Data di Pubblicazione:
2008
Citazione:
Cut-based abduction / M. D'Agostino, M. Finger, D. Gabbay. - In: LOGIC JOURNAL OF THE IGPL. - ISSN 1367-0751. - 16:6(2008), pp. 537-560.
Abstract:
In this paper we explore a generalization of traditional abduction which as simultaneously perform two different tasks: (i) given an unprovable sequent Gamma proves G, find a sentence II such that Gamma, II proves G is provable (hypothesis generation); (ii) given a provable sequent Gamma proves G, find a sentence II such that Gamma proves II and the proof of Gamma, II proves G is simpler than the proof of Gamma proves 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 tablean-like system KE and we argue for its advantages over existing adduction methods based on traditional Smullyan-style Tableaux.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Abduction; cut rule; KE method
Elenco autori:
M. D'Agostino, M. Finger, D. Gabbay
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