Abstract
We analyze the McCulloch–Pitts seminal 1943 paper on a logical calculus for neural networks from the point of view of contemporary mathematical logic. Originally presented as a fragment of Carnap’s Language II, the cited calculus is regarded in this chapter as a simple propositional temporal language with past tense modalities. We rewrite proofs of main results of the McCulloch–Pitts paper using this language.
This work has been supported by Croatian Science Foundation (HRZZ) under the project IP-01-2018-7459.
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Carnap R (1938) The logical syntax of language. Harcourt, Brace and Company, New York
Kleene S (1956) Representation of events in nerve nets and finite automata. In: Shannon C, McCarthy J (eds) Automata studies. Princeton University Press, pp 3–41
McCulloch WS, Pitts W (1943) A logical calculus of ideas immanent in nervous activity. Bull Math Biophys 5:115–133
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Perkov, T. (2020). The McCulloch–Pitts Paper from the Perspective of Mathematical Logic. In: Skansi, S. (eds) Guide to Deep Learning Basics. Springer, Cham. https://doi.org/10.1007/978-3-030-37591-1_2
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DOI: https://doi.org/10.1007/978-3-030-37591-1_2
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