Workshop on

Reasoning about Space

December 22, 2003
Institute for Logic, Language, and Computation, UvA, Amsterdam, The Netherlands

Room E010, Roeterstraat 11 (Department of Economics), Amsterdam.


General Information

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 research.

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.



Invited Contributions

We are proud to announce that the following researchers have accepted our invitation to participate and present their work:

Schedule and Abstracts

All talks will be held in Room E010, Roeterstraat 11 (Department of Economics), Amsterdam.

9:30-10:30 Coffee

9:30-10:30 Valentin Shehtman New results on products of modal logics

10:35-11:35 Ian Pratt Expressive Power and Ontological Commitment in First-Order Mereotopology

11:40-12:40 Marco Aiello A proposal for a book on logics of space


12:40-13:45 Lunch


13:45-14:45 Johan van Benthem
Topological products of modal logics

14:50-15:50 Philippe Balbiani Line-based 2-dimensional geometries: first-order theories and modal logics


16:00 Annual ILLC Party


Organizers


Johan van Benthem
johan@science.uva.nl
ILLC
Amsterdam, The Netherlands.

Darko Sarenac
sarenac@stanford.edu
Department of Philosophy
Stanford University, Stanford, CA, USA.

All inquiries can be directed to the above e-mail addresses.



Abstracts
M. Aiello,
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.



Ian Pratt-Hartmann
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 related.



Valentin Shehtman
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).



Philippe Balbiani
Line-based 2-dimensional geometries: first-order theories and modal logics
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
Topological 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.