Reasoning about Space
December 22, 2003
Institute for Logic, Language, and
Computation, UvA, Amsterdam, The Netherlands
Roeterstraat 11 (Department of Economics), Amsterdam.
Recent years have seen lots of exciting work in spatial
reasoning in computer science, AI, and philosophy. The motivation
for this work ranges from image analysis and geographical
information systems in CS through attempts to exploit properties
of space in diagrammatic reasoning, to purely mathematical issues
of expressivity of languages with respect to particular spatial
domains. As of now, much of the research has been carried out
within the respective fields and without much interaction with
researchers in other fields.
The aim of this workshop is to present some recent advances in
the field with a particular emphasis on bringing researchers in
various fields together for purposes of looking at unifying
logical frameworks (such as, for instance, modal logic) and
getting a better sense of the most fruitful avenues for further
This is the second event in this series. The first was held
during NASSLLI in Bloomington, IN. For more info, see http://dit.unitn.it/~aiellom/nasslli03.
We are proud to announce that the following researchers have
accepted our invitation to participate and present their work:
van Benthem, Univ. of Amsterdam (NL) and Stanford
Shehtman, Moscow University (Russia),
Balbiani , Institut de recherche en informatique de
Pratt, Manchester University (UK),
- Marco Aiello,
University of Trento (Italy),
A proposal for a book
on logics of space
I will present a proposal for a book on spatial logics
highlighting the goals, the proposed outline and format for the
book. If time allows, I will present the structure and concepts
behind the chapter on modal logics of space.
Expressive Power and Ontological Commitment in First-Order Mereotopology
Mereotopology is the approach to topology which takes regions, rather
than points, to be the primitive constituents of space. First-order
mereotopology is the study of first-order theories of various (classes
of) topological spaces, in which the variables range over spatial
regions and the non-logical primitives are given fixed topological
interpretations. This talk concentrates on the first-order
mereotopology of the Cartesian plane and Cartesian 3-space. The two
issues occupying centre stage will be those of expressive power and
ontological commitment. Specifically, we ask: (i) What topological
properties and relations over these Cartesian spaces can be expressed
in first-order mereotopological languages? (ii) What alternative
models of space have the same first-order mereotopological theories as
the familiar Cartesian spaces? We obtain some answers to these
questions, and, in doing so, show that they are surprisingly closely
New results on products of modal logics
Product logics are modal logics determined by product Kripke frames, that is,
Kripke frames with coordinates. Products are a natural kind of many-dimensional
modal logics and are closely connected with other many-dimensional formalisms.
Study of products was very intensive in recent five years; the most
comprehensive exposition can be found in D. Gabbay, A. Kurucz, F. Wolter, M. Zakharyaschev.
Many-dimensional modal logic. Theory and applications. Elsevier, 2003..
The talk discusses some open problems in this field and gives an overview of
recent results beyond the book, in particular
-the fmp for K x K4 and related systems (V. B. Shehtman);
-properties of extensions of the n-dimensional successor logic SL^n (A.G. Kravtsov).
2-dimensional geometries: first-order theories and modal
joint work with Tinko Tinchev
We consider the binary
relations of parallelism and convergence between lines in a
2-dimensional affine space. Associating with parallelism and
convergence the binary predicates P and C, and the modal
connectives [P] and [C], we consider a first-order theory based on
these predicates and a modal logic based on these modal
connectives. We investigate the axiomatization/completeness and
the decidability/complexity of these formal systems.
Johan van Benthem
products of modal logics
I will report on some recent work
with Guram Bezhanishvili, Balder ten Cate, and Darko Sarenac since
last spring on generalizing the Gabbay-Shehtman analysis of
products of modal logics to structures in topology, and the new
phenomena and issues which come to light then.