An axiomatization of Prior's modal calculus $Q$.
Robert A. Bull · Notre Dame Journal of Formal Logic · 1964
Prior defines a model for a modal calculus Q (cf [l], pp.43f):The truth values are infinite sequences of 1's, 2's, and 3's, with the proviso that the first term of each sequence is not 2.The designated values are those with no 3's.The values of propositional operators are found by applying the tablesto the terms of the sequences and .The other propositional operators can be defined from these in the usual way.For formal convenience I shall use L for what is NMN in Prior's system, and L for his L.These operators are given by when a is 2 where a is 2 and 3 elsewhere, when a consists of 1 's and I a is n , 2'a;2 where a is 2 and 3 elsewhere, when a has a 3.2 where a is 2 and 1 elsewhere, when a consists of 1's and LalS 2>s;2 where a is 2 and 3 elsewhere, when a has a 3.