214,817 research outputs found

    Assertion: a function first account

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    This paper aims to develop a novel account of the normativity of assertion. Its core thesis is that assertion has an etiological epistemic function, viz. to generate knowledge in hearers. In conjunction with a general account of etiological functions and their normative import, it is argued that an assertion is epistemically good if and only if it has the disposition to generate knowledge in hearers. In addition, reason is provided to believe that it makes sense to regulate the practice of assertion by a speaker rule—and, more specifically, by a knowledge rule—as so regulating assertion contributes to ensuring that assertion fulfils its etiological function reliably

    The *-composition -A Novel Generating Method of Fuzzy Implications: An Algebraic Study

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    Fuzzy implications are one of the two most important fuzzy logic connectives, the other being t-norms. They are a generalisation of the classical implication from two-valued logic to the multivalued setting. A binary operation I on [0; 1] is called a fuzzy implication if (i) I is decreasing in the first variable, (ii) I is increasing in the second variable, (iii) I(0; 0) = I(1; 1) = 1 and I(1; 0) = 0. The set of all fuzzy implications defined on [0; 1] is denoted by I. Fuzzy implications have many applications in fields like fuzzy control, approximate reasoning, decision making, multivalued logic, fuzzy image processing, etc. Their applicational value necessitates new ways of generating fuzzy implications that are fit for a specific task. The generating methods of fuzzy implications can be broadly categorised as in the following: (M1): From binary functions on [0; 1], typically other fuzzy logic connectives, viz., (S;N)-, R-, QL- implications, (M2): From unary functions on [0,1], typically monotonic functions, for instance, Yager’s f-, g- implications, or from fuzzy negations, (M3): From existing fuzzy implications

    On renormalizability of the massless Thirring model

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    We discuss the renormalizability of the massless Thirring model in terms of the causal fermion Green functions and correlation functions of left-right fermion densities. We obtain the most general expressions for the causal two-point Green function and correlation function of left-right fermion densities with dynamical dimensions of fermion fields, parameterised by two parameters. The region of variation of these parameters is constrained by the positive definiteness of the norms of the wave functions of the states related to components of the fermion vector current. We show that the dynamical dimensions of fermion fields calculated for causal Green functions and correlation functions of left-right fermion densities can be made equal. This implies the renormalizability of the massless Thirring model in the sense that the ultra-violet cut-off dependence, appearing in the causal fermion Green functions and correlation functions of left-right fermion densities, can be removed by renormalization of the wave function of the massless Thirring fermion fields only.Comment: 17 pages, Latex, the contribution of fermions with opposite chirality is added,the parameterisation of fermion determinant by two parameters is confirmed,it is shown that dynamical dimensions of fermion fields calculated from different correlation functions can be made equal.This allows to remove the dependence on the ultra-violet cut-off by the renormalization of the wave function of Thirring fermion fields onl

    Bochner integrals in ordered vector spaces

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    We present a natural way to cover an Archimedean directed ordered vector space EE by Banach spaces and extend the notion of Bochner integrability to functions with values in EE. The resulting set of integrable functions is an Archimedean directed ordered vector space and the integral is an order preserving map

    Group C*-algebras as compact quantum metric spaces

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    Let \ell be a length function on a group GG, and let MM_{\ell} denote the operator of pointwise multiplication by \ell on \bell^2(G). Following Connes, MM_{\ell} can be used as a ``Dirac'' operator for Cr(G)C_r^*(G). It defines a Lipschitz seminorm on Cr(G)C_r^*(G), which defines a metric on the state space of Cr(G)C_r^*(G). We investigate whether the topology from this metric coincides with the weak-* topology (our definition of a ``compact quantum metric space''). We give an affirmative answer for G=ZdG = {\mathbb Z}^d when \ell is a word-length, or the restriction to Zd{\mathbb Z}^d of a norm on Rd{\mathbb R}^d. This works for Cr(G)C_r^*(G) twisted by a 2-cocycle, and thus for non-commutative tori. Our approach involves Connes' cosphere algebra, and an interesting compactification of metric spaces which is closely related to geodesic rays.Comment: 53 pages, yet more minor improvements. To appear in Doc. Mat
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