A Gentzen- or Beth-type system, a practical decision procedure and a constructive completeness proof for the counterfactual logics VCand VCS

Autor: de Swart, H. C. M.
Zdroj: Journal of Symbolic Logic; March 1983, Vol. 48 Issue: 1 p1-20, 20p
Abstrakt: In [1] and [2] D. Lewis formulates his counterfactual logic VCas follows. The language contains the connectives ?, ?, ?, ¬ and the binary connective =. A= Bis read as “Ais at least as possible as B”. The following connectives are defined in terms of =.A< B: = ¬(B= A) (it is more possible that Athan that B).? A? ¬(? = A) (? is the false formula; Ais possible).? A? ? = ¬A(Ais necessary).(if Awere the case, then Bwould be the case).(if Awere the case, then Bmight be the case).and are two counterfactual conditional operators. (AB) iff ¬(A¬B).The following axiom system VCis presented by D. Lewis in [1] and [2]: V: (1) Truthfunctional classical propositional calculus.
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