Infinity

This essay surveys the different types of infinity that occur in pure and applied mathematics, with emphasis on: 1. the contrast between potential infinity and actual infinity; 2. Cantor's distinction between transfinite sets and absolute infinity; 3. the constructivist view of infinite quantifiers and the meaning of constructive proof; 4. the concept of feasibility and the philosophical problems surrounding feasible arithmetic; 5. Zeno's paradoxes and modern paradoxes of physical infinity involving supertasks

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

Geographical Research in the Digital Humanities: Spatial Concepts, Approaches and Methods

The richness of social and cultural theory in the humanities offers countless opportunities for using theory-informed concepts in data-based analysis workflows. The contributors to this volume thus encourage further research utilizing out-of-the-box models and approaches to space and place in the field of Digital Humanities. The collection follows the two complementary goals of providing promising conceptualisations of space and place for a broad audience from Digital Humanities, and of presenting current work in Digital Humanities using different conceptualisations of space and place or offering innovative methods for their analysis

Can humain association norm evaluate latent semantic analysis?

This paper presents the comparison of word association norm created by a psycholinguistic experiment to association lists generated by algorithms operating on text corpora. We compare lists generated by Church and Hanks algorithm and lists generated by LSA algorithm. An argument is presented on how those automatically generated lists reflect real semantic relations

Dwelling on ontology - semantic reasoning over topographic maps

The thesis builds upon the hypothesis that the spatial arrangement of topographic features, such as buildings, roads and other land cover parcels, indicates how land is used. The aim is to make this kind of high-level semantic information explicit within topographic data. There is an increasing need to share and use data for a wider range of purposes, and to make data more definitive, intelligent and accessible. Unfortunately, we still encounter a gap between low-level data representations and high-level concepts that typify human qualitative spatial reasoning. The thesis adopts an ontological approach to bridge this gap and to derive functional information by using standard reasoning mechanisms offered by logic-based knowledge representation formalisms. It formulates a framework for the processes involved in interpreting land use information from topographic maps. Land use is a high-level abstract concept, but it is also an observable fact intimately tied to geography. By decomposing this relationship, the thesis correlates a one-to-one mapping between high-level conceptualisations established from human knowledge and real world entities represented in the data. Based on a middle-out approach, it develops a conceptual model that incrementally links different levels of detail, and thereby derives coarser, more meaningful descriptions from more detailed ones. The thesis verifies its proposed ideas by implementing an ontology describing the land use ‘residential area’ in the ontology editor Protégé. By asserting knowledge about high-level concepts such as types of dwellings, urban blocks and residential districts as well as individuals that link directly to topographic features stored in the database, the reasoner successfully infers instances of the defined classes. Despite current technological limitations, ontologies are a promising way forward in the manner we handle and integrate geographic data, especially with respect to how humans conceptualise geographic space

Semantic-driven modeling and reasoning for enhanced safety of cyber-physical systems

This dissertation is concerned with the development of new methodologies and semantics for model-based systems engineering (MBSE) procedures for the behavior modeling of cyber-physical systems (CPS). Our main interest is to enhance system-level safety through effective reasoning capabilities embedded in procedures for CPS design. This class of systems is defined by a tight integration of software and physical processes, the need to satisfy stringent constraints on performance, safety and a reliance on automation for the management of system functionality. Our approach employs semantic–driven modeling and reasoning : (1) for the design of cyber that can understand the physical world and reason with physical quantities, time and space, (2) to improve synthesis of component-based CPS architectures, and (3) to prevent under-specification of system requirements (the main cause of safety failures in software). We investigate and understand metadomains, especially temporal and spatial theories, and the role ontologies play in deriving formal, precise models of CPS. Description logic-based semantics and metadomain ontologies for reasoning in CPS and an integrated approach to unify the semantic foundations for decision making in CPS are covered. The research agenda is driven by Civil Systems design and operation applications, especially the dilemma zone problem. Semantic models of time and space supported respectively by Allen’s Temporal Interval Calculus (ATIC) and Region Connectedness Calculus (RCC-8) are developed and demonstrated thanks to the capabilities of Semantic Web technologies. A modular, flexible, and reusable reasoning-enabled semantic-based platform for safety-critical CPS modeling and analysis is developed and demonstrated. The platform employs formal representations of domains (cyber, physical) and metadomains (temporal and spatial) entities using decidable web ontology language (OWL) formalisms. Decidable fragments of temporal and spatial calculus are found to play a central role in the development of spatio-temporal algorithms to assure system safety. They rely on formalized safety metrics developed in the context of cyber-physical transportation systems and collision avoidance for autonomous systems. The platform components are integrated together with Whistle, a small scripting language (under development) able to process complex datatypes including physical quantities and units. The language also enables the simulation, visualization and analysis of safety tubes for collision prediction and prevention at signalized and non-signalized traffic intersections

A logical framework for reasoning about space

International audienceIn this paper, we present a theory of space as a framework for spatial reasoning. We believe this formalism is useful for representing geographic space, at least when two constraints are present: a necessity to reason qualitatively over spatial information, and a lack of precise, homogeneous spatial data. This theory is based on mereology, an axiomatic theory of part-whole relation. It includes a formalization of topological concepts as well as some geometric notions, namely distance and orientation. It can be extended to a theory of space-time