The Complexity of Fuzzy Description Logics over Finite Lattices with Nominals

The complexity of reasoning in fuzzy description logics (DLs) over finite lattices usually does not exceed that of the underlying classical DLs. This has recently been shown for the logics between L-IALC and L-ISCHI using a combination of automata- and tableau-based techniques. In this report, this approach is modified to deal with nominals and constants in L-ISCHOI. Reasoning w.r.t. general TBoxes is ExpTime-complete, and PSpace-completeness is shown under the restriction to acyclic terminologies in two sublogics. The latter implies two previously unknown complexity results for the classical DLs ALCHO and SO

Quantitative Methods for Similarity in Description Logics

Description Logics (DLs) are a family of logic-based knowledge representation languages used to describe the knowledge of an application domain and reason about it in formally well-defined way. They allow users to describe the important notions and classes of the knowledge domain as concepts, which formalize the necessary and sufficient conditions for individual objects to belong to that concept. A variety of different DLs exist, differing in the set of properties one can use to express concepts, the so-called concept constructors, as well as the set of axioms available to describe the relations between concepts or individuals. However, all classical DLs have in common that they can only express exact knowledge, and correspondingly only allow exact inferences. Either we can infer that some individual belongs to a concept, or we can't, there is no in-between. In practice though, knowledge is rarely exact. Many definitions have their exceptions or are vaguely formulated in the first place, and people might not only be interested in exact answers, but also in alternatives that are "close enough". This thesis is aimed at tackling how to express that something "close enough", and how to integrate this notion into the formalism of Description Logics. To this end, we will use the notion of similarity and dissimilarity measures as a way to quantify how close exactly two concepts are. We will look at how useful measures can be defined in the context of DLs, and how they can be incorporated into the formal framework in order to generalize it. In particular, we will look closer at two applications of thus measures to DLs: Relaxed instance queries will incorporate a similarity measure in order to not just give the exact answer to some query, but all answers that are reasonably similar. Prototypical definitions on the other hand use a measure of dissimilarity or distance between concepts in order to allow the definitions of and reasoning with concepts that capture not just those individuals that satisfy exactly the stated properties, but also those that are "close enough"

Fuzzy Description Logics with General Concept Inclusions

Description logics (DLs) are used to represent knowledge of an application domain and provide standard reasoning services to infer consequences of this knowledge. However, classical DLs are not suited to represent vagueness in the description of the knowledge. We consider a combination of DLs and Fuzzy Logics to address this task. In particular, we consider the t-norm-based semantics for fuzzy DLs introduced by Hájek in 2005. Since then, many tableau algorithms have been developed for reasoning in fuzzy DLs. Another popular approach is to reduce fuzzy ontologies to classical ones and use existing highly optimized classical reasoners to deal with them. However, a systematic study of the computational complexity of the different reasoning problems is so far missing from the literature on fuzzy DLs. Recently, some of the developed tableau algorithms have been shown to be incorrect in the presence of general concept inclusion axioms (GCIs). In some fuzzy DLs, reasoning with GCIs has even turned out to be undecidable. This work provides a rigorous analysis of the boundary between decidable and undecidable reasoning problems in t-norm-based fuzzy DLs, in particular for GCIs. Existing undecidability proofs are extended to cover large classes of fuzzy DLs, and decidability is shown for most of the remaining logics considered here. Additionally, the computational complexity of reasoning in fuzzy DLs with semantics based on finite lattices is analyzed. For most decidability results, tight complexity bounds can be derived

Film, Relay, and System: A Systems Theory Approach to Cinema

Film theory is replete with references to systems, yet no theory has emerged to provide a cohesive explanation of how cinema, as both technology and institution, operates as a relay system. Interdisciplinary in nature, my dissertation proposes a systems theory of cinema deriving largely from the work of social scientist Niklas Luhmann. Systems theory is especially productive for the ways that it intervenes at crucial sites of conflict and irresolution within film studies. With its emphasis on nonhuman agencies, systems theory calls for reappraisal of the significance of the human to the cinema apparatus--a significance long assumed to be simply a given. With its claim that the reasoning adduced by an observer is never in fact the logic of the observed, systems theory has major implications for thinking about the role of narrative in film and film theory. And with its stress on contingency, systems theory can be seen to upset the terms of debates within the field about cultural and technological determinism, and to provide further grounding for recent work on contingency and cinematic time. Chapter one examines a defining staple of early cinema, the chase film, as a quintessential example of the construction of movement, in the evolution of film editing, via a chain of interlinked segments that relay--and tend to abrogate--human figures. Chapter two focuses on a film conceived by Rube Goldberg at the transition from silent to sound cinema, with particular attention to how the coming of sound complicates the visual relays characteristic of silent slapstick\u27s gag structures. Chapter three examines the dynamism of the long take in classical and post-classical cinema, emphasizing the gradual and incremental disclosure of elements by the camera and revealing the cinema recording process itself as a type of Goldbergian contraption. The last chapter reflects on the computerization of film and media, showing that systems theory provides a useful avenue to thinking about the continuity between analog and digital cinema due in part to an unusual but rich and suggestive conception of the notion of medium

