Tense and dynamic algebras related to GFA

The present paper is an attempt to suggest and scru-tinize tense operators in the dynamic logic B which is regarded as a set of propositions about the general fuzzy automaton F˜, in which its underlying structure has been a bounded poset. Here, the operators Tδ, Pδ, Hδ and Fδ are proposed regardless of what propositional connectives the logic comprises. For this purpose, the axiomatiza-tion 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 (Tδ, Pδ) 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 B is representable in its Dedekind-MacNeille completion. Representation the-orems for dynamic and tense algebra are explicated in details in the related given theorems.