Mechanised Uniform Interpolation for Modal Logics K, GL, and iSL

The uniform interpolation property in a given logic can be understood as the definability of propositional quantifiers. We mechanise the computation of these quantifiers and prove correctness in the Coq proof assistant for three modal logics, namely: (1) the modal logic K, for which a pen-and-paper proof exists; (2) Gödel-Löb logic GL, for which our formalisation clarifies an important point in an existing, but incomplete, sequent-style proof; and (3) intuitionistic strong Löb logic iSL, for which this is the first proof-theoretic construction of uniform interpolants. Our work also yields verified programs that allow one to compute the propositional quantifiers on any formula in this logic

Mechanised Uniform Interpolation for Modal Logics K, GL, and iSL

The uniform interpolation property in a given logic can be understood as the definability of propositional quantifiers. We mechanise the computation of these quantifiers and prove correctness in the Coq proof assistant for three modal logics, namely: (1) the modal logic K, for which a pen-and-paper proof exists; (2) Gödel-Löb logic GL, for which our formalisation clarifies an important point in an existing, but incomplete, sequent-style proof; and (3) intuitionistic strong Löb logic iSL, for which this is the first proof-theoretic construction of uniform interpolants. Our work also yields verified programs that allow one to compute the propositional quantifiers on any formula in this logic

A program logic for fresh name generation

This thesis introduces a program logic for an extension of the call-by-value simply typed λ-calculus (STLC), with a mechanism for the generation of fresh names via gensym, which is an adaptation of Pitts and Stark s ν-calculus 52 . Names can be compared for equality and inequality, producing programs with subtle observable properties. Hidden names, produced by interactions between name generation and λ-abstraction, are captured logically with a new restricted quantification. The restrictions require only derived values from previously derived terms, ensuring hidden names are not revealed. The concept of derivation is extended to type contexts and models, ensuring hidden names are not revealed at later stages. Type contexts are adapted to include an order and the ability to represent future extensions. The logic quantifies over future extensions, using a second-order quantification over future type contexts. This quantification names the future context to allow for them to be reasoned about within the logic. A new model construction is introduced to replicate the order in which names and values are produced with potentially hidden names. The semantics of the logic in the new model are used to prove each axiom and rule sound and as such the soundness of the logic. A proof that the logic is an extension of the STLC logic is given alongside a sketch of the proof that the extension is conservative. Usage of the logic is illustrated through reasoning about numerous examples. These ex- amples range from simple STLC and ν-calculus examples to well-known difficult programs from the literature

The Machinic Imaginary: A Post-Phenomenological Examination of Computational Society

The central claim of this thesis is the postulation of a machinic dimension of the social imaginary—a more-than-human process of creative expression of the social world. With the development of machine learning and the sociality of interactive media, computational logics have a creative capacity to produce meaning of a radically machinic order. Through an analysis of computational functions and infrastructures ranging from artificial neural networks to large-scale machine ecologies, the institution of computational logics into the social imaginary is nothing less than a reordering of the conditions of social-historical creation. Responding to dominant technopolitical propositions concerning digital culture, this thesis proposes a critical development of Cornelius Castoriadis’ philosophy of the social imaginary. To do so, a post phenomenological framework is constructed by tracing a trajectory from Maurice Merleau-Ponty’s late ontological turn, through to the process-relational philosophies of Gilbert Simondon and Castoriadis. Introducing the concept of the machinic imaginary, the thesis maps the extent to which the dynamic, interactive paradigm of twenty-first century computation is changing how meaning is socially instituted in ways incomprehensible to human sense. As social imaginary significations are increasingly created and carried by machines, the articulation of the social diverges into human and non-human worlds. This inaccessibility of the machinic imaginary is a core problematic raised by this thesis, indicating a fragmentation of the social imaginary and a novel form of existential alienation. Any political theorisation of the contemporary social condition must therefore work within this alienation and engage with the transsubjective character of social-historical creation

Fixing meaning: intertextuality, inferencing and genre in interpretation

The intertextual theories of V. N. Voloshinov, Mikhail Bakhtin and the early Julia Kristeva provide the most convincing account of the processes of textual production, conceived as constitutively social, cultural and historical. However, the ways in which intertextual accounts of reading (or 'use') have extended such theories have foreclosed their potential. In much contemporary literary and cultural theory, it is assumed that reading, conceived intertextually, is no simple decoding process, but there is little interest in what interpretation, as a process, is, and its relations to reading. It is these questions which this thesis seeks to answer. The introduction sets the scene both for the problem and its methodological treatment: drawing certain post-structuralist and pragmatic theories of meaning into confrontation, and producing a critical synthesis. Part one (chapters one to three) elaborate these two traditions of meaning and stages the encounter. Chapter one offers detailed expositions of Voloshinov, Bakhtin and Kristeva, contrasting these with other intertextual theories of production and reception. Chapter two examines inferential accounts of communication within pragmatics, focusing on Paul Grice and on Dan Sperber and Deirdre Wilson's Relevance theory. Chapter three stages an encounter between these radically different traditions. A common ground is identified: both are rhetorical approaches to meaning, focusing on the relations between texts, contexts and their producers and interpreters. Each tradition is then subjected to the theoretical scrutiny of the other. Inferential theories expose the lack of specificity in intertextual accounts which completely ignore inferencing as a process. Intertextual theories reveal that text and context have semantically substantive intertextual dimensions, most particularly genre and register (conceived intertextually) which are ignored by inferential theories. Text and context are therefore far more semantically fixed than such theories suppose. Both traditions ignore the role of production practices other than 'speech' or 'writing', i.e. they ignore how publishing practices - editing, design, production and marketing - constitute genre and shape reading. In Part Two (chapters four to six), the critique is developed into an account of interpretation. Interpretation, conceived intertextually, is significantly, though not exclusively, inferential, but inferential processes do not 'work' in the ways proposed by existing inferential theories. Patterns of inference are ordered by the relations between discourses (in Foucault's sense) and genres in the text, the reader's knowledge and the conditions of reading. Chapter four elaborates the concepts required for such an account of interpretation, centring on the role of publishing processes and the text's material form in shaping interpretation. The limits of existing accounts of the edition and publishing, specifically Gerard Genette's Paratexts and work in the 'new' textual studies, call for a more expansive account of how publishing shapes genre and interpretation. Chapters five and six develop two case-studies which extend these concepts and arguments. These examine two contemporary publishing categories: 'classics' (Penguin, Everyman etc.) and literary theory textbooks (Introductions and Readers). Through the detailed analyses of particular editions, I develop and substantiate a stronger and richer account of interpretation as process and practice and its relation to reading. This is expanded in the final chapter

