Titlebook: Artificial Mathematical Intelligence; Cognitive, (Meta)mat Danny A. J. Gómez Ramírez Book 2020 Springer Nature Switzerland AG 2020 foundati

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https://doi.org/10.1057/9781403981431al scenarios. Thus, the ontological reality of mathematics is supported, at least partially, in the physical realm. On the other hand, we claim that mathematics plays an existential structural role within the whole (meta-)physical reality, which is supported by the meta-cosmological fact that one of

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Conclusion: A Continuing Dilemma, features and intuitions of this ancient numerical system are classified into physically supported parts and meta-physical (or mental) ones. A new numerical system consisting of . is proposed which has an initial and a final element, and is essentially grounded in the physical realm. Semantic founda

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Conclusion: A Continuing Dilemma,ermelo–Fraenkel set theory with Choice. Effectively, we will construct a first-order logic theory D-ZFC (dual theory of ZFC) strictly based on (a particular sub-collection of) proper classes with a corresponding special membership relation, such that ZFC and D-ZFC are meta-isomorphic frameworks (tog

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https://doi.org/10.1007/978-1-349-16779-1reation/invention. Explicitly, a specific version of a well-known formalization of conceptual blending is given in terms of colimits of many-sorted first-order theories. With these formalisms, new nine meta-theorems are proved, describing how to generate recursively fundamental concepts of Fields an

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https://doi.org/10.1007/978-1-349-19114-7 analogy,” “analogical space,” (syntactic) “depth,” and “index” of propositions (and subsequently of formulas) are described. Moreover, the notion of “best analogy” between two propositions is introduced as the atomic analogy with maximal depth and minimal index. Furthermore, a generalization of the

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https://doi.org/10.1057/9780230245204lly, formalizations of each of them are described in a conceptual setting broad enough to include virtually any classic mathematical sub-discipline which possesses a sufficiently “robust” logic. All of this is grounded in general formalizations of the notions of mathematical concept and mathematical

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Prologue: No Silk-Blouse Social Worker, program, specific cognitive meta-generations (or pseudo-pre-code) of dozens of (mathematical) concepts and proofs are presented. In particular, two classic proofs in elementary geometry and number theory are meta-generated. Moreover, around 30 fundamental notions are constructed belonging to severa

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The Culture of Working-Class Girls,ve formal refinements of fundamental ((meta-)mathematical) notions like set, proof, and exemplification, as well as the systematic (cognitive) meta-analysis of hundreds of domain-specific proofs in the most relevant mathematical sub-disciplines. This is aimed to be done along the lines of the global