Abstract
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, based either on condensed detachment or on the resolution rule of J. A. Robinson, to investigate 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.
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Kalman, J.A. The two-property and condensed detachment. Stud Logica 41, 173–179 (1982). https://doi.org/10.1007/BF00370343
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DOI: https://doi.org/10.1007/BF00370343