518 research outputs found
Generic substitutions
Up to equivalence, a substitution in propositional logic is an endomorphism
of its free algebra. On the dual space, this results in a continuous function,
and whenever the space carries a natural measure one may ask about the
stochastic properties of the action. In classical logic there is a strong
dichotomy: while over finitely many propositional variables everything is
trivial, the study of the continuous transformations of the Cantor space is the
subject of an extensive literature, and is far from being a completed task. In
many-valued logic this dichotomy disappears: already in the finite-variable
case many interesting phenomena occur, and the present paper aims at displaying
some of these.Comment: 22 pages, 2 figures. Revised version according to the referee's
suggestions. To appear in the J. of Symbolic Logi
An introduction to DSmT
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
introduction, we present a survey of our recent theory of plausible and
paradoxical reasoning, known as Dezert-Smarandache Theory (DSmT), developed for
dealing with imprecise, uncertain and conflicting sources of information. We
focus our presentation on the foundations of DSmT and on its most important
rules of combination, rather than on browsing specific applications of DSmT
available in literature. Several simple examples are given throughout this
presentation to show the efficiency and the generality of this new approach
An introduction to Dezert-Smarandache Theory (DSmT)
The management and combination of uncertain, imprecise, fuzzy and even paradoxical or highly 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 introduction, we present a survey of our recent theory of plausible and paradoxical reasoning, known as Dezert-Smarandache Theory (DSmT), developed for dealing with imprecise, uncertain and conflicting sources of information. We focus our presentation on the foundations of DSmT and on its most important rules of combination, rather than on browsing specific applications of DSmT available in literature. Several simple examples are given throughout this presentation to show the efficiency and the generality of this new theor
Advances and Applications of Dezert-Smarandache Theory (DSmT) for Information Fusion (Collected works), Vol. 2
This second volume dedicated to Dezert-Smarandache Theory (DSmT) in Information Fusion brings in new fusion quantitative rules (such as the PCR1-6, where PCR5 for two sources does the most mathematically exact redistribution of conflicting masses to the non-empty sets in the fusion literature), qualitative fusion rules, and the Belief Conditioning Rule (BCR) which is different from the classical conditioning rule used by the fusion community working with the Mathematical Theory of Evidence.
Other fusion rules are constructed based on T-norm and T-conorm (hence using fuzzy logic and fuzzy set in information fusion), or more general fusion rules based on N-norm and N-conorm (hence using neutrosophic logic and neutrosophic set in information fusion), and an attempt to unify the fusion rules and fusion theories.
The known fusion rules are extended from the power set to the hyper-power set and comparison between rules are made on many examples.
One defines the degree of intersection of two sets, degree of union of two sets, and degree of inclusion of two sets which all help in improving the all existing fusion rules as well as the credibility, plausibility, and communality functions.
The book chapters are written by Frederic Dambreville, Milan Daniel, Jean Dezert, Pascal Djiknavorian, Dominic Grenier, Xinhan Huang, Pavlina Dimitrova Konstantinova, Xinde Li, Arnaud Martin, Christophe Osswald, Andrew Schumann, Tzvetan Atanasov Semerdjiev, Florentin Smarandache, Albena Tchamova, and Min Wang
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