Neutrality and Many-Valued Logics

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dc.creatorSchumann, Andrew
dc.creatorSmarandache, Florentin
dc.date2007-07-21
dc.date.accessioned2026-07-07T08:19:36Z
dc.date.available2026-07-07T08:19:36Z
dc.descriptionIn this book, we consider various many-valued logics: standard, linear, hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We survey also results which show the tree different proof-theoretic frameworks for many-valued logics, e.g. frameworks of the following deductive calculi: Hilbert's style, sequent, and hypersequent. We present a general way that allows to construct systematically analytic calculi for a large family of non-Archimedean many-valued logics: hyperrational-valued, hyperreal-valued, and p-adic valued logics characterized by a special format of semantics with an appropriate rejection of Archimedes' axiom. These logics are built as different extensions of standard many-valued logics (namely, Lukasiewicz's, Goedel's, Product, and Post's logics). The informal sense of Archimedes' axiom is that anything can be measured by a ruler. Also logical multiple-validity without Archimedes' axiom consists in that the set of truth values is infinite and it is not well-founded and well-ordered. On the base of non-Archimedean valued logics, we construct non-Archimedean valued interval neutrosophic logic INL by which we can describe neutrality phenomena.
dc.description119 pages
dc.identifierhttps://arxiv.org/abs/0707.3205
dc.identifierhttp://arxiv.org/abs/0707.3205
dc.identifierA. Schumann, F. Smarandache, Neutrality and Many-Valued Logics. American Research Press, 2007
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/134815
dc.subjectLogic in Computer Science
dc.subjectArtificial Intelligence
dc.subjectF.4.1; I.2.3; I.2.4
dc.titleNeutrality and Many-Valued Logics
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