273 research outputs found
A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, NEUTROSOPHIC SET, NEUTROSOPHIC PROBABILITY AND STATISTICS
In 1960s Abraham Robinson has developed the non-standard analysis, a formalization of analysis and a branch of mathematical logic, which rigorously defines the infinitesimals
A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, NEUTROSOPHIC SET, NEUTROSOPHIC PROBABILITY AND STATISTICS - 6th ed.
It was a surprise for me when in 1995 I received a manuscript from the mathematician, experimental writer and innovative painter Florentin Smarandache, especially because the treated subject was of philosophy - revealing paradoxes - and logics. He had generalized the fuzzy logic, and introduced two new concepts: a) âneutrosophyâ â study of neutralities as an extension of dialectics; b) and its derivative âneutrosophicâ, such as âneutrosophic logicâ, âneutrosophic setâ, âneutrosophic probabilityâ, and âneutrosophic statisticsâ and thus opening new ways of research in four fields: philosophy, logics, set theory, and probability/statistics. It was known to me his setting up in 1980âs of a new literary and artistic avant-garde movement that he called âparadoxismâ, because I received some books and papers dealing with it in order to review them for the German journal âZentralblatt fur Mathematikâ. It was an inspired connection he made between literature/arts and science, philosophy. We started a long correspondence with questions and answers. Because paradoxism supposes multiple value sentences and procedures in creation, antisense and non-sense, paradoxes and contradictions, and itâs tight with neutrosophic logic, I would like to make a small presentation
A Unifying Field in Logics: Neutrosophic Logic.
The author makes an introduction to non-standard analysis, then extends the dialectics to Âneutrosophy  which became a new branch of philosophy. This new concept helps in generalizing the intuitionistic, paraconsistent, dialetheism, fuzzy logic to Âneutrosophic logic  which is the first logic that comprises paradoxes and distinguishes between relative and absolute truth. Similarly, the fuzzy set is generalized to Âneutrosophic setÂ. Also, the classical and imprecise probabilities are generalized to Âneutrosophic probabilityÂ
Negation and Dichotomy
The present contribution might be regarded as a kind of defense of the common sense in logic. It is demonstrated that if the classical negation is interpreted as the minimal negation with n = 2 truth values, then deviant logics can be conceived as extension of the classical bivalent frame. Such classical apprehension of negation is possible in non- classical logics as well, if truth value is internalized and bivalence is replaced by bipartition
Stone-type representations and dualities for varieties of bisemilattices
In this article we will focus our attention on the variety of distributive
bisemilattices and some linguistic expansions thereof: bounded, De Morgan, and
involutive bisemilattices. After extending Balbes' representation theorem to
bounded, De Morgan, and involutive bisemilattices, we make use of Hartonas-Dunn
duality and introduce the categories of 2spaces and 2spaces. The
categories of 2spaces and 2spaces will play with respect to the
categories of distributive bisemilattices and De Morgan bisemilattices,
respectively, a role analogous to the category of Stone spaces with respect to
the category of Boolean algebras. Actually, the aim of this work is to show
that these categories are, in fact, dually equivalent
The Combination of Paradoxical, Uncertain, and Imprecise Sources of Information based on DSmT and Neutro-Fuzzy Inference
The management and combination of uncertain, imprecise, fuzzy and even
paradoxical or high conflicting sources of information has always been, and
still remains today, of primal importance for the development of reliable
modern information systems involving artificial reasoning. In this chapter, we
present a survey of our recent theory of plausible and paradoxical reasoning,
known as Dezert-Smarandache Theory (DSmT) in the literature, developed for
dealing with imprecise, uncertain and paradoxical sources of information. We
focus our presentation here rather on the foundations of DSmT, and on the two
important new rules of combination, than on browsing specific applications of
DSmT available in literature. Several simple examples are given throughout the
presentation to show the efficiency and the generality of this new approach.
The last part of this chapter concerns the presentation of the neutrosophic
logic, the neutro-fuzzy inference and its connection with DSmT. Fuzzy logic and
neutrosophic logic are useful tools in decision making after fusioning the
information using the DSm hybrid rule of combination of masses.Comment: 20 page
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