Copies of Classical Logic in Intuitionistic Logic

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...

Reduction Properties in Classical and Intuitionistic Logic

1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2: Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3: The Classical Calculus . . ....

Deciding Intuitionistic Propositional Logic via Translation into Classical Logic

W. McCune, ed. 14 International Conference on Automated Deduction (CADE-14), LNAI 1249, pp. 131–145, c ©Springer Verlag, 1997. Abstract. We present a technique that efficiently translates propositional intuitionistic formulas into propositional classical formulas. This technique allows the use of arbitrary classical theorem provers for deciding the intuitionistic validity of a given proposition...