Extending the mathematics in Qualitative Process theory

Reasoning about physical systems requites the integration of a range of knowledge and reasoning techniques. P. Hayes has named the enterprise of identifying and formalizing the common-sense knowledge people use for th.is task "naive physics." Qualitative Process theory by K. Forbus proposes a structure and some of the content of naive theories about dynamics, (i.e., the way things change in a physical situation). Any physical theory, however, rests on an underlying mathematics. QP theory assumes a qualitative mathematics which captures only simple topological relationships between values of contin­uous parameters. While the results are impressive, this mathematics is unable to support the full range of deduction needed for a complete naive physics reasoner. A more complete naive mathematics must be capable of represent­ing measure information about parameter values as well as shape and strength characterizations of the partial derivatives relating these values. This article proposes a naive mathematics meeting these requirements, and shows that it considerably expands the scope and power of deductions which QP theory can perform

Towards an integrated discovery system

Previous research on machine discovery has focused on limited parts of the empirical discovery task. In this paper we describe IDS, an integrated system that addresses both qualitative and quantitative discovery. The program represents its knowledge in terms of qualitative schemas, which it discovers by interacting with a simulated physical environment. Once IDS has formulated a qualitative schema, it uses that schema to design experiments and to constrain the search for quantitative laws. We have carried out preliminary tests in the domain of heat phenomena. In this context the system has discovered both intrinsic properties, such as the melting point of substances, and numeric laws, such as the conservation of mass for objects going through a phase change

Goal → New Heuristic Model of Ideality: Logos → Coincidentia Oppositorum → Primordial Generating Structure

Fundamental knowledge endures deep conceptual crisis manifested in total crisis of understanding, crisis of interpretation and representation, loss of certainty, troubles with physics, crisis of methodology. Crisis of understanding in fundamental science generates deep crisis of understanding in global society. What way should we choose for overcoming total crisis of understanding in fundamental science? It should be the way of metaphysical construction of new comprehensive model of ideality on the basis of the "modified ontology". Result of quarter-century wanderings: sum of ideas, concepts and eidoses, new understanding of space, time, consciousness

Striving against invalidity in qualitative research: Discussing a reflective framework

The aim of this paper is to discuss a reflective validation framework related with the study of teaching approaches, teaching styles or teaching orientations of university academics. In the recent years, and particularly since the eighties, there have been a growing number of investigations linking teaching conceptions with teaching practices. The majority of investigations dealing with university teachers’ conceptions and practices draw their conclusions based on indirect observation, since data gathering involves mainly semi-structured interviews or the application of questionnaires and inventories. Therefore ‘only-half-the-story’ has been reported. The presented validation framework has a five-part three-stage structure and was built upon earlier work (Selvaruby, O’Sullivan, & Watts, 2007). In this model validity is conceptualized as an ‘iterative-interactive-process’, therefore integrating a set of specific strategies envisaging the maximization of scientific quality. The application of the model is illustrated by using it for the discussion of a longitudinal study involving the investigation of the relationship between questioning practices and Trigwell and co-workers’ concept of preferential teaching approaches (Trigwell, Prosser & Taylor, 1994). Field work of this naturalistic-interpretative research was conducted during two academic years (2009/2010 and 2010/2011) and implied close collaboration with a group of four university teachers lecturing biology to undergraduates.This work was financed by Fundação para a Ciência e a Tecnologia (SFRH/BD/44611/2008) and by Fundos FEDER através do Programa Operacional Fatores de Competitividade – COMPETE e por Fundos Nacionais através da FCT (PTDC/CPE-CED/117516/2010)

