Extending SMTCoq, a Certified Checker for SMT (Extended Abstract)

This extended abstract reports on current progress of SMTCoq, a communication tool between the Coq proof assistant and external SAT and SMT solvers. Based on a checker for generic first-order certificates implemented and proved correct in Coq, SMTCoq offers facilities both to check external SAT and SMT answers and to improve Coq's automation using such solvers, in a safe way. Currently supporting the SAT solver zChaff, and the SMT solver veriT for the combination of the theories of congruence closure and linear integer arithmetic, SMTCoq is meant to be extendable with a reasonable amount of effort: we present work in progress to support the SMT solver CVC4 and the theory of bit vectors.Comment: In Proceedings HaTT 2016, arXiv:1606.0542

Efficient Certified Resolution Proof Checking

We present a novel propositional proof tracing format that eliminates complex processing, thus enabling efficient (formal) proof checking. The benefits of this format are demonstrated by implementing a proof checker in C, which outperforms a state-of-the-art checker by two orders of magnitude. We then formalize the theory underlying propositional proof checking in Coq, and extract a correct-by-construction proof checker for our format from the formalization. An empirical evaluation using 280 unsatisfiable instances from the 2015 and 2016 SAT competitions shows that this certified checker usually performs comparably to a state-of-the-art non-certified proof checker. Using this format, we formally verify the recent 200 TB proof of the Boolean Pythagorean Triples conjecture

Automated metamorphic testing of variability analysis tools

Variability determines the capability of software applications to be configured and customized. A common need during the development of variability–intensive systems is the automated analysis of their underlying variability models, e.g. detecting contradictory configuration options. The analysis operations that are performed on variability models are often very complex, which hinders the testing of the corresponding analysis tools and makes difficult, often infeasible, to determine the correctness of their outputs, i.e. the well–known oracle problem in software testing. In this article, we present a generic approach for the automated detection of faults in variability analysis tools overcoming the oracle problem. Our work enables the generation of random variability models together with the exact set of valid configurations represented by these models. These test data are generated from scratch using step–wise transformations and assuring that certain constraints (a.k.a. metamorphic relations) hold at each step. To show the feasibility and generalizability of our approach, it has been used to automatically test several analysis tools in three variability domains: feature models, CUDF documents and Boolean formulas. Among other results, we detected 19 real bugs in 7 out of the 15 tools under test.CICYT TIN2012-32273CICYT IPT-2012- 0890-390000Junta de Andalucía TIC-5906Junta de Andalucía P12-TIC- 186

Philosophy of mathematics education

PHILOSOPHY OF MATHEMATICS EDUCATION\ud This thesis supports the view that mathematics teachers should be aware of differing views of the nature of mathematics and of a range of teaching perspectives. The first part of the thesis discusses differing ways in which the subject 'mathematics' can be identified, by relying on existing philosophy of mathematics. The thesis describes three traditionally recognised philosophies of mathematics: logicism, formalism and intuitionism. A fourth philosophy is constructed, the hypothetical, bringing together the ideas of Peirce and of Lakatos, in particular. The second part of the thesis introduces differing ways of teaching mathematics, and identifies the logical and sometimes contingent connections that exist between the philosophies of mathematics discussed in part 1, and the philosophies of mathematics teaching that arise in part 2. Four teaching perspectives are outlined: the teaching of mathematics as aestheticallyorientated, the teaching of mathematics as a game, the teaching of mathematics as a member of the natural sciences, and the teaching of mathematics as technology-orientated. It is argued that a possible fifth perspective, the teaching of mathematics as a language, is not a distinctive approach. A further approach, the Inter-disciplinary perspective, is recognised as a valid alternative within previously identified philosophical constraints. Thus parts 1 and 2 clarify the range of interpretations found in both the philosophy of mathematics and of mathematics teaching and show that they present realistic choices for the mathematics teacher. The foundations are thereby laid for the arguments generated in part 3, that any mathematics teacher ought to appreciate the full range of teaching 4 perspectives which may be chosen and how these link to views of the nature of mathematics. This would hopefully reverse 'the trend at the moment... towards excessively narrow interpretation of the subject' as reported by Her Majesty's Inspectorate (Aspects of Secondary Education in England, 7.6.20, H. M. S. O., 1979). While the thesis does not contain infallible prescriptions it is concluded that the technology-orientated perspective supported by the hypothetical philosophy of mathematics facilitates the aims of those educators who show concern for the recognition of mathematics in the curriculum, both for its intrinsic and extrinsic value. But the main thrust of the thesis is that the training of future mathematics educators must include opportunities for gaining awareness of the diversity of teaching perspectives and the influence on them of philosophies of mathematics

Knowledge Resistance in High-Choice Information Environments

This book offers a truly interdisciplinary exploration of our patterns of engagement with politics, news, and information in current high-choice information environments. Putting forth the notion that high-choice information environments may contribute to increasing misperceptions and knowledge resistance rather than greater public knowledge, the book offers insights into the processes that influence the supply of misinformation and factors influencing how and why people expose themselves to and process information that may support or contradict their beliefs and attitudes. A team of authors from across a range of disciplines address the phenomena of knowledge resistance and its causes and consequences at the macro- as well as the micro-level. The chapters take a philosophical look at the notion of knowledge resistance, before moving on to discuss issues such as misinformation and fake news, psychological mechanisms such as motivated reasoning in processes of selective exposure and attention, how people respond to evidence and fact-checking, the role of political partisanship, political polarization over factual beliefs, and how knowledge resistance might be counteracted. This book will have a broad appeal to scholars and students interested in knowledge resistance, primarily within philosophy, psychology, media and communication, and political science, as well as journalists and policymakers

