EXTENSIONS OF INTUITIONISTIC LOGIC WITHOUT THE DEDUCTION THEOREM: SOME SIMPLE EXAMPLES
Lloyd Humberstone · Reports on Mathematical Logic · 2006
A b s t r a c t. We provide some illustrations of consequence relations extending that associated with intuitionistic propositional logic but lacking the Deduction Theorem, together with a discussion of issues|of some interest in their own right|raised by these examples. There are two main examples, with some minor variations: one in which the language of intuitionistic logic is retained, and one in which this language is expanded.