A formal theory of actions

Abstract

This paper presents a formal theory of actions which may serve as a foundation for different domains, such as theory of organization, theory of planning, etc. The basic idea underlying the construction is that actions may be concatenated into strings, by performing them one after another, and that not all strings of actions so obtained are physically feasible. This allows us to draw an analogy between the class of admissible strings and a language: actions play the role of words in a certain vocabulary, and the admissible strings of actions play the role of sentences. One may therefore speak of a language of actions, characteristic for a given situation, and analyse it by means of mathematical linguistics. Moreover, a string of actions leads to certain outcomes. If one considers only those outcomes which are inherently connected with this string, i.e., occur whenever this string is performed, one may enrich the language of actions with a semantic structure: the well determined outcomes of a given string of actions play very much the same role as meanings of sentences. The above linguistic intuitions apply to the case of linear concatenations, where simultaneous actions are excluded; thus, the main, but not the only one, interpretation is in terms of actions of a single person. One may, however, consider also simultaneous strings of actions, for which the interpretation is in terms of team actions. In this case, some methods of mathematical linguistics are still applicable, leading to formal explication of such concepts as cooperation, blocking, etc.