Empiricism and Philosophy

Though Quine's argument against the analytic-synthetic distinction is widely disputed, one of the major effects of his argument has been to popularise the belief that there is no sharp distinction between science and philosophy. This thesis begins by distinguishing reductive from holistic empiricism, showing why reductive empiricism is false, refuting the major objections to holistic empiricism and stating the limits on human knowledge it implies. Quine's arguments (and some arguments that have been mistakenly attributed to him) from holism against the analytic-synthetic are considered, and while many of them are found wanting one good argument is presented. Holism does not, however, imply that there is no sharp distinction between science and philosophy, and indeed implies that the distinction between scientific and philosophical disputes is perfectly sharp. The grounds upon which philosophical disputes may be resolved are then sought for and deliniated

Empiricism and Philosophy

Though Quine's argument against the analytic-synthetic distinction is widely disputed, one of the major effects of his argument has been to popularise the belief that there is no sharp distinction between science and philosophy. This thesis begins by distinguishing reductive from holistic empiricism, showing why reductive empiricism is false, refuting the major objections to holistic empiricism and stating the limits on human knowledge it implies. Quine's arguments (and some arguments that have been mistakenly attributed to him) from holism against the analytic-synthetic are considered, and while many of them are found wanting one good argument is presented. Holism does not, however, imply that there is no sharp distinction between science and philosophy, and indeed implies that the distinction between scientific and philosophical disputes is perfectly sharp. The grounds upon which philosophical disputes may be resolved are then sought for and deliniated

Knowledge Resistance in High-Choice Information Environments

This book offers a truly interdisciplinary exploration of our patterns of engagement with politics, news, and information in current high-choice information environments. Putting forth the notion that high-choice information environments may contribute to increasing misperceptions and knowledge resistance rather than greater public knowledge, the book offers insights into the processes that influence the supply of misinformation and factors influencing how and why people expose themselves to and process information that may support or contradict their beliefs and attitudes. A team of authors from across a range of disciplines address the phenomena of knowledge resistance and its causes and consequences at the macro- as well as the micro-level. The chapters take a philosophical look at the notion of knowledge resistance, before moving on to discuss issues such as misinformation and fake news, psychological mechanisms such as motivated reasoning in processes of selective exposure and attention, how people respond to evidence and fact-checking, the role of political partisanship, political polarization over factual beliefs, and how knowledge resistance might be counteracted. This book will have a broad appeal to scholars and students interested in knowledge resistance, primarily within philosophy, psychology, media and communication, and political science, as well as journalists and policymakers

How do women say ‘I’ online?

Creative Submission: My digital narrative, Seed, seeks to re-work conventional notions of ‘character’ and ‘plot’ in fiction, via a the polyphonic first person narrative of an unnamed 1980s Ophelia who is searching for ways to represent unspoken and unspeakable experiences of girlhood in the late twentieth century. Coming of age in 1988, a year in which misinformation about AIDS, Chernobyl and CJD peaked, Seed’s narrator is haunted by fears of infection, aware that bodily experience (breathing, eating, sex) could lead to illness or even death. Living in isolation in the raw industrial countryside outside a new town, the poverty of narratives available to her render Seed’s narrator, like Shakespeare's heroine, multi-vocal with borrowed voices. In her case these are garnered from fashion magazines, pop songs, media reports, and the words Ophelia speaks in Hamlet—but, as Gertrude says of Ophelia, she is ”incapable of her own distress". Presented as a digital app, seed-story.com, (with later iterations as a multi-vocal performance, and a print book), Seed grows into a rhizomatic structure which—aware of its experimental forbears including Julio Cortazar, B. S. Johnson and Shelley Jackson—can be read via a number of different paths. Time and space are collapsed and expanded into a nonhierarchical, explorable reading ‘landscape’, decentring ideas of 'author' and ‘character’ via a patchworked narrative inspired by post-Lacanian feminist and queer writing on subjectivity (especially Irigaray and Wittig). In keeping with its examination of restriction, the script of Seed is tied by a hidden linguistic constraint. Critical Submission: My critical thesis, /A USER MANIFESTO is a polyvocal investigation of the constraints and opportunities of constructing a female persona on the digital screen, for those constrained by aspects of female identity offline. Particularly concerned with the experiences of motherhood and gendered precarity in the arts and gig economy, I draw especially on the work of Berlant, Butler and Ngai to examine the poetics of commodifiable (female) gender-presentation in creative acts of self-identification online, taking in (amongst other iterations of online subjectivity) the digital speech act, the gif, the meme, the 'dead' site, and the blog-novel. My work draws direct comparisons between hierarchical structures in programming languages and vocabulary (chiefly Javascript) and digital Boolean logic, and offline constructions of the ‘female’. It asks questions about the nature of digital writing and reading for women via mimetic strategies of identification and exemplarity. Proceeding by example, it takes the form of moral vignettes, thought experiments, diary entries and coded scripts, both digital and social, taking into account the history of cyber-feminist thought and creativity to create a manifesto for those who use, and are used by, digital femininity