Intuitionistic Logic with A "Definitely" Operator, Research Report 97.05 [1 citations — 1 self]
Abstract:
This paper introduces a logic ILED derived from standard intuitionistic predicate logic by adding two operators Dj for "Definitely j " and ~j for "Experience rejects j". A further negation j = def (j��^) � � ~j, which we call real negation, is introduced. Real negation is like intuitionistic negation when there are no D-operators but deviates when there are. We see that Dj j is valid but Dj � � j is not and hence that contraposition fails for real negation. We give a semantics for this logic, axiomatise it and prove the axiomatisation complete. Finally we show that real negation behaves as standard intuitionistic negation within D-free contexts. The logic ILED is proposed as an extension of intuitionistic logic apt for use as a general logic.
