Logic of Non-Monotonic Interactive Proofs (Formal Theory of Temporary Knowledge Transfer)

We propose a monotonic logic of internalised non-monotonic or instant interactive proofs (LiiP) and reconstruct an existing monotonic logic of internalised monotonic or persistent interactive proofs (LiP) as a minimal conservative extension of LiiP. Instant interactive proofs effect a fragile epistemic impact in their intended communities of peer reviewers that consists in the impermanent induction of the knowledge of their proof goal by means of the knowledge of the proof with the interpreting reviewer: If my peer reviewer knew my proof then she would at least then (in that instant) know that its proof goal is true. Their impact is fragile and their induction of knowledge impermanent in the sense of being the case possibly only at the instant of learning the proof. This accounts for the important possibility of internalising proofs of statements whose truth value can vary, which, as opposed to invariant statements, cannot have persistent proofs. So instant interactive proofs effect a temporary transfer of certain propositional knowledge (knowable ephemeral facts) via the transmission of certain individual knowledge (knowable non-monotonic proofs) in distributed systems of multiple interacting agents.Comment: continuation of arXiv:1201.3667 ; published extended abstract: DOI:10.1007/978-3-642-36039-8_16 ; related to arXiv:1208.591

Emergency preparedness and response in New Zealand schools : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Emergency Management at Massey University, Wellington, New Zealand

International disaster risk reduction efforts prioritise school safety. Providing a safe learning environment for students and ensuring their continued access to education after an emergency has a positive influence on student, family, and community resilience. Existing school-based emergency management literature is limited. The project aimed to investigate current emergency preparedness and response activities in New Zealand schools, and identify key practices that support efforts to keep students safe during emergencies. A multiphase mixed methods research design, underpinned by a pragmatic philosophical approach, was employed to conduct three separate but linked studies that investigated: Emergency preparedness in schools (Study 1); Emergency management requirements and expectations of schools (Study 2); and Emergency response in schools (Study 3). Study 1 employed a survey to collect quantitative (n=355) and qualitative (n=514) data from schools throughout New Zealand about their experiences participating in the nationwide 2012 New Zealand ShakeOut earthquake drill, and the types of emergency preparedness activities undertaken. Findings identified lessons learned, and presented ways in which drills can be linked to other aspects of school preparedness. Schools were also found to undertake a range of preparedness activities (e.g., develop emergency plans, conduct frequent drills, and provide students with hazards education). However, differences in preparedness levels were identified, suggesting that some schools may be under-prepared to keep students safe in emergencies. A lack of clarity in the legislative requirements for school-based emergency management was proposed as a possible reason for differences in preparedness. Study 2 combined interviews of three emergency management practitioners with a review of New Zealand legislation, policy, and guidelines to identify the preparedness activities New Zealand schools are required to undertake to ensure the safety of the students in their care. The legislation was found to be generic, at times ambiguous, and schools were not provided with clear guidance. As a result, it was recommended that preparedness benchmarks be established and that standard operating procedures for core emergency response actions (i.e., shelter-in-place, lockdown, building evacuation, relocation, and family reunification) be developed to provide a consistent approach to school-based preparedness efforts. Studies 1 and 2 discussed emergency preparedness in New Zealand schools. However, there remained a need to investigate the link between preparing for and responding to emergencies by investigating how schools responded to real emergency events. Study 3 used three case studies to explore how three schools responded in a range of emergency events. Findings included the identification of generic, recurring response activities across a selection of emergency types, which were used to develop a six-stage school-based emergency response model. The lessons learned from participant’s first hand experiences of various emergency events enabled the identification of factors that contribute to an effective emergency response, including activities undertaken before, during, and after an emergency. Research exploring emergency management in New Zealand schools is still in its infancy. This project has contributed significant knowledge to understanding how New Zealand schools prepare for and respond to emergencies to keep their students safe. Findings from the research may also have relevance for an international audience

Reflexivity and rigidity for complexes, II: Schemes

We prove basic facts about reflexivity in derived categories over noetherian schemes; and about related notions such as semidualizing complexes, invertible complexes, and Gorenstein-perfect maps. Also, we study a notion of rigidity with respect to semidualizing complexes, in particular, relative dualizing complexes for Gorenstein-perfect maps. Our results include theorems of Yekutieli and Zhang concerning rigid dualizing complexes on schemes. This work is a continuation of part I, which dealt with commutative rings.Comment: 40 page

