Logic, Decision, and Interactions
24 – 28 October 2016 Lorentz Center @ Oort
The workshop “Logics, Decisions, and Interactions” has focused on the interaction and
cross-fertilization between nonclassical logics, and decision theory, game theory and social choice.
Decision theory, game theory and social choice is a research area interfacing economics, social
sciences, philosophy and artificial intelligence. The workshop has aimed at bringing together the
following communities:
 logicians using nonclassical methods (including algebraic, topological, order-theoretic,
proof-theoretic and category-theoretic methods);
 researchers working in decision theory, game theory and social choice.
Researchers in group (a) can benefit from the challenges posed by the formalization of problems in
the area of decision theory, game theory and social choice; researchers in group (b) have only been
exposed to a fragment of the available logical formalisms and techniques, namely to those pertaining
to classical (modal) logic and model theory, and have largely not been exposed to the tools and
results of researchers in group (a).
In order to foster interaction between the various communities, the program consisted of nine
keynote lectures (of one hour each) and nine discussion sessions (of one hour each), with the rest of
the schedule given over to free-form discussion and work sessions. Each morning or afternoon
consisted of one keynote and one discussion session, separated by a fifteen minute coffee break,
and then followed by a one-hour work session. This format worked extremely well, because it left a
lot of time for informal discussion and interaction, and provided plenty of scheduling flexibility. Each
of the formal presentations generated abundant discussion, which inevitably spilled over into the
coffee break or work session which followed. Because of the very large amount of discussion, we
often fell behind the formal schedule. But because the schedule was not too tightly packed with
events, this did not create problems. All participants found these protracted discussions very
interesting, stimulating, and informative, and appreciated the fact that there was enough time in the
schedule for discussions to unfold in a relaxed fashion without hard time constraints.
The main goal of the workshop was to create a scientific platform and to define a common language
that could be shared by all the communities involved so as to improve communication among
participants and ground future interdisciplinary research. In addition to different conceptual
frameworks and terminologies, participants in groups (a) and (b) have fundamentally different
research paradigms: they have different ideas about what constitutes an interesting research
question, and what constitutes a satisfactory answer to such a question. For example, participants in
group (a) are often concerned about whether a certain mathematical result can be obtained in a
constructible way (roughly speaking, this means it is something you could obtain through a
computation) —a question which is largely absent from the research of group (b). On the other
hand, participants from group (b) are often concerned about incentive-compatibility —something
which is not an issue for group (a). Likewise, group (a) is often sensitive to certain criteria of
“mathematical elegance” —for example, is a certain construction functorial? Does it have certain
universality properties? In contrast, group (b) is concerned less with mathematical beauty and more
with “economic significance”. But one outcome of the workshop was to recognize that these two
objectives are not as unrelated as they seem. For example, functoriality or universality are not just
“aesthetic” criteria —they can sometimes be interpreted as the sort of “non-arbitrariness” or
“invariance to model specification” which could be important to an economic theorist
For group (a), a precise description of the process of formal reasoning is just as important as the
outcome of that reasoning —for example, it is often the case that a mathematical statement which
can be proved using formal system X cannot be proved (or perhaps, even expressed) using formal
system Y, and for group (a) this is a significant observation. Oddly enough, although group (b)
concerns itself almost entirely with the study of “reasoners” (i.e. rational agents), participants of
group (b) have focussed very little attention on the technical details (and limitations) of formal
reasoning itself. So it was valuable for group (b) to be exposed to the methodology of group (a) in
this light. On the other hand, group (b) is sensitive to metatheoretical distinctions which are absent
in group (a) —for example, the distinction between normative and descriptive investigations.
Roughly speaking, a normative statement is a statement about how an ideal agent “should” behave
in a certain situation —it is a description of ideal rational behaviour or ethical behaviour. In contrast,
a descriptive statement is a statement about how actually-existing agents do behave in situations.
The normative/descriptive divide arises because economics straddles the threshold between moral
philosophy and social science. A common fallacy is to elide normative and descriptive questions, and
practitioners of group (b) are (usually) careful to avoid this sort of mistake.
Another difference is in the representation of knowledge and belief. Participants from group (a) are
mainly comfortable with representing knowledge and belief in terms of formal languages and the
semantics of these languages. (A variety of semantic frameworks are available —e.g. algebraic,
topological, and order-theoretic.) In contrast, participants from group (b) work mainly within a
Bayesian paradigm, where “beliefs” are represented by probability distributions on a state space,
and “knowledge” is represented via a Boolean algebra of subsets of that state space. These two
paradigms are not entirely incompatible, but they are significantly different, with different strengths
and weaknesses.
Because of these paradigmatic differences, there is much potential for miscommunication or
miscoordination when advancing an interdisciplinary research project between these two
communities. One of the chief benefits of this workshop is that it exposed both sides to the
conceptual frameworks and research paradigms of the other side, thereby fostering increased
interdisciplinary understanding which will be invaluable in future interactions between these two
communities. The active, enthusiastic, and ongoing interaction among the participants testify that
this goal has been largely achieved.
Alessandra Palmigiano (Delft, Netherlands)
Marcus Pivato (Ontario, Canada)
Tomasso Flaminio (Milan, Italy)
Elias Tsakas ( Maastricht, Netherlands)