Hierarchical Uncertainty Metatheory Based Upon Modal Logic

Resconi, Germano; Klir, George J.; Clair, Ute St.

doi:10.1080/03081079208945051

Cited by 75 publications

(31 citation statements)

References 9 publications

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“…Resconi, Klir and Clair [1992], , and Harmanec, proposed a unifying framework for the study of various uncertainty theories. The present investigation is closely related to their work.…”

Section: Resultsmentioning

confidence: 99%

“…Using this normalized measure f , one can analyzing the correspondence between non-numeric axioms (A1)-(A9) and their numeric counterparts, and classify non-numeric functions in the same manner that numeric measures are classified. It is interesting to note that Resconi, Klir and Clair [1992], used a similar numeric function in their study of various types of numeric measures.…”

Section: Non-numeric Representation Of Un-certaintymentioning

confidence: 99%

“…Based on modal logic, Resconi, Klir and Clair [1992], , and Harmanec, Klir and Resconi [1993] established a unifying framework within which various uncertainty theories can be formalized, compared and organized hierarchically.…”

Section: Introductionmentioning

confidence: 99%

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A Non-Numeric Approach to Uncertain Reasoning

Yao

Wong

Wang

1995

International Journal of General Systems

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This paper presents a non-numeric approach to uncertain reasoning by extending the incidence calculus. In parallel to the well known fuzzy, belief/plausibility, probability, and necessity/possibility measures, the corresponding classes of non-numeric functions are examined. A method of constructing non-numeric functions is discussed using the notion of compatibility relations. Non-numeric functions are used to interpret uncertain reasoning by providing possible-worlds semantics for both qualitative and quantitative methods.INDEX TERMS: Belief/plausibility, fuzzy measure, incidence calculus, interval structure, necessity/possibility, probability, non-numeric functions, rough sets, uncertain reasoning.

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“…Resconi, Klir and Clair [1992], , and Harmanec, proposed a unifying framework for the study of various uncertainty theories. The present investigation is closely related to their work.…”

Section: Resultsmentioning

confidence: 99%

Section: Non-numeric Representation Of Un-certaintymentioning

confidence: 99%

See 1 more Smart Citation

A Non-Numeric Approach to Uncertain Reasoning

Yao

Wong

Wang

1995

International Journal of General Systems

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“…The dynamic logic of action aspect of truth is about the feasibility and temporal sequencing of our behavior and physical actions. Zadeh, Dubois, Prade and others have the merit to have connected the possibility and necessity modal logic with fuzzy logic in the possibility theory [4] but only later were fuzzy semantic models for fuzzy modal logic created to fundament the modal logic approach to fuzzy logic [5]- [7].…”

Section: The Fractal Modal Logic Of Kabbalah As a Structural Framewormentioning

confidence: 99%

“…For a start, truth values are more than just numbers and Goguen's L-fuzzy set theory [3] addressed that by proposing a general lattice L instead of [0.1]. Zadeh's, Dubois and Prade's and others Possibility Theory [4] and the modal logic approach to fuzzy semantics in [5]- [7] speak for acknowledging this need for the meaning of truth. Modal logic was developed to better capture the many facets of truth and its application to build a hierarchical meta-theory of fuzzy sets is a promising path that needs to be continued.…”

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confidence: 99%

Kabbalah Logic and Semantic Foundations for a Postmodern Fuzzy Set and Fuzzy Logic Theory

Burstein¹,

Negoiţă²,

Kranz³

2014

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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.

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