A three-valued interpretation for a relevance logic
Fred R. Johnson · PhilPapers (PhilPapers Foundation) · 1976
A Three-Valued Interpretation for a Relevance Logic • In thi.s paper an entailment relation which holds between certain propositions of ,the propositional calculus will be defined both syntactically and semantically.Some theorems about this relation will show why one could not follow Lewis to prove that a contradiction entails, for the notion of entailment discussed below, every proposition.We will develop a system RC in which the primitive symbols are the five symbols v c ) and the propositional variablesThe formation rules of RC arei 1) A variable standing alone is a well-formed formula (wff).2) If A and B are well-formed (wf) then (A v B) is wf.3) If A and B are wf then (A • B) is wf. 4) If A is wf then -A is wf.5) If A is wf it is so in virtue of 1) ~ 4).We will let capital letters with or without subscripts be variables which range over occurre~ces of wffs.Following Church (see I'ntroduction to Mathematical Logi~, pp.135-6) we will say that X is the full disjunctive normal form of A (the FDNF of A), where pi , ... , 1 pi are all and the only n