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On Interpolation in...
On Interpolation in Automated Theorem Proving
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- Bonacina, M.P. (author)
- Universita degli Studi di Verona,Verona University
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- Johansson, Moa, 1981 (author)
- Chalmers tekniska högskola,Chalmers University of Technology
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(creator_code:org_t)
- 2014-10-19
- 2015
- English.
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In: Journal of Automated Reasoning. - : Springer Science and Business Media LLC. - 0168-7433 .- 1573-0670. ; 54:1, s. 69-97
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http://dx.doi.org/10...
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Abstract
Subject headings
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- Given two inconsistent formul', a (reverse) interpolant is a formula implied by one, inconsistent with the other, and only containing symbols they share. Interpolation finds application in program analysis, verification, and synthesis, for example, towards invariant generation. An interpolation system takes a refutation of the inconsistent formul' and extracts an interpolant by building it inductively from partial interpolants. Known interpolation systems for ground proofs use colors to track symbols. We show by examples that the color-based approach cannot handle non-ground refutations by resolution and paramodulation/superposition. We present a two-stage approach that works by tracking literals, computes a provisional interpolant, which may contain non-shared symbols, and applies lifting to replace non-shared constants by quantified variables. We obtain an interpolation system for non-ground refutations, and we prove that it is complete, if the only non-shared symbols in provisional interpolants are constants.
Subject headings
- NATURVETENSKAP -- Data- och informationsvetenskap (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences (hsv//eng)
Keyword
- Superposition
- Resolution
- Interpolation systems
Publication and Content Type
- art (subject category)
- ref (subject category)
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