An Interactive Derivation Viewer

Trac, Steven; Puzis, Yury; Sutcliffe, Geoff

doi:10.1016/j.entcs.2006.09.025

Cited by 29 publications

(18 citation statements)

References 9 publications

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“…The TRAMP-system by Meier [14] transforms resolution proofs into natural deduction proofs at the assertion level. The interactive derivation viewer IDV by Trac et al [15] displays a derivation in the TPTP-format as a directed acyclic graph. In [16], Denzinger and Schulz show how to obtain human-readable proof presentations in the context of distributed equational reasoning.…”

Section: Introductionmentioning

confidence: 99%

Understanding Resolution Proofs through Herbrand’s Theorem

Hetzl

Libal

Riener

et al. 2013

Lecture Notes in Computer Science

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Abstract. Computer-generated proofs are usually difficult to grasp for a human reader. In this paper we present an approach to understanding resolution proofs through Herbrand's theorem and the implementation of a tool based on that approach. The information we take as primitive is which instances have been chosen for which quantifiers, in other words: an expansion tree. After computing an expansion tree from a resolution refutation, the user is presented this information in a graphical user interface that allows flexible folding and unfolding of parts of the proof. This interface provides a convenient way to focus on the relevant parts of a computer-generated proof. In this paper, we describe the prooftheoretic transformations, the implementation and demonstrate its usefulness on several examples.

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Section: Introductionmentioning

confidence: 99%

Understanding Resolution Proofs through Herbrand’s Theorem

Hetzl

Libal

Riener

et al. 2013

Lecture Notes in Computer Science

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“…A proof may be, e.g., 1) communicated to another tool within a combined reasoning system such as a static program analyser, 2) used for extracting interpolants [29,35], or 3) visualised [54]. An important category of tools which rely on ATPs and on proofs generated by them are the so called hammers [40,30,1].…”

Section: Why (Mechanically Checkable) Proofs?mentioning

confidence: 99%

Checkable Proofs for First-Order Theorem Proving

Reger¹,

Suda²

EPiC Series in Computing

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Inspired by the success of the DRAT proof format for certification of boolean satisfiability (SAT), we argue that a similar goal of having unified automatically checkable proofs should be sought by the developers of automatic first-order theorem provers (ATPs). This would not only help to further increase assurance about the correctness of prover results, but would also be indispensable for tools which rely on ATPs, such as "hammers" employed within interactive theorem provers. The current situation, represented by the TSTP format, is unsatisfactory, because this format does not have a standardised semantics and thus cannot be checked automatically. Providing such semantics, however, is a challenging endeavour. One would ideally like to have a proof format which covers only-satisfiability-preserving operations such as Skolemisation and is versatile enough to encompass various proving methods (i.e. not just superposition) or is perhaps even open-ended towards yet to be conceived methods or at least easily extendable in principle. Going beyond pure first-order logic to theory reasoning in the style of SMT, or beyond proofs to certification of satisfiability are further interesting challenges. Although several projects have already provided partial solutions in this direction, we would like to use the opportunity of ARCADE to further promote the idea and gather critical mass needed for its satisfactory realisation. The challengeWe would like to propose to the first-order ATP community the challenge of designing, implementing and bringing into practice a unified mechanically checkable proof format along with an efficient proof checker. The format should support the whole reasoning pipeline including formula preprocessing, be sufficiently general to cover all the solving techniques currently employed by ATPs, and be open to future extensions for proof recording of techniques yet to be developed. In this paper, we summarise the current situation regarding proof output of ATPs, explain why we think striving for a mechanically checkable proof format is a worthy effort, list the main properties we believe an ideal format should satisfy, attempt to give an overview of work already done in the first-order ATP community and related areas, and, finally, suggest possible avenues and the next steps to be taken for meeting the challenge.At this point we add the disclaimer that other people have already examined this challenge in various ways. We attempt to present this previous work and do not claim that what we are suggesting is novel, but instead we are calling for further work in this area. Our main aim at ARCADE is to solicit opinions from experts on why the proposed idea has not yet made its way to practice and on how exactly should the community proceed to achieve the envisioned goal.

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“…cnf(26,plain,(~big_q(X1)),inference(csr,[], [9,21])). cnf(27,plain,(big_p(esk1_0)),inference(sr,[], [16,26])). cnf(28,plain,(~big_p(X1)),inference(sr,[], [25,26])).…”

Section: Representing Derivations In the Tableau Calculusmentioning

confidence: 99%

“…cnf(27,plain,(big_p(esk1_0)),inference(sr,[], [16,26])). cnf(28,plain,(~big_p(X1)),inference(sr,[], [25,26])). cnf(29,plain,($false),inference(sr,[], [27,28] A derivation for SYN054+1 in the resolution calculus using the TPTP syntax into two branches.…”

Section: Representing Derivations In the Tableau Calculusmentioning

confidence: 99%

“…This is a proposed format, not yet formally established as a TPTP standard; community feedback with suggestions for improvement are welcome. The goal is to produce a format that is compatible with the existing format for representing derivations (reviewed in Section 2.2), so that existing TPTP infrastructure for proof processing, e.g., the GDV proof verifier [21] and the IDV proof visualizer [26], can be used with little or no modification.…”

Section: Introductionmentioning

confidence: 99%

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Using the TPTP Language for Representing Derivations in Tableau and Connection Calculi

Otten

Sutcliffe

EPiC Series in Computing

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The TPTP language, developed within the framework of the TPTP library, allows the representation of problems and solutions in first-order and higher-order logic. Whereas the writing of solutions in resolution calculi is well documented and used, an appropriate representation of solutions in tableau or connection calculi using the TPTP syntax has not yet been specified. This paper describes how the TPTP language can be used to represent derivations and solutions in standard tableau, sequent and connection calculi for classical first-order logic.

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An Interactive Derivation Viewer

Cited by 29 publications

References 9 publications

Understanding Resolution Proofs through Herbrand’s Theorem

Understanding Resolution Proofs through Herbrand’s Theorem

Checkable Proofs for First-Order Theorem Proving

Using the TPTP Language for Representing Derivations in Tableau and Connection Calculi

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