Cut-Based Abduction

Logic Journal of the IGPL 16 (6):537-560 (2008)
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Abstract

In this paper we explore a generalization of traditional abduction which can simultaneously perform two different tasks: given an unprovable sequent Γ ⊢ G, find a sentence H such that Γ, H ⊢ G is provable ; given a provable sequent 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 . 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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Marcello D'Agostino
Università degli Studi di Milano

Citations of this work

Cognitive Economics and the Logic of Abduction.John Woods - 2012 - Review of Symbolic Logic 5 (1):148-161.
An Analytic Tableau System for Natural Logic.Reinhard Muskens - 2010 - In Maria Aloni, H. Bastiaanse, T. De Jager & Katrin Schulz (eds.), Logic, Language and Meaning. Springer. pp. 104-113.

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References found in this work

Advice on Abductive Logic.Dov Gabbay & John Woods - 2006 - Logic Journal of the IGPL 14 (2):189-219.
Don't Eliminate Cut.George Boolos - 1984 - Journal of Philosophical Logic 13 (4):373 - 378.
Are Tableaux an Improvement on Truth-Tables?Marcello D'Agostino - 1992 - Journal of Logic, Language and Information 1 (3):235-252.
Surviving Abduction.Walter Carnielli - 2006 - Logic Journal of the IGPL 14 (2):237-256.

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