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
Formal Logic.Arthur N. Prior - 1955 - Oxford, Clarendon Press.
Selected Works.Jan Łukasiewicz - 1970 - Amsterdam: North-Holland Pub. Co..
Entailment. Vol. 1.Alan Ross Anderson & Nuel D. Belnap - 1977 - Canadian Journal of Philosophy 7 (2):405-411.
Notes on the Axiomatics of the Propositional Calculus.C. A. Meredith & A. N. Prior - 1963 - Notre Dame Journal of Formal Logic 4 (3):171-187.

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Condensed Detachment as a Rule of Inference.J. A. Kalman - 1983 - Studia Logica 42 (4):443 - 451.

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