Logic Journal of the IGPL 27 (4):451-477 (2019)
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Abstract |
In Jaśkowski’s model of discussion, discussive connectives represent certain interactions that can hold between debaters. However, it is not possible within the model for participants to use explicit modal operators. In the paper we present a modal extension of the discussive logic $\textbf{D}_{\textbf{2}}$ that formally corresponds to an extended version of Jaśkowski’s model of discussion that permits such a use. This logic is denoted by $\textbf{m}\textbf{D}_{\textbf{2}}$. We present philosophical motivations for the formulation of this logic. We also give syntactic characterizations of the logic and propose a comparison with certain other modal systems. In particular, we prove that $\textbf{m}\textbf{D}_{\textbf{2}}$ is neither normal nor regular. On the basis of the axiomatization of $\textbf{D}_{\textbf{2}}$, we give an axiomatization of $\textbf{m}\textbf{D}_{\textbf{2}}$. We also give another axiomatization which is not based on the axiomatization of $\textbf{D}_{\textbf{2}}$. Furthermore, we give a natural Kripke-style semantics for $\textbf{m}\textbf{D}_{\textbf{2}}$ and prove the respective adequacy theorems.
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DOI | 10.1093/jigpal/jzz014 |
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References found in this work BETA
Propositional Calculus for Contradictory Deductive Systems.Stanisław Jaśkowski - 1969 - Studia Logica 24 (1):143 - 160.
A Propositional Calculus for Inconsistent Deductive Systems.Stanisław Jaśkowski - 1999 - Logic and Logical Philosophy 7:35.
On the Discussive Conjunction in the Propositional Calculus for Inconsistent Deductive Systems.Stanisław Jaśkowski - 1999 - Logic and Logical Philosophy 7:57.
The Axiomatization of S. Jaśkowski's Discussive System.Jerzy Kotas - 1974 - Studia Logica 33 (2):195-200.
Remarks on Discussive Propositional Calculus.Tomasz Furmanowski - 1975 - Studia Logica 34 (1):39 - 43.
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