An Extended Branching-Time Ockhamist Temporal Logic

For branching-time temporal logic based on an Ockhamist semantics, we explore a temporal language extended with two additional syntactic tools. For reference to the set of all possible futures at a moment of time we use syntactically designated “restricted variables” called fan-names. For reference to all possible futures alternative to the actual one we use a modification of a difference modality, localized to the set of all possible futures at the actual moment of time. We construct an axiomatic system for this extended branching-time logic and prove its soundness and completeness with respect to bundle tree semantics. Finally, we show how our axiomatic system can be extended with a variety of important additional operators, such as Since and Until, a global difference operator, operators for undivided and divided histories, reference pointers, etc.