The two-property and condensed detachment

Studia Logica 41 (2-3):173 - 179 (1982)
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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DOI 10.1007/BF00370343
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References found in this work BETA
Arthur N. Prior (1962). Formal Logic. Oxford, Clarendon Press.
Jan Łukasiewicz (1970). Selected Works. Amsterdam,North-Holland Pub. Co..
Alan Ross Anderson & Nuel D. Belnap (1977). Entailment. Vol. 1. Canadian Journal of Philosophy 7 (2):405-411.
C. A. Meredith & A. N. Prior (1968). Equational Logic. Notre Dame Journal of Formal Logic 9 (3):212-226.

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