HYPERSOLVER: A graphical tool for commonsense set theory

jdot, Mü; Pakkan, dat; Akman, Varol

doi:10.1016/0020-0255(94)00114-q

Cited by 5 publications

(3 citation statements)

References 13 publications

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“…Formally, a set of circular (coss-referent and recursive) definitions can be handled rigorously using non-well-founded set theories, see Aczel (1988), Barwise and Etchemendy (1987), and Barwise and Moss (1996). Computationally, circularly defined data sets can be represented, stored and manipulated using appropriate data structures, see Akman and Pakkan (1996), Iordanov (2010), and Pakkan and Akman (1995).…”

Section: Objects Are Tokens For Eigen-solutions: Precision Stabilitymentioning

confidence: 99%

A sharper image: the quest of science and recursive production of objective realities

Stern

2020

Principia

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This article explores the metaphor of Science as provider of sharp images of ourenvironment, using the epistemological framework of Objective Cognitive Constructivism.These sharp images are conveyed by precise scientific hypotheses that, in turn, are encodedby mathematical equations. Furthermore, this article describes how such knowledge is pro-duced by a cyclic and recursive development, perfection and reinforcement process, leadingto the emergence of eigen-solutions characterized by the four essential properties of preci-sion, stability, separability and composability. Finally, this article discusses the role playedby ontology and metaphysics in the scientific production process, and in which sense theresulting knowledge can be considered objective.

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Section: Objects Are Tokens For Eigen-solutions: Precision Stabilitymentioning

confidence: 99%

A sharper image: the quest of science and recursive production of objective realities

Stern

2020

Principia

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“…The variation in these predictions can be explained by a combination of the level of imprecision in the theory and by properties of the end-user's experiment. For instance, the latter source of variation is influenced by properties of the equipment, including the precision, accuracy, and resolution of measuring devices [16,17], and also error bounds for fundamental constants and calibration factors [18][19][20][21][22][23][24][25][26]. We propose to choose a pragmatic hypothesis in such a way that the imprecision in the end-user's predictions is mostly due to his experimental conditions and not due to the level of imprecision in the theory that he uses.…”

Section: Introductionmentioning

confidence: 99%

Pragmatic Hypotheses in the Evolution of Science

Esteves

Izbicki

Stern

et al. 2019

Entropy

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This paper introduces pragmatic hypotheses and relates this concept to the spiral of scientific evolution. Previous works determined a characterization of logically consistent statistical hypothesis tests and showed that the modal operators obtained from this test can be represented in the hexagon of oppositions. However, despite the importance of precise hypothesis in science, they cannot be accepted by logically consistent tests. Here, we show that this dilemma can be overcome by the use of pragmatic versions of precise hypotheses. These pragmatic versions allow a level of imprecision in the hypothesis that is small relative to other experimental conditions. The introduction of pragmatic hypotheses allows the evolution of scientific theories based on statistical hypothesis testing to be interpreted using the narratological structure of hexagonal spirals, as defined by Pierre Gallais.

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“…This technique of solving equations in the universe of hypersets can be useful in modeling information which can be cast in the form of equations (Akman and Pakkan, 1993), e.g., situation theory (Barwise and Perry, 1983), databases, etc. since it allows us to assert the existence of some graphs (the solutions of the equations) without having to depict them with graphs.…”

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confidence: 99%