The most fully developed theory in this area is von Wright's action logic described in his book Norm and Action (1963). Von Wright builds his logic on a rather unusual tense-logic of his own. The basis is a binary modal connective T, so that p T q, where p and q are propositions, means `p, then q'. Thus the action, for instance, of opening the window is: (the window is closed) T (the window is open). The formal development of the calculus was taken a long way in the book cited above, but some problems of interpretation remained as Castaneda points out in his review (1965). In a more recent paper von Wright (1967) has altered and extended his formalism so as to answer these and other criticisms, and also has provided a sort of semantic theory based on the notion of a life-tree.
We know of no other attempts at constructing a single theory of actions which have reached such a degree of development, but there are several discussions of difficulties and surveys which seem important. Rescher (1967) discusses several topics very neatly, and Davidson (1967) also makes some cogent points. Davidson's main thesis is that, in order to translate statements involving actions into the predicate calculus, it appears necessary to allow actions as values of bound variables, that is (by Quine's test) as real individuals. The situation calculus of course follows this advice in that we allow quantification over strategies, which have actions as a special case. Also important are Simon's papers (1965, 1967) on command-logics. Simon's main purpose is to show that a special logic of commands is unnecessary, ordinary logic serving as the only deductive machinery; but this need not detain us here. He makes several points, most notably perhaps that agents are most of the time not performing actions, and that in fact they only stir to action when forced to by some outside interference. He has the particularly interesting example of a serial processor operating in a parallel-demand environment, and the resulting need for interrupts. Action logics such as von Wright's and ours do not distinguish between action and inaction, and we are not aware of any action-logic which has reached a stage of sophistication adequate to meet Simon's implied criticism.
There is a large body of purely philosophical writings on action, time, determinism, etc., most of which is irrelevant for present purposes. However, we mention two which have recently appeared and which seem interesting: a paper by Chisholm (1967) and another paper by Evans (1967), summarizing the recent discussion on the distinctions between states, performances and activities.