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|  Title:Univalent Foundations and the Constructive View of Theories Authors:Andrei Rodin Conference:HoTT/UF18 Tags:Axiomatic Method, Constructive View of Theories, Semantic View of Theories and Univalent Foundations Abstract: Univalent Foundation (UF) has been recently proposed as a novel foundation of mathematics. We explore a possibility of using UF beyond the pure mathematics as a general formal semantic framework for representing scientific theories. This project is parallel to the project of formal semantic representation of theories by means of Bourbaki-style set-theoretic foundations of mathematics and Tarski-style Model theory, which has been started by Suppes back in 1950-ies and is presently known under the name of “semantic view of theories” . We argue that UF as a prospective representational tool for science and technology has important advantages since it allows for a uniform mathematical representation of various extra-logical methods, which are abound in these fields. This leads us to a new view of theories that at the absence of a better name we call constructive. According to this view a scientific theory is essentially characterised by its methods including the methods of verification and justification of its theoretical statements. Univalent Foundations and the Constructive View of Theories  Univalent Foundations and the Constructive View of Theories | ||||
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