=Paper=
{{Paper
|id=None
|storemode=property
|title=The Issue of Perspectivality in Formal Theories of Spatial Representation
|pdfUrl=https://ceur-ws.org/Vol-897/ecs_6.pdf
|volume=Vol-897
|dblpUrl=https://dblp.org/rec/conf/icbo/Haemmerli12
}}
==The Issue of Perspectivality in Formal Theories of Spatial Representation==
https://ceur-ws.org/Vol-897/ecs_6.pdf
The Issue of Perspectivality in Formal
Theories of Spatial Representation
Author Marion Haemmerli
Supervisors Michael Esfeld, University of Lausanne and Achille Varzi,
Columbia University
Studies/Stag PhD 2nd year
e
Affiliation University of Lausanne, Switzerland
E-Mail marion.haemmerli@unil.ch
Aims and Objectives of the Research
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 perspective-
dependent 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.
Justification for the Research Topic
Ever since Hayes’ Naïve Physics Manifesto [4], Qualitative Spatial Reasoning has been a
flourishing branch of a common-sense approach to modelling human behaviour in
autonomous machines. The question of perspectivality in spatial orientation and of
perspective-dependent spatial relations has again and again been in the focus of qualitative
calculi of spatial representation (see e.g., [5]). Moreover, perspective-dependent locational
concepts are widespread in human discourse and appear in the language practices of a
variety of disciplines (ranging from geographic navigation to the bio-medical practice).
However, the question of perspective-dependent spatial concepts and their relation to the
framework of absolute locational concepts has not been examined so far from a
philosophical perspective on formal ontology. As a result, important parts of the relevant
literature ignore issues that are related to the question of embedding perspectivality into
existent location theories in a conceptually and ontologically adequate manner. In my
research, I try to develop a framework for both computationally adequate theories of
perspective-dependent spatial representation and philosophically intriguing questions as to
the precise nature of perspective-dependent location. I build this framework on
mereotopological background structures (often found in bio-medical ontologies) that are able
to support entities of different metaphysical kinds.
Research Questions
1 Definition of perspectival spatial representations:
- What kind of spatial representations count as perspective-dependent representations?
- What is the formal structure of perspective-dependent spatial expressions?
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 formal-
ontological 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.