Many-valued tense logic and the problem of determination

A three-valued tense logic based on the three-valued Lukasiewiczian propositional logic is constructed. The aim of the construction is formalization of the argument from the principle of causality in favor of the thesis of determinism. It is shown that, if density of time is assumed, the argument fails. The time is divided into real and possible time. Facts which take place in real time are determined, and those that take place in possible time are only possible. Lukasiewicz´s notion of possibility seems to be founded on sound arguments, and his three-valued logic appears to be a proper tool for formalization of the questions of determination. The three-valued tense logic is compared with the Priorean tense logic. If the possible time is empty, the three-valued tense logic collapses into the Priorean tense logic.