Abstract
The present paper is to be considered as a sequel to [1], [2]. It is known that Johansson's minimal logic is not uniform, i.e. there is no single matrix which determines this logic. Moreover, the logic C J is 2-uniform. It means that there are two uniform logics C 1, C 2 (each of them is determined by a single matrix) such that the infimum of C 1 and C 2 is C J. The aim of this paper is to give a detailed description of the logics C 1 and C 2. It is performed in a lattice-theoretical language.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Hawranek and J. Zygmunt, On the degree of complexity of sentential logics. A couple of examples, Studia Logica, vol. 40 (1981), pp. 141–153.
J. Hawranek and J. Zygmunt, On the degree of complexity of sentential logics. II. An example of the logic with semi-negation, Studia Logica, vol. 43 (1984), pp. 405–413.
H. Rasiowa, An Algebraic Approach to Non-Classical Logics, North-Holland, Amsterdam 1974.
E. Wójcicki, Some remarks on the consequence operation in sentential logics, Fundamenta Mathematicae, vol. 68 (1970), pp. 269–279.
A. Wroński, On cardinalities of matrices strongly adequate for the intuitionistic propositional logic, Reports on Mathematical Logic 3 (1974), pp. 67–72.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hawranek, J. On the degree of complexity of sentential logics, III. An example of Johansson's minimal logic. Stud Logica 46, 283–289 (1987). https://doi.org/10.1007/BF00370640
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00370640