A new regular constant in intuitionistic propositional logic
type: Item
instance of: scholarly article
title: A new regular constant in intuitionistic propositional logic
zbMATH Open document ID: 0876.03005
DOI: 10.1007/BF02106749
published in: Siberian Mathematical Journal
publication date: 1997-06-18T00:00:00Z
review text: The author considers intuitionistic propositional logic where, besides the operations \(\&,\vee, \supset\), and \(\neg\), and besides the usual constants 0 and 1, there is an additional constant \(\varphi\). As models the author uses Kripke models. One such logic, denoted by Reg, is characterized through the following properties: 1) \(\neg\neg \varphi\) and \(\varphi\) are equivalent; 2) \(\varphi\vee\neg\varphi\) is the smallest \(\gamma\) for which \(\neg\gamma=0\). The intuitionistic deductive system is expanded for Reg and completeness of the expanded system is proved. For a further expansion of this logic, the author considers a special type of models, i.e., finite Kripke models whose last but one vertices are followed exactly by two last ones, forming in this way a forking, such that \(\varphi\) is valid exactly in one of the end vertices of each forking. The logic for these models is denoted by \(\text{Reg}^+\). The deductive system of Reg is extended for \(\text{Reg}^+\) and completeness of the extended system is proved.
Mathematics Subject Classification ID: 03B20
zbMATH DE Number: 1023898
zbMATH Keywords: intuitionistic logic
zbMATH Keywords: additional constant
zbMATH Keywords: Kripke models
author: Aleksandr D. Yashin
reviewed by: Ants Tauts
MaRDI profile type: Publication
cites work: Q5650663
cites work: The Smetanich logic \(T^ \Phi\) and two definitions of a new intuitionistic connective
cites work: A Characterization of the Classes of Finite Tree Frames Which are Adequate for the Intuitionistic Logic
full work available at URL: https://doi.org/10.1007/bf02106749
OpenAlex ID: W2062045360
description: scientific article; zbMATH DE number 1023898