Robust Computer Algebra, Theorem Proving, and Oracle AI

In the context of superintelligent AI systems, the term "oracle" has two meanings. One refers to modular systems queried for domain-specific tasks. Another usage, referring to a class of systems which may be useful for addressing the value alignment and AI control problems, is a superintelligent AI system that only answers questions. The aim of this manuscript is to survey contemporary research problems related to oracles which align with long-term research goals of AI safety. We examine existing question answering systems and argue that their high degree of architectural heterogeneity makes them poor candidates for rigorous analysis as oracles. On the other hand, we identify computer algebra systems (CASs) as being primitive examples of domain-specific oracles for mathematics and argue that efforts to integrate computer algebra systems with theorem provers, systems which have largely been developed independent of one another, provide a concrete set of problems related to the notion of provable safety that has emerged in the AI safety community. We review approaches to interfacing CASs with theorem provers, describe well-defined architectural deficiencies that have been identified with CASs, and suggest possible lines of research and practical software projects for scientists interested in AI safety.Comment: 15 pages, 3 figure

Crisis of Fundamentality → Physics, Forward → Into Metaphysics → The Ontological Basis of Knowledge: Framework, Carcass, Foundation

The present crisis of foundations in Fundamental Science is manifested as a comprehensive conceptual crisis, crisis of understanding, crisis of interpretation and representation, crisis of methodology, loss of certainty. Fundamental Science "rested" on the understanding of matter, space, nature of the "laws of nature", fundamental constants, number, time, information, consciousness. The question "What is fundametal?" pushes the mind to other questions → Is Fundamental Science fundamental? → What is the most fundamental in the Universum?.. Physics, do not be afraid of Metaphysics! Levels of fundamentality. The problem №1 of Fundamental Science is the ontological justification (basification) of mathematics. To understand is to "grasp" Structure ("La Structure mère"). Key ontological ideas for emerging from the crisis of understanding: total unification of matter across all levels of the Universum, one ontological superaxiom, one ontological superprinciple. The ontological construction method of the knowledge basis (framework, carcass, foundation). The triune (absolute, ontological) space of eternal generation of new structures and meanings. Super concept of the scientific world picture of the Information era - Ontological (structural, cosmic) memory as "soul of matter", measure of the Universum being as the holistic generating process. The result of the ontological construction of the knowledge basis: primordial (absolute) generating structure is the most fundamental in the Universum

Poincaré on the Foundation of Geometry in the Understanding

This paper is about Poincaré’s view of the foundations of geometry. According to the established view, which has been inherited from the logical positivists, Poincaré, like Hilbert, held that axioms in geometry are schemata that provide implicit definitions of geometric terms, a view he expresses by stating that the axioms of geometry are “definitions in disguise.” I argue that this view does not accord well with Poincaré’s core commitment in the philosophy of geometry: the view that geometry is the study of groups of operations. In place of the established view I offer a revised view, according to which Poincaré held that axioms in geometry are in fact assertions about invariants of groups. Groups, as forms of the understanding, are prior in conception to the objects of geometry and afford the proper definition of those objects, according to Poincaré. Poincaré’s view therefore contrasts sharply with Kant’s foundation of geometry in a unique form of sensibility. According to my interpretation, axioms are not definitions in disguise because they themselves implicitly define their terms, but rather because they disguise the definitions which imply them

The Formula of Justice: The OntoTopological Basis of Physica and Mathematica*

Dialectica: Mathematica and Physica, Truth and Justice, Trick and Life. Mathematica as the Constructive Metaphysica and Ontology. Mathematica as the constructive existential method. Сonsciousness and Mathematica: Dialectica of "eidos" and "logos". Mathematica is the Total Dialectica. The basic maternal Structure - "La Structure mère". Mathematica and Physica: loss of existential certainty. Is effectiveness of Mathematica "unreasonable"? The ontological structure of space. Axiomatization of the ontological basis of knowledge: one axiom, one principle and one mathematical object. The main ideas and concepts of the ontological construction/ "Point with a vector germ" and "heavenly triangle". "Ordo geometricus" and "Ordo onto-topological". Architecture of the onto-topological basis of knowledge: general framework structure, carcass and foundation. The absolute space and the absolute field. The absolute (natural) system of coordinates of Universum. Eidos of "idea of ideas", the symbol and the "formula of Justice"