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The Logic of Action

First published Tue Mar 31, 2009; substantive revision Tue Apr 2, 2013

In this article we provide a brief overview of the logic of action in philosophy, linguistics, computer science, and artificial intelligence. The logic of action is the formal study of action in which formal languages are the main tool of analysis.

The concept of action is of central interest to many disciplines: the social sciences including economics, the humanities including history and literature, psychology, linguistics, law, computer science, artificial intelligence, and probably others. In philosophy it has been studied since the beginning because of its importance for epistemology and, particularly, ethics; and since a few decades it is even studied for its own sake. But it is in the logic o faction that action is studied in the most abstract way.

The logic of action began in philosophy. But it has also played a certain role in linguistics. And currently it is of great importance in computer science and artificial intelligence. For our purposes it is natural to separate the accounts of these developments.

1. The Logic of Action in Philosophy 1.1 Historical overview 1.2 The stit saga 1.3 Intentions 1.4 Logics of special kinds of action

2. The Logic of Action in Linguistics 2.1 Speech acts 2.2 Action sentences 2.3 Dynamic semantics

3. The Logic of Action in Computer Science

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The Logic of Action

3.1 Reasoning about programs 4. The Logic of Action in Artificial Intelligence

4.1 Representing and reasoning about actions 4.2 Description and specification of intelligent agents Conclusion Bibliography Academic Tools Other Internet Resources Related Entries

1. The Logic of Action in Philosophy

1.1 Historical overview

Already St. Anselm studied the concept of action in a way that must be classified as logical; had he known symbolic logic, he would certainly have made use of it (Henry 1967; Walton 1976). In modern times the subject was introduced by, among others, Alan Ross Anderson, Frederick B. Fitch, Stig Kanger, and Georg Henrik von Wright; Kanger's work was further developed by his students Ingmar P?rn and Lars Lindahl. The first clearly semantic account was given by Brian F. Chellas (1969). (For a more detailed account, see Segerberg 1992 or the mini-history in Belnap 2001.)

Today there are two rather different groups of theories that may be described as falling under the term logic of action. One, the result of the creation of Nuel Belnap and his many collaborators, may be called stit theory (a term that will be explained in the next paragraph). The other is dynamic logic. Both are connected with modal logic, but in different ways. Stit theory grew out of the philosophical tradition of modal logic. Dynamic logic, on the other hand, was invented by computer scientists in

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Stanford Encyclopedia of Philosophy

Krister Segerberg, John-Jules Meyer, and Marcus Kracht

order to analyse computer action; only after the fact was it realized that it could be viewed as modal logic of a very general kind. One important difference between the two is that (for the most part) actions are not directly studied in stit theory: the ontology does not (usually) recognize a category of actions or events. But dynamic logic does. Among philosophers such ontological permissiveness has been unusual. HectorNeri Casta?eda, with his distinction between propositions and practitions, provides one notable exception.

The stit tradition is treated in this section, the dynamic logic one in the next.

1.2 The stit saga

The term "stit" is an acronym based on "sees to it that". The idea is to add, to an ordinary classical propositional language, a new propositional operator , interpreting i, where i stands for an agent and for a proposition, as i sees to it that . (The official notation of the Belnap school is more laborious: [i : ].) Note that is allowed to contain nestings of the new operator.

In order to develop formal meaning conditions for the stit operator a semantics is defined. A stit frame has four components: a set T, the nodes of which are called moments; an irreflexive tree ordering < of T; a set of agents; and a choice function C. A maximal branch through the tree is called a history.

The tree (T, ................
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