In this dissertation, a qualitative research project has been conducted focusing on two theatres for persons with intellectual disabilities. The aim of the dissertation was to analyze the ideological tension between artistic practises and the institutional setting in which they are arranged. The aim of the thesis was answered through the following questions: What happens when a new and innovative logic is introduced on a well established organisational field? How do Rebellerna and Ållateatern translate and manage the institutional setting under which they are working? How do Rebellerna and Ållateatern relate to the surrounding environment? The analysis is based on a qualitative research project conducted over a period of two years on Ållateatern and six mounts on Rebellerna. Theoretically, the analysis has been inspired by disability theory and neo-institutional theory. In the dissertation I argue that Rebellerna and Ållateatern, in their formal structure, reflect two different logics, which have influenced their relationship with the institutional environment as well as with the actors working at the theatres. These logics have been interpreted as a consequence of the need for human service organizations to obtain legitimacy from the institutional environment. However, on an individual level the tension between an artistic logic and a therapeutic logic has had a social meaning for the actors working at Rebellerna and Ållateatern. It has generated a selfunderstanding which besides the role of a client to the welfare state also includes the role of an actor. These experiences have generated a stronger belief in their own capabilities and a sense of pride. It has also challenged established social meanings on intellectual disabilities. However, one conclusion in the thesis is that both Ållateatern and Rebellerna have had an impact in influence the organisational field of daily activities. Another conclusion is that the tension between therapy and art on an individual level represents an important building block to generate a formation of identity and sub-cultural belonging.

Description logics knowledge bases are a popular approach to represent terminological and assertional knowledge suitable for computers to work with. Despite that, the practicality of description logics is impaired by the difficulties one has to overcome to construct such knowledge bases. Previous work has addressed this issue by providing methods to learn valid terminological knowledge from data, making use of ideas from formal concept analysis. A basic assumption here is that the data is free of errors, an assumption that can in general not be made for practical applications. This thesis presents extensions of these results that allow to handle errors in the data. For this, knowledge that is "almost valid" in the data is retrieved, where the notion of "almost valid" is formalized using the notion of confidence from data mining. This thesis presents two algorithms which achieve this retrieval. The first algorithm just extracts all almost valid knowledge from the data, while the second algorithm utilizes expert interaction to distinguish errors from rare but valid counterexamples.

Inevitably, it becomes more and more important to verify that the systems surrounding us have certain properties. This is indeed unavoidable for safety-critical systems such as power plants and intensive-care units. We refer to the term system in a broad sense: it may be man-made (e.g. a computer system) or natural (e.g. a patient in an intensive-care unit). Whereas in Model Checking it is assumed that one has complete knowledge about the functioning of the system, we consider an open-world scenario and assume that we can only observe the behaviour of the actual running system by sensors. Such an abstract sensor could sense e.g. the blood pressure of a patient or the air traffic observed by radar. Then the observed data are preprocessed appropriately and stored in a fact base. Based on the data available in the fact base, situation-awareness tools are supposed to help the user to detect certain situations that require intervention by an expert. Such situations could be that the heart-rate of a patient is rather high while the blood pressure is low, or that a collision of two aeroplanes is about to happen. Moreover, the information in the fact base can be used by monitors to verify that the system has certain properties. It is not realistic, however, to assume that the sensors always yield a complete description of the current state of the observed system. Thus, it makes sense to assume that information that is not present in the fact base is unknown rather than false. Moreover, very often one has some knowledge about the functioning of the system. This background knowledge can be used to draw conclusions about the possible future behaviour of the system. Employing description logics (DLs) is one way to deal with these requirements. In this thesis, we tackle the sketched problem in three different contexts: (i) runtime verification using a temporalised DL, (ii) temporalised query entailment, and (iii) verification in DL-based action formalisms.

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.

Answering object queries (i.e. instance retrieval) is a central task in ontology based data access (OBDA). Performing this task involves reasoning with respect to a knowledge base K (i.e. ontology) over some description logic (DL) dialect L. As the expressive power of L grows, so does the complexity of reasoning with respect to K. Therefore, eliminating the need to reason with respect to a knowledge base K is desirable. In this work, we propose an optimization to improve performance of answering object queries by eliminating the need to reason with respect to the knowledge base and, instead, utilizing cached query results when possible. In particular given a DL dialect L, an object query C over some knowledge base K and a set of cached query results S={S1, ..., Sn} obtained from evaluating past queries, we rewrite C into an equivalent query D, that can be evaluated with respect to an empty knowledge base, using cached query results S' = {Si1, ..., Sim}, where S' is a subset of S. The new query D is an interpolant for the original query C with respect to K and S. To find D, we leverage a tool for enumerating interpolants of a given sentence with respect to some theory. We describe a procedure that maps a knowledge base K, expressed in terms of a description logic dialect of first order logic, and object query C into an equivalent theory and query that are input into the interpolant enumerating tool, and resulting interpolants into an object query D that can be evaluated over an empty knowledge base. We show the efficacy of our approach through experimental evaluation on a Lehigh University Benchmark (LUBM) data set, as well as on a synthetic data set, LUBMMOD, that we created by augmenting an LUBM ontology with additional axioms.

