Notre Dame Journal of Formal Logic

A Closer Look at Some Subintuitionistic Logics

Sergio Celani and Ramon Jansana


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 in Abstract Algebraic Logic.

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Notre Dame J. Formal Logic, Volume 42, Number 4 (2001), 225-255.

First available in Project Euclid: 12 September 2003

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Zentralblatt MATH identifier

Primary: 03B20: Subsystems of classical logic (including intuitionistic logic) 03B6D 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}
Secondary: 03699

subintuitionistic logic modal logic intuitionistic logic protoalgebraic logics equivalential logics algebraizable logics


Celani, Sergio; Jansana, Ramon. A Closer Look at Some Subintuitionistic Logics. Notre Dame J. Formal Logic 42 (2001), no. 4, 225--255. doi:10.1305/ndjfl/1063372244.

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