An axiomatization of Lamport's temporal logic of actions

Abstract

We have presented a complete proof system for a propositional temporal logic of actions, PTLA. Lamport has considered extensions of the basic temporal logic of actions, and it seems worthwhile to search for axiomatizations of some of them as well.

The simplest extension consists in adding formulas of the form [A] _{P 0},...,P _n to the logic; this yields the general temporal logic of actions. Roughly, [A] _{P 0},...,P _n says that the action A will take place the next time that one of P ₀, ..., _{P n} changes value. A further extension consists in adding existential quantification over propositions, for hiding internal state. These extensions make it possible to formulate proofs that a program implements another program, and lead to a simple compositional semantics for concurrent systems. As the logic becomes more powerful, however, it becomes more difficult to choose appropriate proof principles. A complete axiomatization might help in this choice.