A Mini-Guide to Logic in Action
Johan van Benthem · 2006
The dynamic turnClassical logic is about propositions which we can know or believe, and unchanging inferential relationships between them.But inference is fi rst and foremost an activity, for which propositions are merely the input, and the result.In recent years, there has been a growing awareness that various activities of reasoning, evaluation, belief revision, or communication, are themselves typical themes for logical investigation, and that their dynamic structure can be studied explicitly by logical means. 1 For instance, it seems strange to study only the statics of what it means to 'know' a proposition, when knowledge usually results from basic actions of learning that we perform all the time, such as asking a question and getting an answer.Indeed, asking questions and giving answers are just as much logical core activities as drawing conclusions!Th is line can be extended: the natural dynamic counterpart of static epistemic logic is the theory of arbitrary individual or social learning mechanisms.Similar trajectories from static to dynamic arise when we look at inference in such stages, fi rst as a zero-agent mathematical relationship between static propositions, then as a one-agent activity of drawing conclusions, and fi nally as a many-agent interactive process of argumentation.Th is broadening of perspective, sometimes called the 'Dynamic Turn', started around 1980 with work on interpretation procedures for natural language, as well as belief revision in artifi cial intelligence.But how should logic incorporate actions as fi rst-class citizens into its scope?Plausible formal frameworks to this eff ect come from the philosophy of action, temporal logic, and systems for analyzing programs in computer science, such as dynamic logic.Moreover, further infl uences have come from process theories in computer science, as well as game theory, and this contact between disciplines is 1 Th e same 'static'/'dynamic' distinction makes sense when we extend our notion of classical logic, e.g. by including defi nitions and expressive power of languages.Expressive power has to do with activities of evaluation of statements, making distinctions between given situations, and so on.