Formal Analogical Reasoning in Concrete Mathematical Research

Danny A. J. Gómez Ramírez
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Danny A. J. Gómez Ramírez: Instituto Tecnológico Metropolitano (ITM), Research’s Labs Center Parque i

Chapter Chapter 8 in Artificial Mathematical Intelligence, 2020, pp 133-146 from Springer

Abstract: Abstract A cognitively-based natural framework for analogical reasoning in propositional and first-order logic is presented. Specifically, notions like “atomic 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 former notion(s) is described for predicate logic. Finally, it is shown through concrete examples how these new notions can help to naturally meta-model the way in which our mind solves formal proofs starting with elementary, but not entirely trivial, theorems in a classic Hilbert’s style (propositional) calculus.

Date: 2020
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DOI: 10.1007/978-3-030-50273-7_8

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