Abstract:
By means of investigating basic properties of maximally consistent theories in ukasiewicz fuzzy propositional logic, it is proved that each maximally consistent theory is the kernel of some valuation and vice versa, and consequently a structural characterization of maximally consistent theories in this logic is obtained. By virtue of the continuity of ukasiewicz implication operator, a fuzzy topology as well as its cut topology on the set of all maximally consistent theories is introduced. It is proved that this fuzzy topological space is zero-dimensional and nice-compact, but not covering-compact, and its cut space is covering-compact and metrizable.
