411 research outputs found
Ecumenical modal logic
The discussion about how to put together Gentzen's systems for classical and
intuitionistic logic in a single unified system is back in fashion. Indeed,
recently Prawitz and others have been discussing the so called Ecumenical
Systems, where connectives from these logics can co-exist in peace. In Prawitz'
system, the classical logician and the intuitionistic logician would share the
universal quantifier, conjunction, negation, and the constant for the absurd,
but they would each have their own existential quantifier, disjunction, and
implication, with different meanings. Prawitz' main idea is that these
different meanings are given by a semantical framework that can be accepted by
both parties. In a recent work, Ecumenical sequent calculi and a nested system
were presented, and some very interesting proof theoretical properties of the
systems were established. In this work we extend Prawitz' Ecumenical idea to
alethic K-modalities
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
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
Multivalued Logic, Neutrosophy and Schrodinger equation
This book was intended to discuss some paradoxes in Quantum Mechanics from the viewpoint of Multi-Valued-logic pioneered by Lukasiewicz, and a recent concept Neutrosophic Logic. Essentially, this new concept offers new insights on the idea of âidentityâ, which too often it has been accepted as given. Neutrosophy itself was developed in attempt to generalize Fuzzy-Logic introduced by L. Zadeh. While some aspects of theoretical foundations of logic are discussed, this book is not intended solely for pure mathematicians, but instead for physicists in the hope that some of ideas presented herein will be found useful. The book is motivated by observation that despite almost eight decades, there is indication that some of those paradoxes known in Quantum Physics are not yet solved. In our knowledge, this is because the solution of those paradoxes requires re-examination of the foundations of logic itself, in particular on the notion of identity and multi-valuedness of entity.
The book is also intended for young physicist fellows who think that somewhere there should be a âcompleteâ explanation of these paradoxes in Quantum Mechanics. If this book doesnât answer all of their questions, it is our hope that at least it offers a new alternative viewpoint for these old questions
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