A natural negation completion of Urquhart's many-valued logic \(C\) (Q1386684)

Urquhart's logic C is designed as a preliminary to Łukasiewicz's infinite-valued logic Lw; it may also be seen as the positive part of Dummett's LC minus contraction. The present paper supplements C with a semi-intuitionistic negation, \(\neg A =_{\text{df}}A\to F\), for \(F\) the propositional constant falsity. Axiomatically, add \(F\to A\) to C. This system, CI, is given a Routley-Meyer relational semantics and proved to be sound and complete.