664 research outputs found

    First-order Goedel logics

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    First-order Goedel logics are a family of infinite-valued logics where the sets of truth values V are closed subsets of [0, 1] containing both 0 and 1. Different such sets V in general determine different Goedel logics G_V (sets of those formulas which evaluate to 1 in every interpretation into V). It is shown that G_V is axiomatizable iff V is finite, V is uncountable with 0 isolated in V, or every neighborhood of 0 in V is uncountable. Complete axiomatizations for each of these cases are given. The r.e. prenex, negation-free, and existential fragments of all first-order Goedel logics are also characterized.Comment: 37 page

    n-Valued Refined Neutrosophic Logic and Its Applications to Physics

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    In this paper we present a short history of logics: from particular cases of 2-symbol or numerical valued logic to the general case of n-symbol or numerical valued logic. We show generalizations of 2-valued Boolean logic to fuzzy logic, also from the Kleene and Lukasiewicz 3-symbol valued logics or Belnap 4-symbol valued logic to the most general n-symbol or numerical valued refined neutrosophic logic. Two classes of neutrosophic norm (n-norm) and neutrosophic conorm (n-conorm) are defined. Examples of applications of neutrosophic logic to physics are listed in the last section. Similar generalizations can be done for n-Valued Refined Neutrosophic Set, and respectively n- Valued Refined Neutrosopjhic Probability.Comment: 9 page

    Robust Linear Temporal Logic

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    Although it is widely accepted that every system should be robust, in the sense that "small" violations of environment assumptions should lead to "small" violations of system guarantees, it is less clear how to make this intuitive notion of robustness mathematically precise. In this paper, we address this problem by developing a robust version of Linear Temporal Logic (LTL), which we call robust LTL and denote by rLTL. Formulas in rLTL are syntactically identical to LTL formulas but are endowed with a many-valued semantics that encodes robustness. In particular, the semantics of the rLTL formula φ⇒ψ\varphi \Rightarrow \psi is such that a "small" violation of the environment assumption φ\varphi is guaranteed to only produce a "small" violation of the system guarantee ψ\psi. In addition to introducing rLTL, we study the verification and synthesis problems for this logic: similarly to LTL, we show that both problems are decidable, that the verification problem can be solved in time exponential in the number of subformulas of the rLTL formula at hand, and that the synthesis problem can be solved in doubly exponential time

    Interval Neutrosophic Sets and Logic: Theory and Applications in Computing

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    A neutrosophic set is a part of neutrosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. The neutrosophic set is a powerful general formal framework that has been recently proposed. However, the neutrosophic set needs to be specified from a technical point of view. Here, we define the set-theoretic operators on an instance of a neutrosophic set, and call it an Interval Neutrosophic Set (INS). We prove various properties of INS, which are connected to operations and relations over INS. We also introduce a new logic system based on interval neutrosophic sets. We study the interval neutrosophic propositional calculus and interval neutrosophic predicate calculus. We also create a neutrosophic logic inference system based on interval neutrosophic logic. Under the framework of the interval neutrosophic set, we propose a data model based on the special case of the interval neutrosophic sets called Neutrosophic Data Model. This data model is the extension of fuzzy data model and paraconsistent data model. We generalize the set-theoretic operators and relation-theoretic operators of fuzzy relations and paraconsistent relations to neutrosophic relations. We propose the generalized SQL query constructs and tuple-relational calculus for Neutrosophic Data Model. We also design an architecture of Semantic Web Services agent based on the interval neutrosophic logic and do the simulation study
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