On the form of witness terms

Hetzl, Stefan

doi:10.1007/s00153-010-0186-7

Cited by 7 publications

(4 citation statements)

References 36 publications

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“…Let us now compare this result with another upper bound that has previously been obtained in [Het10]. To that aim let G 0 pπq denote the regular tree grammar underlying Gpπq which can be obtained by setting all non-terminals to non-rigid.…”

Section: Herbrand-contentmentioning

confidence: 76%

“…This corollary shows that rrπss is an upper bound on the Herbrand-disjunctions obtainable by cut-elimination from π. Let us now compare this result with another upper bound that has previously been obtained in [Het10]. To that aim let G 0 pπq denote the regular tree grammar underlying Gpπq which can be obtained by setting all non-terminals to non-rigid.…”

Section: Herbrand-contentmentioning

confidence: 76%

“…To that aim let G 0 pπq denote the regular tree grammar underlying Gpπq which can be obtained by setting all non-terminals to non-rigid. In this notation, a central result of [Het10], adapted to this paper's setting is Theorem 7.4. Let π be a proof of a formula of the shape Dx 1 .…”

Section: Herbrand-contentmentioning

confidence: 99%

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Herbrand-Confluence

Hetzl¹,

Straßburger²

2013

Logical Methods in Computer Science

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Abstract. We consider cut-elimination in the sequent calculus for classical first-order logic. It is well known that this system, in its most general form, is neither confluent nor strongly normalizing. In this work we take a coarser (and mathematically more realistic) look at cut-free proofs. We analyze which witnesses they choose for which quantifiers, or in other words: we only consider the Herbrand-disjunction of a cut-free proof. Our main theorem is a confluence result for a natural class of proofs: all (possibly infinitely many) normal forms of the non-erasing reduction lead to the same Herbrand-disjunction.

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Section: Herbrand-contentmentioning

confidence: 76%

Section: Herbrand-contentmentioning

confidence: 76%

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Herbrand-Confluence

Hetzl¹,

Straßburger²

2013

Logical Methods in Computer Science

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“…one that has been generated algorithmically) the task is to transform it into a shorter and more structured proof of the same theorem by the introduction of cuts which -on the mathematical level -represent lemmas. An algorithmic reversal of cut-elimination is rendered possible by recent groundbreaking results (like [10,8] and [12], see also [9]) that establish a new connection between proof theory and formal language theory.…”

Section: Theoretical Foundationsmentioning

confidence: 99%

Project Presentation: Algorithmic Structuring and Compression of Proofs (ASCOP)

Hetzl

2012

Lecture Notes in Computer Science

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Computer-generated proofs are typically analytic, i.e. they essentially consist only of formulas which are present in the theorem that is shown. In contrast, mathematical proofs written by humans almost never are: they are highly structured due to the use of lemmas. The ASCOP-project aims at developing algorithms and software which structure and abbreviate analytic proofs by computing useful lemmas. These algorithms will be based on recent groundbreaking results establishing a new connection between proof theory and formal language theory. This connection allows the application of efficient algorithms based on formal grammars to structure and compress proofs.

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A Sequent Calculus with Implicit Term Representation

Hetzl

2010

Computer Science Logic

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We investigate a modification of the sequent calculus which separates a first-order proof into its abstract deductive structure and a unifier which renders this structure a valid proof. We define a cutelimination procedure for this calculus and show that it produces the same cut-free proofs as the standard calculus, but, due to the implicit representation of terms, it provides exponentially shorter normal forms. This modified calculus is applied as a tool for theoretical analyses of the standard calculus and as a mechanism for a more efficient implementation of cut-elimination.

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On the form of witness terms

Cited by 7 publications

References 36 publications

Herbrand-Confluence

Herbrand-Confluence

Project Presentation: Algorithmic Structuring and Compression of Proofs (ASCOP)

A Sequent Calculus with Implicit Term Representation

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