Magically Constraining the Inverse Method Using Dynamic Polarity Assignment

Chaudhuri, Kaustuv

doi:10.1007/978-3-642-16242-8_15

Cited by 2 publications

(3 citation statements)

References 18 publications

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“…The closest related work to the present paper is on dynamic polarity assignment [5] in the inverse method. The main goal of that paper is similar -to use the inverse method to perform proof search in such a way that forward reasoning is guaranteed to terminate.…”

Section: Related Workmentioning

confidence: 99%

“…The main goal of that paper is similar -to use the inverse method to perform proof search in such a way that forward reasoning is guaranteed to terminate. There are, however, substantial differences: the input in [5] is a collection of Horn clauses that is assumed to be both mode-correct and terminating on all well-moded queries. In constrast, our method does not require anything apart from the presence of forward subsumption.…”

Section: Related Workmentioning

confidence: 99%

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Disproving Using the Inverse Method by Iterative Refinement of Finite Approximations

Brock-Nannestad

Chaudhuri

2015

Lecture Notes in Computer Science

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International audienceIn first-order logic, forward search using a complete strategy such as the inverse method can get stuck deriving larger and larger consequence sets when the goal query is unprovable. This is the case even in trivial theories where backward search strategies such as tableaux methods will fail finitely. We propose a general mechanism for bounding the consequence sets by means of finite approximations of infinite types. If the inverse method also implements forward subsumption and globalization, then the search space under this approximation is finite. We therefore obtain a type-directed iterative refinement algorithm for disproving queries. The method has been implemented for intuitionistic first-order logic, and we discuss its performance on a variety of problems

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Disproving Using the Inverse Method by Iterative Refinement of Finite Approximations

Brock-Nannestad

Chaudhuri

2015

Lecture Notes in Computer Science

Self Cite

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“…First, the subformula property, which is the sine qua non of automation; and second, polarity and focusing, wherein the ordinary sequent rules coalesce into synthetic "macro" forms to make larger logical steps without sacrificing completeness [1]. The careful use of focusing enables a general search strategy to implement a wide variety of operational strategies directly [8,6].…”

Section: Introductionmentioning

confidence: 99%

Compact Proof Certificates for Linear Logic

Chaudhuri

2012

Certified Programs and Proofs

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Abstract. Linear logic is increasingly being used as a tool for communicating reasoning agents in domains such as authorization, access control, electronic voting, etc., where proof certificates represent evidence that must be verified by proof consumers as part of higher protocols. Controlling the size of these certificates is critical. We assume that the proof consumer is allowed to do some search to reconstruct details of the full proof that are omitted from the certificates. Because the decision problem for linear logic is unsolvable, the certificate must contain at least enough information to bound the search: we show how to use the sequence of contractions in the sequent proof for this bound. The remaining content of the proof, in particular the information about resource divisions, can then be omitted from the certificate. We also describe a technique for giving a variable amount of additional search hints to the proof consumer to limit its non-determinism.

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Magically Constraining the Inverse Method Using Dynamic Polarity Assignment

Cited by 2 publications

References 18 publications

Disproving Using the Inverse Method by Iterative Refinement of Finite Approximations

Disproving Using the Inverse Method by Iterative Refinement of Finite Approximations

Compact Proof Certificates for Linear Logic

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