TY - JOUR
ID - 127100
TI - Tense and dynamic algebras related to GFA
JO - Journal of Algebraic Hyperstructures and Logical Algebras
JA - JAHLA
LA - en
SN - 2676-6000
AU - Abolpour, Kh.
AU - Zahedi, M. M
AU - shamsizadeh, marzieh
AD - Department of Mathemathics, Shiraz Branch, Islamic Azad University, Shiraz, Iran
AD - Department of Mathemathics, Graduate University of Advanced Technology, Kerman, Iran
AD - Khatam Alanbia University of Technology, Behbahan, Iran
Y1 - 2021
PY - 2021
VL - 2
IS - 1
SP - 33
EP - 46
KW - Dynamic algebra
KW - general fuzzy automata
KW - tense algebra
KW - modal
KW - transition frame
KW - representable
DO - 10.52547/HATEF.JAHLA.2.1.3
N2 - The present paper is an attempt to suggest and scrutinize tense operators in the dynamic logic $textbf{B}$ which is regarded as a set of propositions about the general fuzzy automaton $ tilde{F} $, in which its underlying structure has been a bounded poset. Here, the operators $ T_{delta}, P_{delta}, H_{delta}$ and $ F_{delta} $ are proposed regardless of what propositional connectives the logic comprises. For this purpose, the axiomatization of universal quantifiers is applied as a starting point and these axioms are modified. In this study, firstly, we demonstrate that the operators can be identified as modal operators and the pairs $ (T_{delta},P_{delta}) $ are examined as the so-called dynamic pairs. In addition, constructions of these operators are attained in the corresponding algebra and in the following a transition frame is suggested. Besides, the problem of finding a transition frame is solved in the case when the tense operators are given. Specifically, this study shows that the tense algebra $ textbf{B} $ is representable in its Dedekind-MacNeille completion. Representation theorems for dynamic and tense algebra are explicated in details in the related given theorems.
UR - http://jahla.hatef.ac.ir/article_127100.html
L1 - http://jahla.hatef.ac.ir/article_127100_9b1bdd27cdcb2dfb1e4146b534417f0b.pdf
ER -