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, M. 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 - https://jahla.hatef.ac.ir/article_127100.html L1 - https://jahla.hatef.ac.ir/article_127100_9b1bdd27cdcb2dfb1e4146b534417f0b.pdf ER -