Binarism and indeterminacy in the novels of Thomas Pynchor

Bibliography: pages 397-401.I attempt in this thesis, to graft together a close critical, and predominantly thematic, reading of Thomas Pynchon's novels with selected issues treated in the work of Jacques Derrida on philosophy and textuality, illustrating how this work demands the revision and interrogation of several major critical issues, concepts, dualisms and presuppositions. The thesis consists of an Introduction which sets forth a brief rationale for the graft described above, followed by a short and unavoidably inadequate synopsis of Derrida's work with a brief review and explication of those of his 'concepts' which play an important role in my reading of Pynchon's texts. The Introduction is succeeded by three lengthy chapters in which I discuss, more or less separately, each of Pynchon's three novels to date. These are V. (1963), The Crying of Lot 49, (1966) and Gravity's Rainbow (1973), and I discuss them in the order of their appearance, devoting a chapter to each. I attempt to treat different but related issues, preoccupations, themes and tropes in each of the novels to avoid repeating myself, engaging the apparatuses derived from Derrida's writing where deemed strategic and instructive. I suggest moreover, that several of the issues examined apropos the novel under consideration in any one chapter apply mutandis rnutandi to the other novels. Each chapter therefore to some extent conducts a reading of the novels which it does not treat directly. Finally, supervising these separate chapters is a sustained focus on the epistemology of binarism and digitalism, and the conceptual dualisms which structure and inform major portions of the thematic and rhetorical dimensions The thesis concludes with a Bibliography and a summary Epilogue which seeks to assess briefly the 'achievement' of Pynchon's writing

To and Fro Between Tableaus and Automata for Description Logics

Beschreibungslogiken (Description logics, DLs) sind eine Klasse von Wissensrepraesentationsformalismen mit wohldefinierter, logik-basierter Semantik und entscheidbaren Schlussfolgerungsproblemen, wie z.B. dem Erfuellbarkeitsproblem. Zwei wichtige Entscheidungsverfahren fuer das Erfuellbarkeitsproblem von DL-Ausdruecken sind Tableau- und Automaten-basierte Algorithmen. Diese haben aufgrund ihrer unterschiedlichen Arbeitsweise komplementaere Eigenschaften: Tableau-Algorithmen eignen sich fuer Implementierungen und fuer den Nachweis von PSPACE- und NEXPTIME-Resultaten, waehrend Automaten sich besonders fuer EXPTIME-Resultate anbieten. Zudem ermoeglichen sie eine vom Standpunkt der Theorie aus elegantere Handhabung von unendlichen Strukturen, eignen sich aber wesentlich schlechter fuer eine Implementierung. Ziel der Dissertation ist es, die Gruende fuer diese Unterschiede zu analysieren und Moeglichkeiten aufzuzeigen, wie Eigenschaften von einem Ansatz auf den anderen uebertragen werden koennen, um so die positiven Eigenschaften von beiden Ansaetzen miteinander zu verbinden. Unter Anderem werden Methoden entwickelt, mit Hilfe von Automaten PSPACE-Resultate zu zeigen, und von einem Tableau-Algorithmus automatisch ein EXPTIME-Resultat abzuleiten.Description Logics (DLs) are a family of knowledge representation languages with well-defined logic-based semantics and decidable inference problems, e.g. satisfiability. Two of the most widely used decision procedures for the satisfiability problem are tableau- and automata-based algorithms. Due to their different operation, these two classes have complementary properties: tableau algorithms are well-suited for implementation and for showing PSPACE and NEXPTIME complexity results, whereas automata algorithms are particularly useful for showing EXPTIME results. Additionally, they allow for an elegant handling of infinite structures, but they are not suited for implementation. The aim of this thesis is to analyse the reasons for these differences and to find ways of transferring properties between the two approaches in order to reconcile the positive properties of both. For this purpose, we develop methods that enable us to show PSPACE results with the help of automata and to automatically derive an EXPTIME result from a tableau algorithm

Deviancy and Disorder – The Visual Legacy of the Hottentot Venus in the Novels of Toni Morrison

Sarah Bartmann came to Europe in 1808 as one of the thousands of people exhibited and transformed into medical spectacles during the course of the nineteenth century. My thesis explores the historical roots and intersecting perspectives surrounding this charged icon and her transformation into the Hottentot Venus through the works of Toni Morrison. Forming a living, breathing embodiment of ultimate difference, establishing nationalistic boundaries through the dissection and reconstruction of her bodily image, Bartmann highlights the way that science and popular culture work to mutually inform and regulate cultural behaviour. Utilising an exploration of Toni Morrison’s ‘aesthetics of resistance’ – at once ‘highly political and passionately aesthetic,’ Fred Moten’s consideration of the black radical tradition, and Roland Barthes’ contemplation on the function of photography, this research suggests that a difference needs to be drawn between the image of ‘race’ and that of the ‘racial image’ within cultural production and re-presentation of iconography. Evident in the association of historic and timeless stereotype, traced from early engravings of the Hottentot Venus to her life-size silhouettes produced by artist Kara Walker, aligned with Morrison’s uncanny depiction of the Africanist presence and lynching spectacle, Bartmann is no longer an image in which black female sexuality is present as an intelligibly visual object. Instead, she becomes a racial icon with a charged political presence in which race is derived as an articulation of the visual. Bartmann’s iconography reveals how cultural memory binds the past to the present and to the future, in a continual process of subversion, displacement and resurrection. An interdisciplinary thesis that juxtaposes the historic with the postmodern, the literary with the political, the aesthetic with the ideological, revealing the socio-political realities that have influenced the emergence of race and the transformation of the black female body