Cut-based abduction

Marcello D'Agostino; Marcelo Finger; Dov Gabbay

doi:10.1093/jigpal/jzn020

Cut-based abduction

Marcello D'Agostino, Marcelo Finger, Dov Gabbay

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

In this paper we explore a generalization of traditional abduction which can simultaneously perform two different tasks: (i) given an unprovable sequent Γ⊢G, find a sentence H such that Γ,H⊢G is provable (hypothesis generation); (ii) given a provablesequent Γ⊢G, find a sentence H such that Γ⊢H and the proof of Γ,H⊢G is simpler than the proof of Γ⊢G (lemma generation). We argue that the two tasks should not be distinguished, and present a general procedure for finding suitable hypotheses or lemmas. When the original sequent is provable, the abduced formula can be seen as a cut formula with respect to Gentzen's sequent calculus, so the abduction method is cut-based. Our method is based on the tableau-like system KE and we argue for its advantages over existing abduction methods based on traditional Smullyan-style Tableaux.

Original language	English
Pages (from-to)	537-560
Number of pages	24
Journal	Logic Journal of the IGPL
Volume	16
Issue number	6
DOIs	https://doi.org/10.1093/jigpal/jzn020
State	Published - 2008

Bibliographical note

Funding Information:
∗Partly supported by CNPq grant PQ 301294/2004-6 and FAPESP project 04/14107-2. 1“Abduction consists in studying facts and devising a theory to explain them.” (C. P. Peirce, Collected Papers, vol. V, par. 145.) “Abduction is the process of forming an explanatory hypothesis. It is the only logical operation which introduces any new idea” (C. P. Peirce, Collected Papers, vol. V, par. 171).

Funding

∗Partly supported by CNPq grant PQ 301294/2004-6 and FAPESP project 04/14107-2. 1“Abduction consists in studying facts and devising a theory to explain them.” (C. P. Peirce, Collected Papers, vol. V, par. 145.) “Abduction is the process of forming an explanatory hypothesis. It is the only logical operation which introduces any new idea” (C. P. Peirce, Collected Papers, vol. V, par. 171).

Funders	Funder number
Fundação de Amparo à Pesquisa do Estado de São Paulo	04/14107-2
Conselho Nacional de Desenvolvimento Científico e Tecnológico	PQ 301294/2004-6

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N2 - In this paper we explore a generalization of traditional abduction which can simultaneously perform two different tasks: (i) given an unprovable sequent Γ⊢G, find a sentence H such that Γ,H⊢G is provable (hypothesis generation); (ii) given a provablesequent Γ⊢G, find a sentence H such that Γ⊢H and the proof of Γ,H⊢G is simpler than the proof of Γ⊢G (lemma generation). We argue that the two tasks should not be distinguished, and present a general procedure for finding suitable hypotheses or lemmas. When the original sequent is provable, the abduced formula can be seen as a cut formula with respect to Gentzen's sequent calculus, so the abduction method is cut-based. Our method is based on the tableau-like system KE and we argue for its advantages over existing abduction methods based on traditional Smullyan-style Tableaux.

AB - In this paper we explore a generalization of traditional abduction which can simultaneously perform two different tasks: (i) given an unprovable sequent Γ⊢G, find a sentence H such that Γ,H⊢G is provable (hypothesis generation); (ii) given a provablesequent Γ⊢G, find a sentence H such that Γ⊢H and the proof of Γ,H⊢G is simpler than the proof of Γ⊢G (lemma generation). We argue that the two tasks should not be distinguished, and present a general procedure for finding suitable hypotheses or lemmas. When the original sequent is provable, the abduced formula can be seen as a cut formula with respect to Gentzen's sequent calculus, so the abduction method is cut-based. Our method is based on the tableau-like system KE and we argue for its advantages over existing abduction methods based on traditional Smullyan-style Tableaux.

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Cut-based abduction

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