What is an action? The agent observes two states at different times; if there is a change, then an action occurred. This implicit definition of action is adopted in this paper. At the beginning of artificial intelligence (AI), first-order logic was used to represent and reason on actions. However, humans use imperatives to specify actions, so linguistics is necessary to understand them.

Here, the authors start with imperatives, both in linguistics, with the perspectives of speaker and addressee, and in logic, where many expressions of imperatives exist. In the reductionist approach, imperatives are translated into propositions, but this is not without shortcomings. Non-reductionists treat imperatives as a fundamental unit, developing representation and reasoning. Those imperative logics are not used in real knowledge-based systems, but are representation formalisms. The authors also look at ways to represent actions in logics, from situation calculus and STRIPS, continuing with intuitionistic and dynamic logics, to arrive at theories of rational acts.

The second part of the paper takes a test case from the Little Red Riding Hood story and develops its knowledge representation with the various approaches. To analyze the results, the authors propose a schema according to seven criteria, namely: whether the approach is fundamental, the considered perspectives (speaker/addressee/action), whether the agent is explicitly referenced, whether actions are represented, whether intention is considered, whether imperatives and actions are evaluated, and the granularity of the system.

It is quite hard to navigate the massive literature produced in about 50 years in AI, not to mention literature in linguistics and the cognitive sciences. So this paper does a useful job in integrating views from linguistics and AI, and in proposing some selection criteria.

However, many researchers do not use the methods illustrated here, often powerful in representation but poorly performing in real-time and in sensor analysis. Probabilistic or hybrid methods are adopted in many fields. Moreover, robotics is also looking from the bottom up at how motor and sensor systems are interacting in the brain and how planning may work. Indeed, many open problems remain to connect such different views of actions. This paper is a step in that direction.