Intuitionistic Choice and Restricted Classical Logic

Intuitionistic Choice and Restricted Classical Logic

Recently, Coquand and Palmgren considered systems of intuitionistic arithmetic in all finite types together with various forms of the axiom of choice and a numerical omniscience schema (NOS) which implies classical logic for arithmetical formulas. Feferman subsequently observed that the proof theoretic strength of such systems can be determined by functional interpretation based on a non-constr...

Intuitionistic choice and classical logic

Intuitionistic Logic with Classical Atoms

In this paper, we define a Hilbert-style axiom system IPCCA that conservatively extends intuitionistic propositional logic (IPC) by adding new classical atoms for which the law of excluded middle (LEM) holds. We establish completeness of IPCCA with respect to an appropriate class of Kripke models. We show that IPCCA is a conservative extension of both classical propositional logic (CPC) and als...

Epistemic semantics for classical and intuitionistic logic

1 In this paper I propose to explain how several nonstandard semantic systems for the propositional logic can be seen as employing essentially the same principles for defining the notion of logical entailment and the more basic idea of assignment of truth-values to molecular sentences. The systems are Kleene's three-valued matrix for the strong connectives, Lukasiewicz's three-valued matrix, su...

Classical and Intuitionistic Logic Are Asymptotically Identical

This paper considers logical formulas built on the single binary connector of implication and a finite number of variables. When the number of variables becomes large, we prove the following quantitative results: asymptotically, all classical tautologies are simple tautologies. It follows that asymptotically, all classical tautologies are intuitionistic.