A Closer Look at Some Subintuitionistic Logics

Notre Dame Journal of Formal Logic 42 (4):225-255 (2001)
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Abstract

In the present paper we study systematically several consequence relations on the usual language of propositional intuitionistic logic that can be defined semantically by using Kripke frames and the same defining truth conditions for the connectives as in intuitionistic logic but without imposing some of the conditions on the Kripke frames that are required in the intuitionistic case. The logics so obtained are called subintuitionistic logics in the literature. We depart from the perspective of considering a logic just as a set of theorems and also depart from the perspective taken by Restall in that we consider standard Kripke models instead of models with a base point. We study the relations between subintuitionistic logics and modal logics given by the translation considered by Došen. Moreover, we classify the logics obtained according to the hierarchy considered inAlgebraic Logic

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References found in this work

What is strict implication?Ian Hacking - 1963 - Journal of Symbolic Logic 28 (1):51-71.
Basic Propositional Calculus I.Mohammad Ardeshir & Wim Ruitenburg - 1998 - Mathematical Logic Quarterly 44 (3):317-343.
Subintuitionistic Logics.Greg Restall - 1994 - Notre Dame Journal of Formal Logic 35 (1):116-129.
Weak Logics with Strict Implication.Giovanna Corsi - 1987 - Mathematical Logic Quarterly 33 (5):389-406.

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