The two-property and condensed detachment

✍ Scribed by J. A. Kalman

• Publisher: Springer Netherlands
• Year: 1982
• Tongue: English
• Weight: 438 KB
• Volume: 41
• Category: Article
• ISSN: 0039-3215
• DOI: 10.1007/bf00370343

✦ Synopsis

In the first part of this paper we indicate how Meredith's condensed detachment may be used to give a new proof of Belnap's theorem that if every axiom x of a calculus S has the "two-property" that every variable which occurs in x occurs exactly twice in x, then every theorem of S is a substitution instance of a theorem of S which has the two-property. In the remainder of the paper we discuss the use of mechanical theorem-provers, base4 either on condensed detachment or on the resolution rule of J. A. Robinson, to iuvcstigate various calculi whose axioms all have the two-property. Particular attention is given to "D-groupoids', i.e. sets of formulae which are closed under condensed detachment.