The Issue of Perspectivality in Formal Theories of Spatial Representation

Abstract

The aim of my research is to develop a formal theory of spatial representation able to account for perspective-dependent spatial concepts. In my current project I develop a formal ontological theory for reasoning about perspective-dependent locations and I show how perspective-dependent spatial concepts relate to the framework of detached locational concepts. Thus, my aim is to investigate both the philosophical nature of perspectivedependent locational concepts and the way in which they fit into formal ontological theories of spatial representation. While interested in a computationally efficient theory, my main focus is on the conceptual adequacy of the framework I shall propose.

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Affiliation 2 Formal account of perspectivality - How should perspective-dependency be formally captured? What is a “point of view” and what is its role in a formal account of perspective-dependency? - How should the dependency between a point of view and the corresponding entity be expressed? - What principles rule perspective-dependent spatial expressions? 3 Perspectivality within a theory of spatial representation - What is the conceptually correct account of the relationship between detached, absolute concepts of spatial location and their perspective-dependent counterparts? - What kind of mereo-topological background theory is best suited to support an extension towards location theories that account for perspective-dependent locations?

Research Methodology

The aim of developing a framework for perspectival spatial concepts translates into two different, though related subtasks. First of all, my concern is to determine a theory of spatial representation that provides an adequate background theory for a formalism able to account for perspectival spatial concepts. In this respect I am focusing on mereotopological theories in the spirit of Achille Varzi’s and Roberto Casati’s theory of spatial representation [ 1 ], [ 2 ], able to support complex extended formalisms that distinguish between a variety of metaphysical categories (e.g., spatial regions and tenants, material objects and events, abstracta and concrete, etc., see [ 3 ]). I shall propose new axiomatic principles for the mereotopological background theory to make it even more suitable as a unified formalontological framework for entities of different metaphysical kinds.

Second, I shall propose a first-order extension of the adequate meretopological background theory with the aim to include perspective-dependent locational concepts. I am concerned with both an adequate semantics and the relevant corresponding axiomatic principles that rule my first-order formalism for perspective-dependent locations.

Research Results to Date

- Clarification of the nature and definition of perspectival locational concepts. - Development of a first-order formalism for expressing perspective-dependent spatial concepts on the basis of Achille Varzi’s Kuratowski Extension of General Extensional Mereology (KGEMT) and his theory of location [ 2 ]. - Development of a semantic model for my theory. - New mereo-topological axioms for KGEMT - Some first axiomatic principles for my formalism.

References

1. Varzi A , Casati R ( 1999 ), Parts and Places , Cambridge, Mass., The MIT Press.

2. Varzi A ( 2007 ), Parts, Wholes, and Locations, in: I Pratt-Hartmann (ed.), Handbook on Spatial Logic , Berlin : Springer Verlag.

3. Gangemi A , Guarino N , Masolo C , Oltramari A ( 2003 ) Sweetening Ontologies with DOLCE , in: Proceedings of EKAW02 , Siguenza, Spain, Springer, 166 - 181 .

4. Hayes P ( 1979 ), The Naïve Physics Manifesto , in: D Michie (ed.), Expert Systems , Edinburgh: Edinburgh University Press.

5. Cohn A , Renz J ( 2008 ), Qualitative Spatial Representation and Reasoning , in: Harmelen F, Lifschitz V , Porter B (eds.) , Handbook of Knowledge Representation , Amsterdam, The Netherlands and Oxford, UK, Elsevier.