Logical Characterisation of A.N. Prior's System Q

Farshad Badie (Aalborg University)

Through his philosophical and logical analysis of ‘Time and Modality’ in 1957, Arthur Norman Prior proposed the logical system Q. In Prior’s view, the three-valued logic Q was a ‘correct’ modal logic. Actually he developed Q in order to offer a logic for contingent beings, in which one could intelligibly and rationally state that some beings are contingent and some are necessary in the world. From the philosophical point of view, Q can be regarded as an ‘actualist’ modal logic (with natural semantics). In this discussion, I have logically characterised Q and, subsequently, reviewed Q’s deficiencies. Also, I have taken into account some other works which have been carried out based on Q in recent decades.