Prof. Diderik Batens (Ghent University)

Adaptive Logics.
The Logics You Always Wanted (But Thought Impossible)*

Key words: adaptive logics, dynamic proofs, non-monotony

Adaptive logics are not alternatives for classical logic (or for any other standard of deduction). They are meant as means to characterize, in a strictly formal way, forms of reasoning that hitherto were not recognized as formal, notwithstanding their being formal and notwithstanding their frequent occurrence, both in scientific contexts and in everyday contexts. In this sense, adaptive logics broaden the domain of formal logic; they explicate a large set of reasoning forms that were often considered as mistaken or as too indistinct to allow for formal treatment.

A large number of adaptive logics has been studied. Most of them have a common formal structure, which is called the standard format. The syntax (leading to dynamic proofs) and semantics of adaptive logics in standard format derive directly from this structure. While adaptive logics have several unusual properties, it is possible to prove the presence of these properties in a way that complies with the usual meta-theoretic requirements. Actually, most of the meta-theoretic properties (including soundness and strong completeness) have been demonstrated in terms of the standard format (without referring to the particular logic). With these difficulties out of the way, formulating a new adaptive logic (for a given reasoning form of the right structure) is a manageable task. Incidentally, there are several easy ways for combining adaptive logics.

Many existing logical systems, for example certain non-monotonic logics, have been characterized in terms of adaptive logics. So the adaptive logic program has a systematizing and unifying effect. The ultimate aim is to incorporate all dynamic reasoning forms.

Specific examples will be presented and illustrated, some relating to scientific contexts, others relating to more pedestrian contexts. This will illustrate the impressive diversity of reasoning processes that are explicated by adaptive logics.

Diderik Batens is professor of logic and philosophy of science and Director of the Centre for Logic and Philosophy of Science at Ghent University, Belgium ( Previously, he taught at Hasselt University and at the Free University of Brussels (VUB). His interest in logic is application driven; it mainly concerns the explication of actual human reasoning processes, especially those that are studied in or required for the philosophy of science (including problem-solving processes). His aim is to study those reasoning processes with due precision and by means of the formal machinery that was developed by twentieth century metatheory.

*Research for this paper was supported by subventions from Ghent University and from the Fund for Scientific Research Flanders.