Topological Foundations of Cognitive Science

A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers: ** Topological Foundations of Cognitive Science, Barry Smith ** The Bounds of Axiomatisation, Graham White ** Rethinking Boundaries, Wojciech Zelaniec ** Sheaf Mereology and Space Cognition, Jean Petitot ** A Mereotopological Definition of 'Point', Carola Eschenbach ** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel ** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda ** Defining a 'Doughnut' Made Difficult, N .M. Gotts ** A Theory of Spatial Regions with Indeterminate Boundaries, A.G. Cohn and N.M. Gotts ** Mereotopological Construction of Time from Events, Fabio Pianesi and Achille C. Varzi ** Computational Mereology: A Study of Part-of Relations for Multi-media Indexing, Wlodek Zadrozny and Michelle Ki

Pieces of a Theory

A survey of theories of part, whole and dependence from Aristotle to the Gestalt psychologists, with special attention to Husserl’s Third Logical Investigation “On the Theory of Parts and Wholes”

Generating Relation Algebras for Qualitative Spatial Reasoning

Basic relationships between certain regions of space are formulated in natural language in everyday situations. For example, a customer specifies the outline of his future home to the architect by indicating which rooms should be close to each other. Qualitative spatial reasoning as an area of artificial intelligence tries to develop a theory of space based on similar notions. In formal ontology and in ontological computer science, mereotopology is a first-order theory, embodying mereological and topological concepts, of the relations among wholes, parts, parts of parts, and the boundaries between parts. We shall introduce abstract relation algebras and present their structural properties as well as their connection to algebras of binary relations. This will be followed by details of the expressiveness of algebras of relations for region based models. Mereotopology has been the main basis for most region based theories of space. Since its earliest inception many theories have been proposed for mereotopology in artificial intelligence among which Region Connection Calculus is most prominent. The expressiveness of the region connection calculus in relational logic is far greater than its original eight base relations might suggest. In the thesis we formulate ways to automatically generate representable relation algebras using spatial data based on region connection calculus. The generation of new algebras is a two pronged approach involving splitting of existing relations to form new algebras and refinement of such newly generated algebras. We present an implementation of a system for automating aforementioned steps and provide an effective and convenient interface to define new spatial relations and generate representable relational algebras

Ontological foundations for structural conceptual models

In this thesis, we aim at contributing to the theory of conceptual modeling and ontology representation. Our main objective here is to provide ontological foundations for the most fundamental concepts in conceptual modeling. These foundations comprise a number of ontological theories, which are built on established work on philosophical ontology, cognitive psychology, philosophy of language and linguistics. Together these theories amount to a system of categories and formal relations known as a foundational ontolog

A study in empirical knowledge: The preconditions and structure of measurement

This is an epistemological study, in which measure ment is taken as a paradigm of perceptual recognition---a notion in which perception is joined with judgment as a factor in understanding. Hence it has proved necessary to give an analysis of such recognition in general, with metric contexts as a special case. This has been done in terms of a very weak fundamental form of 'theory', as a form of basic comprehension, in which language (as part of the theories analysed) is not essentially involved, but treated as a special development. One type of theory is given thorough formal analysis: those 'recognitive theories' whose elements are taken, in the theory itself, to be recognized directly from perception, or extrapolated as in principle recognizable. Another type consists of 'substantive theories', seen as constructed to provide deeper understanding of the reality underlying recognized structures, but essentially involving elements not taken to be recognizable: this type receivesonly informal treatment, in terms of its associations with the first (especially in measurement). Special consideration is (unusually) given to attention and neglect,not in psychological terms, but as theory-guided selection from total experience. Neglect is seen not merely as negation of attention, but often a positive strategy (in measurement, strictly determined). Part I introduces the basic concepts, distinguishing the general approach from other relevant traditionsfoundational studies in measurement (Suppes et al.); linguistic analysis; some epistemologies (e.g., Goodman); philosophy of science. Part II sets up the formal analysis. Part III applies this analysis to contexts of measurement, with examples (only distance is fully treated others only in synopsis). Probability assessment is analysed as distinct from measurement. Part IV examines consequences for wider philosophical questions: language-based problems of knowledge and meaning; Wittgenstein's 'private language': and theory-based considerations of ontology; identity; truth, falsity and error; and observation in science.<p