL) and provides appropriate proof rules for reasoning about them. ...
Termination is modeled by an inductive domain predicate which follows the structure of the recursion. ...
Jasmin Christian Blanchette, Amine Chaieb, Norbert Schirmer, and Christian Urban commented on drafts of this paper. The anonymous referees gave valuable feedback. ...
doi:10.1007/s10817-009-9157-2
fatcat:etpmyhp3c5hmlfs3nqd7q2m76u
Verifying Termination and Reduction Properties about Higher-Order Logic Programs
2005
Journal of automated reasoning
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We describe two checkers for verifying termination and reduction properties about higher-order logic programs. ...
At the heart of both checkers lies an inference system to reason about structural properties which are described by higher-order subterm relations. ...
Several automated methods to prove termination have been developed for first-order functional and logic programs in the past years (for example [3, 20, 9, 18, 31, 35] ). ...
doi:10.1007/s10817-005-6534-3
fatcat:aqoexkytzzdqlmvjgghrnd7mzy
Combining and automating classical and non-classical logics in classical higher-order logics
2011
Annals of Mathematics and Artificial Intelligence
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We present illustrating example problems and report on experiments with off-the-shelf higher-order automated theorem provers. ...
Numerous classical and non-classical logics can be elegantly embedded in Church's simple type theory, also known as classical higher-order logic. ...
Geoff Sutcliffe, in collaboration with the author and supported by several further contributors, developed the new higher-order TPTP THF infrastructure (EU FP7 grant THFTPTP PIIF-GA-2008-219982). ...
doi:10.1007/s10472-011-9249-7
fatcat:4ppv6v36njcshd327mvguuj52a
Embedding and automating conditional logics in classical higher-order logic
2012
Annals of Mathematics and Artificial Intelligence
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A sound and complete embedding of conditional logics into classical higher-order logic is presented. ...
This embedding enables the application of off-the-shelf higher-order automated theorem provers and model finders for reasoning within and about conditional logics. ...
Acknowledgments: We thank the developers and contributors of the TPTP THF infrastructure and the implementors of the theorem provers and model finders employed in this work. ...
doi:10.1007/s10472-012-9320-z
fatcat:vaqujhbg3nagnm2teabyefrxta
Implementing tactics and tacticals in a higher-order logic programming language
1993
Journal of automated reasoning
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We present an extensive set of examples that have been implemented in the higher-order logic programming language Prolog. ...
We argue that a logic programming language with a higher-order intuitionistic logic as its foundation can be used both to naturally specify and implement tactic style theorem provers. ...
Pfenning 36] adopts LF as the logical foundation of the higher-order logic programming language Elf. ...
doi:10.1007/bf00881900
fatcat:plrrvswjzzhntakfcpmfvap75m
Progress in the Development of Automated Theorem Proving for Higher-Order Logic
[chapter]
2009
Lecture Notes in Computer Science
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The Higher-order TPTP The development of the higher-order part of the TPTP involved three of the steps identified in the introduction: development of the Typed Higher-order Form (THF) part of the TPTP ...
Until recently there has been no corresponding support in higher-order logic. ...
Thanks to Andrei Tchaltsev and Alexandre Riazanov for developing the first-order parts of the Java parser for the TPTP language. ...
doi:10.1007/978-3-642-02959-2_8
fatcat:osm5sbcmnbg6nn3cdwqgunwkle
Automating Emendations of the Ontological Argument in Intensional Higher-Order Modal Logic
[chapter]
2017
Lecture Notes in Computer Science
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A shallow semantic embedding of an intensional higher-order modal logic (IHOML) in Isabelle/HOL is presented. ...
IHOML draws on Montague/Gallin intensional logics and has been introduced by Melvin Fitting in his textbook Types, Tableaus and Gödel's God in order to discuss his emendation of Gödel's ontological argument ...
Introduction The first part of this paper introduces a shallow semantic embedding of an intensional higher-order modal logic (IHOML) in classical higher-order logic (Isabelle/HOL 3 ). ...
doi:10.1007/978-3-319-67190-1_9
fatcat:tiflccsgsndsrgn5cpvweo4tdq
A general formal memory framework in Coq for verifying the properties of programs based on higher-order logic theorem proving with increased automation, consistency, and reusability
[article]
2018
arXiv
pre-print
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in higher-order logic theorem proving assistant tools. ...
Higher-order logic theorem proving is one of the most reliable technologies for verifying the properties of programs. ...
operating environment of the GERM framework to facilitate automated higher-order logic theorem proving. ...
arXiv:1803.00403v3
fatcat:jpgpzx5zxnbpbpzfdj7kowgee4
Automated Reasoning in Higher-Order Logic using the TPTP THF Infrastructure
2010
Journal of Formalized Reasoning
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logic, and the use of higher-order ATP in a range of domains. ...
The extension of the TPTP from first-order form (FOF) logic to typed higher-order form (THF) logic has provided a basis for new development and application of ATP systems for higher-order logic. ...
Thanks to Chad Brown for contributions of THF problems to the TPTP, developing the automated version of TPS, and implementing Satallax. ...
doi:10.6092/issn.1972-5787/1710
dblp:journals/jfrea/SutcliffeB10
fatcat:3j3xtlxvzbdjlofvl4ah62yuru
Model Checking the First-Order Fragment of Higher-Order Fixpoint Logic
[chapter]
Logic for Programming, Artificial Intelligence, and Reasoning
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We present a model checking algorithm for HFL1, the firstorder fragment of Higher-Order Fixpoint Logic. ...
This logic is capable of expressing many interesting properties which are not regular and, hence, not expressible in the modal μ-calculus. ...
Here we use the (branching temporal) fixpoint logic HFL1, the first-order fragment of Higher-Order Fixpoint Logic (HFL) [9] . ...
doi:10.1007/978-3-540-75560-9_7
dblp:conf/lpar/AxelssonL07
fatcat:rklhn3frujhsljpbbcctlkffiu
Deduction Beyond First-Order Logic (Dagstuhl Seminar 17371)
2018
Dagstuhl Reports
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The aim of the seminar was to bring together first-order automated reasoning experts and researchers working on deduction methods and tools that go beyond first-order logic. ...
Other practical problems need a mixture of first-order proof search and some more advanced reasoning (for instance, about higher-order formulas), or simply higher-level reasoning steps. ...
The proposed approach consists of over-approximations, underapproximations and their combination. ...
doi:10.4230/dagrep.7.9.26
dblp:journals/dagstuhl-reports/BlanchetteFST17
fatcat:yfc3wk2fwngc3i2dmjwrz3gsgi
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