TITLE:
Kabbalah Logic and Semantic Foundations for a Postmodern Fuzzy Set and Fuzzy Logic Theory
AUTHORS:
Gabriel Burstein, Constantin Virgil Negoita, Menachem Kranz
KEYWORDS:
L-Fuzzy Sets, Fuzzy Sets, Fuzzy Logic, Modal Logic, Fuzzy Semantics, Kripke Possible Worlds Model, Kabbalah, Sefirot, Partzufim, Tree of Life, Tikkun, Postmodernism, Deconstruction, Logic, Humanistic Systems
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.9,
May
22,
2014
ABSTRACT: Despite half a
century of fuzzy sets and fuzzy logic progress, as fuzzy sets address complex
and uncertain information through the lens of human knowledge and subjectivity,
more progress is needed in the semantics of fuzzy sets and in exploring the
multi-modal aspect of fuzzy logic due to the different cognitive, emotional and
behavioral angles of assessing truth. We lay here the foundations of a
postmodern fuzzy set and fuzzy logic theory addressing these issues by deconstructing
fuzzy truth values and fuzzy set membership functions to re-capture the human
knowledge and subjectivity structure in membership function evaluations. We
formulate a fractal multi-modal logic of Kabbalah which integrates the
cognitive, emotional and behavioral levels of humanistic systems into epistemic
and modal, deontic and doxastic and dynamic multi-modal logic. This is done by
creating a fractal multi-modal Kabbalah possible worlds semantic frame of Kripke
model type. The Kabbalah possible worlds semantic frame integrates together
both the multi-modal logic aspects and their Kripke possible worlds model. We
will not focus here on modal operators and axiom sets. We constructively define
a fractal multi-modal Kabbalistic L-fuzzy set as the central concept of the
postmodern fuzzy set theory based on Kabbalah logic and semantics.