11 research outputs found

    A Qualitative Representation of Spatial Scenes in R2 with Regions and Lines

    Get PDF
    Regions and lines are common geographic abstractions for geographic objects. Collections of regions, lines, and other representations of spatial objects form a spatial scene, along with their relations. For instance, the states of Maine and New Hampshire can be represented by a pair of regions and related based on their topological properties. These two states are adjacent (i.e., they meet along their shared boundary), whereas Maine and Florida are not adjacent (i.e., they are disjoint). A detailed model for qualitatively describing spatial scenes should capture the essential properties of a configuration such that a description of the represented objects and their relations can be generated. Such a description should then be able to reproduce a scene in a way that preserves all topological relationships, but without regards to metric details. Coarse approaches to qualitative spatial reasoning may underspecify certain relations. For example, if two objects meet, it is unclear if they meet along an edge, at a single point, or multiple times along their boundaries. Where the boundaries of spatial objects converge, this is called a spatial intersection. This thesis develops a model for spatial scene descriptions primarily through sequences of detailed spatial intersections and object containment, capturing how complex spatial objects relate. With a theory of complex spatial scenes developed, a tool that will automatically generate a formal description of a spatial scene is prototyped, enabling the described objects to be analyzed. The strengths and weaknesses of the provided model will be discussed relative to other models of spatial scene description, along with further refinements

    Interpolative and extrapolative reasoning in propositional theories using qualitative knowledge about conceptual spaces

    Get PDF
    International audienceMany logical theories are incomplete, in the sense that non-trivial conclusions about particular situations cannot be derived from them using classical deduction. In this paper, we show how the ideas of interpolation and extrapolation, which are of crucial importance in many numerical domains, can be applied in symbolic settings to alleviate this issue in the case of propositional categorization rules. Our method is based on (mainly) qualitative descriptions of how different properties are conceptually related, where we identify conceptual relations between properties with spatial relations between regions in Gärdenfors conceptual spaces. The approach is centred around the view that categorization rules can often be seen as approximations of linear (or at least monotonic) mappings between conceptual spaces. We use this assumption to justify that whenever the antecedents of a number of rules stand in a relationship that is invariant under linear (or monotonic) transformations, their consequents should also stand in that relationship. A form of interpolative and extrapolative reasoning can then be obtained by applying this idea to the relations of betweenness and parallelism respectively. After discussing these ideas at the semantic level, we introduce a number of inference rules to characterize interpolative and extrapolative reasoning at the syntactic level, and show their soundness and completeness w.r.t. the proposed semantics. Finally, we show that the considered inference problems are PSPACE-hard in general, while implementations in polynomial time are possible under some relatively mild assumptions

    Grounding for a computational model of place

    Get PDF
    Thesis (S.M.)--Massachusetts Institute of Technology, School of Architecture and Planning, Program in Media Arts and Sciences, 2006.Text printed 2 columns per page.Includes bibliographical references (leaves 66-70).Places are spatial locations that have been given meaning by human experience. The sense of a place is it's support for experiences and the emotional responses associated with them. This sense provides direction and focus for our daily lives. Physical maps and their electronic decedents deconstruct places into discrete data and require user interpretation to reconstruct the original sense of place. Is it possible to create maps that preserve this sense of place and successfully communicate it to the user? This thesis presents a model, and an application upon that model, that captures sense of place for translation, rather then requires the user to recreate it from disparate data. By grounding a human place-sense for machine interpretation, new presentations of space can be presented that more accurately mirror human cognitive conceptions. By using measures of semantic distance a user can observe the proximity of place not only in distance but also by context or association. Applications built upon this model can then construct representations that show places that are similar in feeling or reasonable destinations given the user's current location.(cont.) To accomplish this, the model attempts to understand place in the context a human might by using commonsense reasoning to analyze textual descriptions of place, and implicit statements of support for the role of these places in natural activity. It produces a semantic description of a place in terms of human action and emotion. Representations built upon these descriptions can offer powerful changes in the cognitive processing of space.Matthew Curtis Hockenberry.S.M

    Blast Theory: Intermedial Performance Praxis and the Generative Conditions for Performance Subjectivity

    Get PDF
    The work of the British theatre company Blast Theory explores intermedial dramaturgies that this thesis claims can be categorized as radical because they present a generative characteristic. Intermediality, understood here as the impact of analogue and digital technologies in theatrical performance, establishes complex relationships between physical and virtual spaces, structures that create a rich polyphony of multiple temporal orchestrations, and narratives that present a multiplicity of performative arrangements. Intermedial performance, as a performative and experiential event, encompasses a triad of performative interactions between performers, spectators and the media itself executed at and concentrated on the moment of the performance encounter. This research argues that this encounter displays a generative character – a moment at which all the attending performance variables come together in a constant process of performative re-activation thus generating the intermedial performance event. Within this descriptive parameter, this research claims that recent performance conceptualizations fail to account for the work of Blast Theory. Contemporary performance and liveness debates focus principally on the ontology of performance. So, notwithstanding their differences, performance theorists such as Lavender (2002), Fischer-Lichte (2008), and Schechner (2003), and presentness/presence theorists such as Phelan (1993) and Power (2008) all agree that performance is an ontological, ephemeral, and fleeting event. While there are many valid points in these diverse approaches, they only offer a partial account of the specificities of the work of Blast Theory and, by extent, the intermedial performance event. This thesis therefore relocates the terms of the debate on a constructivist epistemological basis. In this way, the thesis proposes that an intermedial performance event must be understood beyond the ontological approach by specifically interrogating the conditions of intelligibility; that is, its operative and intelligible architecture of attending elements and the participating subject. The key hypothesis shared is that in introducing a constructivist reading of epistemology, as described by Alfred Whitehead and Gilles Deleuze, a new account of intermediality in performance emerges as a radical dramaturgy, incorporating generative aspects, and with this, a unique type of intermedial performance subjectivity is enabled