Writing the railway: biosemiotic strategies for enforming meaning and dispersing authorship in site-specific text-based artworks

This practice-led PhD is concerned with the subject matter of contemporary art. It proposes methods by which a writer-maker’s authorship can be dispersed throughout reticulated networks of interpretation, and tests the limits of detail articulable in an artwork. To counter the literary and discursive turns that have dominated art theory and practice since the 1970s, the thesis demands a reassessment of the privileging of the viewer and of the adoption of indeterminacy as a generic style. It proposes instead a turn to biosemiotics as a means to situate the artwork materially, bodily, historically. That ambiguity and pluralism can consequently be deployed strategically, affectively and to critical effect is tested and evaluated in the accompanying practice. The thesis gives an account of the theorising and devising of text-based artworks which take the UK railway as site, and considers site-specificity a particular sort of engagement with subject matter. The railway is approached as a complex technical object consisting in multiple entangled intentions and interpretations – social, emotional and political valences, diffracted by a spectrum of practices, knowledges and semiotic ontologies – all of which are available to the writermaker as immanent materials of the artwork. Part One of the thesis presents a transdisciplinary argument that draws on biosemiotics, linguistic anthropology, philosophy of time and socio-psychology as well as art history and critical theory. Part Two performs an analysis of paradigmatic descriptions of the railway, speculates on the social dynamics of a train carriage interior and empirically tests the bureaucratic structures of London Underground. Part Three is an exegesis of three pieces submitted as documentation in the practice portfolio: an audio work, a guided tour and a live performance on a train carriage tabletop

Atoms organised: On the orientations of theory and the theorisations of organisation in the philosophy of Karl Marx

PhDThe contemporary crisis has lead to a renewed interest in Marx's critique of political economy. But today it is hard to read Marx as the prophet of a new and better world, hiswritings on capitalism's self-destructive tendencies seem without hope: where Marxbelieved that capitalist organisation would concentrate, homogenise and organise labour and orientate it toward socialism, in today's globalised capitalism the tendency is the opposite, towards precariousness, disorganisation and competition. This raises the problematic of this thesis, that of the relation between orientation and organisation. Where capitalist organisation atomises and differentiates, the starting point for orientation cannot be capitalist organisation. The question emerges: is there a place and orientation of self-organisation in Marx – and what is its possible relation to the critique of the dynamics of capital? To answer this question, I will not focus on Marx's explicit theory of workers' organisation or the party, which is in crisis, but on his theorisation of the epochal problem of organisation under capitalism. Through a reading of some of Marx's central writings, which is sensitive to their historical context, the thesis asks: what is the orientating role of the concepts of organisation and disorganisation in Marx's theory of capital and of revolutionary, history-making practice? From Kant we learn to think the mutual implication of theory and practice through the concept of orientation. Furthermore, we show that Marx's concept of organisation was inspired by Hegel's Philosophy of Nature, which starts from the problem of atomised individuals whose reproduction is contingent. Thus, organisation, when appropriately historicised in terms of this condition of contingency, does not start from the relation between capital and labour, but from the problem of reproduction. In conclusion we arrive at a concept of struggle that starts from resistances and struggles for reproduction, and which poses the question of their combination, self-organisation, and generalisatio

Unmet goals of tracking: within-track heterogeneity of students' expectations for

Educational systems are often characterized by some form(s) of ability grouping, like tracking. Although substantial variation in the implementation of these practices exists, it is always the aim to improve teaching efficiency by creating homogeneous groups of students in terms of capabilities and performances as well as expected pathways. If students’ expected pathways (university, graduate school, or working) are in line with the goals of tracking, one might presume that these expectations are rather homogeneous within tracks and heterogeneous between tracks. In Flanders (the northern region of Belgium), the educational system consists of four tracks. Many students start out in the most prestigious, academic track. If they fail to gain the necessary credentials, they move to the less esteemed technical and vocational tracks. Therefore, the educational system has been called a 'cascade system'. We presume that this cascade system creates homogeneous expectations in the academic track, though heterogeneous expectations in the technical and vocational tracks. We use data from the International Study of City Youth (ISCY), gathered during the 2013-2014 school year from 2354 pupils of the tenth grade across 30 secondary schools in the city of Ghent, Flanders. Preliminary results suggest that the technical and vocational tracks show more heterogeneity in student’s expectations than the academic track. If tracking does not fulfill the desired goals in some tracks, tracking practices should be questioned as tracking occurs along social and ethnic lines, causing social inequality