The Metaphysics Experiment attempts to explicate a theory and history of universalism in modern physics, through an analysis of its conception of nature. Understood as an axiomatic and hegemonic metaphysical premise through four hundred years of scientific and political history, universalism is defined in terms of its general and persistent claim to nature or truth as an ahistorical reality. Thus, I argue that universalism is directly implicated in, not opposed to, the (Christian) monotheistic conception of God. Moreover, universalism constitutes the logic according to which nature is differentiated from history, culture, and politics. It thus constructs both sides of the same ostensible oppositions in the so-called science and culture wars that determine much of today’s politics of nature. The scientific and political dominance of universalism is demonstrated through a history in five acts. Using the current Large Hadron Collider experiment in Geneva as a principal case study in Act 1, and drawing on contemporary philosopher of science, Isabelle Stengers, I consider four pivotal historical moments in the history of physics and metaphysics that determine the universalist claims of this contemporary experiment. In Act 2, the mid-20th century development of Albert Einstein’s General Relativity framework and Big Bang Theory is read against Martin Heidegger’s critique of identity logic. In Act 3, the mid-17th century emergence of the mathematical universe in modern science and philosophy, through Galileo Galilei and René Descartes, is read against Benedict Spinoza’s univocal metaphysics. In Act 4, the late 19th century invention of particle or quantum physics is read against Henri Bergson’s idea of mind-matter dualism. Finally, in Act 5, considering the contemporary use of natural constants in physics, the insights of Michel Serres, Bruno Latour, Peter Sloterdijk, Heidegger, Stengers and Spinoza are drawn together to problematize the modern historical role of physics and its metaphysical constitution of nature. Beyond these historical event-scenes, I also offer a theoretical explication of five logics, demonstrated individually Act by Act, that comprise different dimensions of science in action. Thus, physics is considered historically both as theoretical and experimental practice and as a form of political mobilization.

[Abridged abstract] The goal is to give structural proof-theoretical analyses of logical constants, and thereby provide a criterion for what a logical constant is. Another goal is to illustrate the thesis that structural assumptions of logic are basic and that alternative logics (later called substructural logics) differ from each other only in their structural assumptions, and not in their assumptions about logical constants.

In this thesis we develop efficient methods for automated proof search within an important class of mathematical logics. The logics considered are the varying, cumulative and constant domain versions of the first-order modal logics K, K4, D, D4, T, S4 and S5, and first-order intuitionistic logic. The use of these non-classical logics is commonplace within Computing Science and Artificial Intelligence in applications in which efficient machine assisted proof search is essential. Traditional techniques for the design of efficient proof methods for classical logic prove to be of limited use in this context due to their dependence on properties of classical logic not shared by most of the logics under consideration. One major contribution of this thesis is to reformulate and abstract some of these classical techniques to facilitate their application to a wider class of mathematical logics. We begin with Bibel's Connection Calculus: a matrix proof method for classical logic comparable in efficiency with most machine orientated proof methods for that logic. We reformulate this method to support its decomposition into a collection of individual techniques for improving the efficiency of proof search within a standard cut-free sequent calculus for classical logic. Each technique is presented as a means of alleviating a particular form of redundancy manifest within sequent-based proof search. One important result that arises from this anaylsis is an appreciation of the role of unification as a tool for removing certain proof-theoretic complexities of specific sequent rules; in the case of classical logic: the interaction of the quantifier rules. All of the non-classical logics under consideration admit complete sequent calculi. We anaylse the search spaces induced by these sequent proof systems and apply the techniques identified previously to remove specific redundancies found therein. Significantly, our proof-theoretic analysis of the role of unification renders it useful even within the propositional fragments of modal and intuitionistic logic.

Defects in computer programs have great social and economic impacts and should be eliminated as much as possible. Since testing and debugging are among the most costly and time consuming tasks in the software development life cycle, a variety of intelligent debugging aids have been proposed within the last three decades. Model-based software debugging (MBSD) is a particular technique that exploits discrepancies between a program execution and the intended behaviour to isolate program fragments that could potentially explain an observed misbehaviour. In contrast to other techniques, model-based debugging does not require a formal specification of a program's behaviour, making the approach suitable for developers without training in formal software engineering practices. A key aspect of model-based debugging is the transformation of the given program into a model suitable for debugging. In this thesis, several models for analysing programs written in an object-oriented language are investigated, with Java as concrete example. The aim of this work is to assess the suitability of value-based models and generalisations thereof for debugging of programs making use of dynamically allocated data structures, recursive methods and polymorphic method invocations.

This is a study of the semantics and proof theory of the logic of bunched implications (BI), which is promoted as a logic of (computational) resources, and is a foundational component of separation logic, an approach to program analysis. BI combines an additive, or intuitionistic, fragment with a multiplicative fragment. The additive fragment has full use of the structural rules of weakening and contraction, and the multiplicative fragment has none. Thus it contains two conjunctive and two implicative connectives. At various points, we illustrate a resource view of BI based upon the Kripke resource semantics. Our first original contribution is the formulation of a proof system for BI in the newly developed proof-theoretical formalism of the calculus of structures. The calculus of structures is distinguished by its employment of deep inference, but we already see deep inference in a limited form in the established proof theory for BI. We show that our system is sound with respect to the elementary Kripke resource semantics for BI, and complete with respect to a formulation of the partially-defined Kripke resource semantics. Our second contribution is the development from a semantic standpoint of preliminary ideas for a hybrid logic of bunched implications (HBI). We give a Kripke semantics for HBI in which nominal propositional atoms can be seen as names for resources, rather than as names for locations, as is the case with related proposals for BI-Loc and for intuitionistic hybrid logic.