Causality Is Logically Definable-Toward an Equilibrium-Based Computing Paradigm of Quantum Agents and Quantum Intelligence (QAQI)

A survey on agents, causality and intelligence is presented and an equilibrium-based computing paradigm of quantum agents and quantum intelligence (QAQI) is proposed. In the survey, Aristotle’s causality principle and its historical extensions by David Hume, Bertrand Russell, Lotfi Zadeh, Donald Rubin, Judea Pearl, Niels Bohr, Albert Einstein, David Bohm, and the causal set initiative are reviewed; bipolar dynamic logic (BDL) is introduced as a causal logic for bipolar inductive and deductive reasoning; bipolar quantum linear algebra (BQLA) is introduced as a causal algebra for quantum agent interaction and formation. Despite the widely held view that causality is undefinable with regularity, it is shown that equilibrium-based bipolar causality is logically definable using BDL and BQLA for causal inference in physical, social, biological, mental, and philosophical terms. This finding leads to the paradigm of QAQI where agents are modeled as quantum ensembles; intelligence is revealed as quantum intelligence. It is shown that the ensembles formation, mutation and interaction of agents can be described as direct or indirect results of quantum causality. Some fundamental laws of causation are presented for quantum agent entanglement and quantum intelligence. Applicability is illustrated; major challenges are identified in equilibrium based causal inference and quantum data mining

Culture, worldview and transformative philosophy of mathematics education in Nepal: a cultural-philosophical inquiry

This thesis portrays my multifaceted and emergent inquiry into the protracted problem of culturally decontextualised mathematics education faced by students of Nepal, a culturally diverse country of south Asia with more than 90 language groups. I generated initial research questions on the basis of my history as a student of primary, secondary and university levels of education in Nepal, my Master’s research project, and my professional experiences as a teacher educator working in a university of Nepal between 2004 and 2006. Through an autobiographical excavation of my experiences of culturally decontextualised mathematics education, I came up with several emergent research questions, leading to six key themes of this inquiry: (i) hegemony of the unidimensional nature of mathematics as a body of pure knowledge, (ii) unhelpful dualisms in mathematics education, (iii) disempowering reductionisms in curricular and pedagogical aspects, (iv) narrowly conceived ‘logics’ that do not account for meaningful lifeworld-oriented thinking in mathematics teaching and learning, (v) uncritical attitudes towards the image of curriculum as a thing or object, and (vi) narrowly conceived notions of globalisation, foundationalism and mathematical language that give rise to a decontextualised mathematics teacher education program.With these research themes at my disposal my aim in this research was twofold. Primarily, I intended to explore, explain and interpret problems, issues and dilemmas arising from and embedded in the research questions. Such an epistemic activity of articulation was followed by envisioning, an act of imagining futures together with reflexivity, perspectival language and inclusive vision logics.In order to carry out both epistemic activities – articulating and envisioning – I employed a multi-paradigmatic research design space, taking on board mainly the paradigms of criticalism, postmodernism, interpretivism and integralism. The critical paradigm offered a critical outlook needed to identify the research problem, to reflect upon my experiences as a mathematics teacher and teacher educator, and to make my lifetime’s subjectivities transparent to readers, whereas the paradigm of postmodernism enabled me to construct multiple genres for cultivating different aspects of my experiences of culturally decontextualised mathematics education. The paradigm of interpretivism enabled me to employ emergence as the hallmark of my inquiry, and the paradigm of integralism acted as an inclusive meta-theory of the multi-paradigmatic design space for portraying my vision of an inclusive mathematics education in Nepal.Within this multi-paradigmatic design space, I chose autoethnography and small p philosophical inquiry as my methodological referents. Autoethnography helped generate the research text of my cultural-professional contexts, whereas small p philosophical inquiry enabled me to generate new knowledge via a host of innovative epistemologies that have the goal of deepening understanding of normal educational practices by examining them critically, identifying underpinning assumptions, and reconstructing them through scholarly interpretations and envisioning. Visions cultivated through this research include: (i) an inclusive and multidimensional image of the nature of mathematics as an im/pure knowledge system, (ii) the metaphors of thirdspace and dissolution for conceiving an inclusive mathematics education, (iii) a multilogical perspective for morphing the hegemony of reductionism-inspired mathematics education, (iv) an inclusive image of mathematics curriculum as montage that provides a basis for incorporating different knowledge systems in mathematics education, and (v) perspectives of glocalisation, healthy scepticism and multilevel contextualisation for constructing an inclusive mathematics teacher education program

