BL – Knowledge and References

Computational Neuroscience and Compartmental Modeling

Published in Bahman Zohuri, Patrick J. McDaniel, Electrical Brain Stimulation for the Treatment of Neurological Disorders, 2019

Bahman Zohuri, Patrick J. McDaniel

Historically, the concept of fuzzy logic was introduced by deceased professor Lotfi A. Zadeh at the University of California at Berkley, where it was introduced not as a control methodology, but as a way of processing data partially rather than crisp set or membership or non-membership. In other words, Fuzzy Logic works around the logic of “Partially False or Partially True” concept in contrast to a Boolean Logic (BL) that works based on either “Absolute False or True” approach.

Axiomatization of non-associative generalisations of Hájek's BL and psBL

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Journal Information

Published in Journal of Applied Non-Classical Logics, 2020

Yaroslav Petrukhin

BL is built over a propositional language which contains a set of propositional variables, left and right parentheses, falsehood constant ⊥, conjunction &, and implication . A set of all -formulas is defined in a standard way. Besides, An evaluation of propositional variables by elements of a BL-algebra is defined in a standard way. An evaluation e of all -formulas is defined as follows: A formula A is an -tautology iff , for each evaluation e in . A formula A is a BL-tautology iff it is -tautology, for each BL-algebra .

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Computational Neuroscience and Compartmental Modeling

Axiomatization of non-associative generalisations of Hájek's BL and psBL