## The Taming of the Cut. Classical Refutations with Analytic Cut (1994)

Venue: | JOURNAL OF LOGIC AND COMPUTATION |

Citations: | 52 - 1 self |

### BibTeX

@ARTICLE{D'Agostino94thetaming,

author = {Marcello D'Agostino and Marco Mondadori},

title = {The Taming of the Cut. Classical Refutations with Analytic Cut},

journal = {JOURNAL OF LOGIC AND COMPUTATION},

year = {1994},

volume = {4}

}

### Years of Citing Articles

### OpenURL

### Abstract

The method of analytic tableaux is a direct descendant of Gentzen's cutfree sequent calculus and is regarded as a paradigm of the notion of analytic deduction in classical logic. However, cut-free systems are anomalous from the proof-theoretical, the semantical and the computational point of view. Firstly, they cannot represent the use of auxiliary lemmas in proofs. Secondly, they cannot express the bivalence of classical logic. Thirdly, they are extremely inefficient, as is emphasized by the "computational scandal" that such systems cannot polynomially simulate the truth-tables. None of these anomalies occurs if the cut rule is allowed. This raises the problem of formulating a proof system which incorporates a cut rule and yet can provide a suitable model of classical analytic deduction. For this purpose we present an alternative refutation system for classical logic, that we call KE. This system, though being "close" to Smullyan's tableau method, is not cut-free but includes a class...