Classical logic, intuitionistic logic, and the Peirce rule.

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...

A modal logic amalgam of classical and intuitionistic propositional logic

We present a modal extension of classical propositional logic in which intuitionistic propositional logic is mirrored by means of the modal operator. In this sense, the modal extension combines classical and intuitionistic propositional logic avoiding the collapsing problem. Adopting ideas from a recent paper (S. Lewitzka, A denotational semantics for a Lewis-style modal system close to S1, 201...

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.