Abstract

This paper is an exercise in formal and philosophical logic. I will show how intuitionistic propositional logic can be extended with a new two-place connective, not expressible in the traditional language of intuitionistic logic (the language of conjunction, disjunction, negation and implication). The new system will be shown to be a conservative extension of intuitionistic logic. After examining the formal properties of this extension, the task will be to consider whether this is an `acceptable' extension of intuitionistic logic. It will turn out that on some

Citations

195	Natural Deduction. A proof Theoretical Study, Almqvist - Prawitz - 1965
118	Elements of Intuitionism - Dummett - 1977
78	Intuitionistic Logic: Model Theory and Forcing - Fitting - 1969
67	Intuitionnistic logic - Dalen - 1986
66	An introduction - Heyting - 1956
57	The Collected Papers of Gerhard Gentzen - Gentzen - 1969
27	Entailment: The Logic of Relevance and Necessity, volume 2 - Anderson, Belnap, et al. - 1992
11	Spaces, volume 3 of Cambridge Studies in Advanced Mathematics - Stone - 1982
7	Inconsistent Mathematics - Mortensen
2	On some new intuitionistic propositional connectives. 1 - Gabbay - 1977
1	de Jongh. A class of intuitionistic connectives - Dick - 1980