    The Resemblance Structure of Natural Kinds: A Formal Model for Resemblance Nominalism

    Get PDF
    278 p.The aim of this thesis is to better understand the ways natural kinds are related to each other by species-genus relations and the ways in which the members of the kind are related to each other by resemblance relations, by making use of formal models of kinds. This is done by first analysing a Minimal Conception of Natural Kinds and then reconstructing it from the ontological assumptions of Resemblance Nominalism. The questions addressed are:(1) What is the external structure of kinds' In what ways are kinds related to each other by species-genus relations'(2) What is the internal structure of kinds' In what sense are the instances of a kind similar enough to each other'According to the Minimal Conception of Kinds, kinds have two components, a set of members of the kind (the extension) and a set of natural attributes common to these objects (the intension). Several interesting features of this conception are discussed by making use of the mathematical theory of concept lattices. First, such structures provide a model for contemporary formulations of syllogistic logic. Second, kinds are ordered forming a complete lattice that follows Kant's law of the duality between extension and intension, according to which the extension of a kind is inversely related to its intension. Finally, kinds are shown to have Aristotelian definitions in terms of genera and specific differences. Overall this results in a description of the specificity relations of kinds as an algebraic calculus.According to Resemblance Nominalism, attributes or properties are classes of similar objects. Such an approach faces Goodman's companionship and imperfect community problems. In order to deal with these, a specific nominalism, namely Aristocratic Resemblance Nominalism, is chosen. According to it, attributes are classes of objects resembling a given paradigm. A model for it is introduced by making use of the mathematical theory of similarity structures and of some results on the topic of quasianalysis. Two other models (the polar model and an order-theoretic model) are considered and shown to be equivalent to the previous one.The main result is that the class of lattices of kinds that a nominalist can recover uniquely by starting from these assumptions is that of complete coatomistic lattices. Several other related results are obtained, including a generalization of the similarity model that allows for paradigms with several properties and properties with several paradigms. The conclusion is that, under nominalist assumptions, the internal structure of kinds is fixed by paradigmatic objects and the external structure of kinds is that of a coatomistic lattice that satisfies the Minimal Conception of Kinds

    The Resemblance Structure of Natural Kinds: A Formal Model for Resemblance Nominalism

    Get PDF
    278 p.The aim of this thesis is to better understand the ways natural kinds are related to each other by species-genus relations and the ways in which the members of the kind are related to each other by resemblance relations, by making use of formal models of kinds. This is done by first analysing a Minimal Conception of Natural Kinds and then reconstructing it from the ontological assumptions of Resemblance Nominalism. The questions addressed are:(1) What is the external structure of kinds' In what ways are kinds related to each other by species-genus relations'(2) What is the internal structure of kinds' In what sense are the instances of a kind similar enough to each other'According to the Minimal Conception of Kinds, kinds have two components, a set of members of the kind (the extension) and a set of natural attributes common to these objects (the intension). Several interesting features of this conception are discussed by making use of the mathematical theory of concept lattices. First, such structures provide a model for contemporary formulations of syllogistic logic. Second, kinds are ordered forming a complete lattice that follows Kant's law of the duality between extension and intension, according to which the extension of a kind is inversely related to its intension. Finally, kinds are shown to have Aristotelian definitions in terms of genera and specific differences. Overall this results in a description of the specificity relations of kinds as an algebraic calculus.According to Resemblance Nominalism, attributes or properties are classes of similar objects. Such an approach faces Goodman's companionship and imperfect community problems. In order to deal with these, a specific nominalism, namely Aristocratic Resemblance Nominalism, is chosen. According to it, attributes are classes of objects resembling a given paradigm. A model for it is introduced by making use of the mathematical theory of similarity structures and of some results on the topic of quasianalysis. Two other models (the polar model and an order-theoretic model) are considered and shown to be equivalent to the previous one.The main result is that the class of lattices of kinds that a nominalist can recover uniquely by starting from these assumptions is that of complete coatomistic lattices. Several other related results are obtained, including a generalization of the similarity model that allows for paradigms with several properties and properties with several paradigms. The conclusion is that, under nominalist assumptions, the internal structure of kinds is fixed by paradigmatic objects and the external structure of kinds is that of a coatomistic lattice that satisfies the Minimal Conception of Kinds

    Rendiconti dell'Istituto di Matematica dell'UniversitĂ  di Trieste. An International Journal of Mathematics. Vol. 44 (2012)

    No full text
    Rendiconti dell’Istituto di Matematica dell’Università di Trieste was founded in 1969 by Arno Predonzan, with the aim of publishing original research articles in all fields of mathematics and has been the first Italian mathematical journal to be published also on-line. The access to the electronic version of the journal is free. All published articles are available on-line. The journal can be obtained by subscription, or by reciprocity with other similar journals. Currently more than 100 exchange agreements with mathematics departments and institutes around the world have been entered in
    corecore