Sharing a Library between Proof Assistants: Reaching out to the HOL Family

We observe today a large diversity of proof systems. This diversity has the negative consequence that a lot of theorems are proved many times. Unlike programming languages, it is difficult for these systems to co-operate because they do not implement the same logic. Logical frameworks are a class of theorem provers that overcome this issue by their capacity of implementing various logics. In this work, we study the STTforall logic, an extension of Simple Type Theory that has been encoded in the logical framework Dedukti. We present a translation from this logic to OpenTheory, a proof system and interoperability tool between provers of the HOL family. We have used this translation to export an arithmetic library containing Fermat's little theorem to OpenTheory and to two other proof systems that are Coq and Matita.Comment: In Proceedings LFMTP 2018, arXiv:1807.0135

The politics of teachers' work in the context of curriculum resources marketisation policy reforms in three secondary schools in Tanzania : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy (PhD) at Massey University, Manawatu Campus, Palmerston North, New Zealand

Before Tanzania enjoyed the fruits of postcolonial education policy reforms, the country was hit by the world economic crises in the 1970s. Consequently, Tanzania and other developing countries turned to the World Bank and International Monetary Fund (IMF) that imposed, financed, and controlled her education and economic policy through the Structural Adjustment Programmes (SAP) of the 1980s. Thus, Tanzania adopted education privatisation and marketisation policies during the 1990s. More specifically, in 1991, the Policy on Production and Distribution of School and College Books, which I will call Marketisation Policy, redefined school and college curriculum resources according to market principles. The purpose of this study was to critically analyse how marketisation policy reforms, reconstructed at societal, institutional, and local classroom levels, reshaped teachers’ subjectivities and practices between 1992 and 2012. Using an ethnographic case study of three secondary schools from northern Tanzania, the study examines teachers’ work histories, politics, and cultures using a combination of Critical Discourse Analysis (CDA) (Fairclough, 1989, 1992, 1995, 2015) and the theory of pedagogic discourse (Bernstein, 1971, 1975, 1990, 1996, 1999, 2000). The study aimed to answer three research questions, namely: (1) What policy texts and discourses were constructed in the process of marketisation policy interpretation in secondary schools? (2) How do marketisation policy texts and discourses reshape secondary school teachers’ subject positions and pedagogical codes? and (3) How do the subject positions and pedagogical codes constructed by marketisation policy texts and discourses reshape teachers’ pedagogic practices and official knowledge construction? Marketisation policy implementation and professional documents, interview and focus group transcripts, and classroom observation notes were collected from the three schools. These were analysed to discern themes that characterised the nature, history, and politics of teachers’ work practices. Findings indicate that marketisation policy texts and discourses positioned secondary school teachers as passive and dependent consumers of marketised curriculum resources (MCR) produced by private publishers and the state. They were also positioned as lacking knowledge to plan, decide, and implement curricula, pedagogic, and evaluation practices. These subject positions constrained teacher creativity and critical thinking, and reproduced capitalist publishers and state power and ideologies through the policy texts and discourses. Curricular, pedagogical, and evaluatative cultural practices were dominated and influenced by capitalist publishers and the state through marketisation policy texts and the discourses of finance, MCR, educational materials’ approval, and advertising. The study documents how marketisation policy aims, objectives, outcomes, and pedagogic strategies reflected the aims and effects of both colonial and postcolonial education policy. Teachers and students constructed multiple power/knowledge and resistance to dominant discourses based on accessible MCR, private tuition, past educational training, collaboration with colleagues, and attending some training. However, although these discourses empowered them to construct and exercise power/knowledge to respond to marketisation policy discursive constraints, they also reconstructed curriculum domination because of students’ limited access to MCR and classroom curriculum discourses

Systematic Verification of the Modal Logic Cube in Isabelle/HOL

We present an automated verification of the well-known modal logic cube in Isabelle/HOL, in which we prove the inclusion relations between the cube's logics using automated reasoning tools. Prior work addresses this problem but without restriction to the modal logic cube, and using encodings in first-order logic in combination with first-order automated theorem provers. In contrast, our solution is more elegant, transparent and effective. It employs an embedding of quantified modal logic in classical higher-order logic. Automated reasoning tools, such as Sledgehammer with LEO-II, Satallax and CVC4, Metis and Nitpick, are employed to achieve full automation. Though successful, the experiments also motivate some technical improvements in the Isabelle/HOL tool.Comment: In Proceedings PxTP 2015, arXiv:1507.0837

Who is she and who are we? A critical essay on reflexivity in research into the rarity of women executives in accountancy

This paper proposes a critical stance on research into the rarity of women at the highest levels of accountancy. The authors aim to unravel the discourses produced on this topic in the accounting literature and question their own experience and perception as scholars building on Bourdieu’s work on reflexivity (Bourdieu & Wacquant, 1992; Bourdieu, 2001, 2003).Gender; accounting profession; methodology; reflexivity