||Prof. Diderik Batens (Ghent University)
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 (http://logica.ugent.be/centrum/).
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.