A Theory of Factfinding: The Logic for Processing Evidence

Academics have never agreed on a theory of proof. The darkest corner of anyone’s theory has concerned how legal decisionmakers logically should find facts. This Article pries open that cognitive black box. It does so by employing multivalent logic, which enables it to overcome the traditional probability problems that impeded all prior attempts. The result is the first-ever exposure of the proper logic for finding a fact or a case’s facts. The focus will be on the evidential processing phase, rather than the application of the standard of proof as tracked in my prior work. Processing evidence involves (1) reasoning inferentially from a piece of evidence to a degree of belief and of disbelief in the element to be proved, (2) aggregating pieces of evidence that all bear to some degree on one element in order to form a composite degree of belief and of disbelief in the element, and (3) considering the series of elemental beliefs and disbeliefs to reach a decision. Zeroing in, the factfinder in step #1 should connect each item of evidence to an element to be proved by constructing a chain of inferences, employing multivalent logic’s usual rules for conjunction and disjunction to form a belief function that reflects the belief and the disbelief in the element and also the uncommitted belief reflecting uncertainty. The factfinder in step #2 should aggregate, by weighted arithmetic averaging, the belief functions resulting from all the items of evidence that bear on any one element, creating a composite belief function for the element. The factfinder in step #3 does not need to combine elements, but instead should directly move to testing whether the degree of belief from each element’s composite belief function sufficiently exceeds the corresponding degree of disbelief. In sum, the factfinder should construct a chain of inferences to produce a belief function for each item of evidence bearing on an element, and then average them to produce for each element a composite belief function ready for the element-by-element standard of proof. This Article performs the task of mapping normatively how to reason from legal evidence to a decision on facts. More significantly, it constitutes a further demonstration of how embedded the multivalent-belief model is in our law

A holistic approach to the examination and analysis of evidence in Anglo-American judicial processes

This thesis is divided into three parts. Part I provides a critique of the dominant approach to the analysis and examination of evidence in Anglo-American writings. The critique consists in showing that the dominant approach, on account of its atomism, does not capture the complexity of judicial fact-finding tasks or codify intuitive judgments about them. Recent attempts offering either mathematical or inductivist structures for the analysis of judicial evidence are explained and criticized as a resurgence of interest in atomistic analysis. Part III identifies a non-atomistic body of thought outside the mainstream of the dominant tradition. This body of thought is used as the starting-point for developing a holistic approach to the examination and analysis of evidence in Anglo-American judicial processes

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

Dual processes in mathematics: reasoning about conditionals

This thesis studies the reasoning behaviour of successful mathematicians. It is based on the philosophy that, if the goal of an advanced education in mathematics is to develop talented mathematicians, it is important to have a thorough understanding of their reasoning behaviour. In particular, one needs to know the processes which mathematicians use to accomplish mathematical tasks. However, Rav (1999) has noted that there is currently no adequate theory of the role that logic plays in informal mathematical reasoning. The goal of this thesis is to begin to answer this specific criticism of the literature by developing a model of how conditional “if…then” statements are evaluated by successful mathematics students. Two stages of empirical work are reported. In the first the various theories of reasoning are empirically evaluated to see how they account for mathematicians’ responses to the Wason Selection Task, an apparently straightforward logic problem (Wason, 1968). Mathematics undergraduates are shown to have a different range of responses to the task than the general well-educated population. This finding is followed up by an eve-tracker inspection time experiment which measured which parts of the task participants attended to. It is argued that Evans’s (1984, 1989, 1996, 2006) heuristic-analytic theory provides the best account of these data. In the second stage of empirical work an in-depth qualitative interview study is reported. Mathematics research students were asked to evaluate and prove (or disprove) a series of conjectures in a realistic mathematical context. It is argued that preconscious heuristics play an important role in determining where participants allocate their attention whilst working with mathematical conditionals. Participants’ arguments are modelled using Toulmin’s (1958) argumentation scheme, and it is suggested that to accurately account for their reasoning it is necessary to use Toulmin’s full scheme, contrary to the practice of earlier researchers. The importance of recognising that arguments may sometimes only reduce uncertainty in the conditional statement’s truth/falsity, rather than remove uncertainty, is emphasised. In the final section of the thesis, these two stages are brought together. A model is developed which attempts to account for how mathematicians evaluate conditional statements. The model proposes that when encountering a mathematical conditional “if P then Q”, the mathematician hypothetically adds P to their stock of knowledge and looks for a warrant with which to conclude Q. The level of belief that the reasoner has in the conditional statement is given by a modal qualifier which they are prepared to pair with their warrant. It is argued that this level of belief is fixed by conducting a modified version of the so-called Ramsey Test (Evans & Over, 2004). Finally the differences between the proposed model and both formal logic and everyday reasoning are discussed

Mathematical Explanation and Ontology: An Analysis of Applied Mathematics and Mathematical Proofs

The present work aims at providing an account of mathematical explanation in two different areas: scientific explanation and within mathematics. The research is addressed from two different perspectives: the one arising from an ontological concern about mathematical entities, and the other originating from a methodological choice: to study our chosen problems (mathematical explanation in science and in mathematics itself) in mathematical practice, that is to say, looking at the way mathematicians understand and perform their work in these diverse areas, including a case study for the context of intra-mathematical explanation. The central target is the analysis of the role that mathematical explanation plays in science and its relevance to the success or failure of scientific theories. The ontological question of whether the explanatory role of abstract objects, mathematical objects in particular, is enough to postulate their existence will be one of the issues to be addressed. Moreover, the possibility of a unified theory of explanation which can accommodate both external and internal mathematical explanation will also be considered. In order to go deeper into these issues, the research includes: (1) an analysis how the question of what is involved in internal mathematical explanation has been addressed in the literature, an analysis of the role of mathematical proof and the reasons why it makes sense to search for more explanatory proofs of already known results, and (2) an analysis of the relation between the use of mathematics in scientific explanation and the ontological commitment that arises from these explanatory tools in science. Part of the present work consists of an analysis of the explanatory role of mathematics through the study of cases reflecting this role. Case studies is one of the main sources of data in order to clarify the role mathematical entities play, among other methodological resources