214,817 research outputs found
Assertion: a function first account
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
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
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
We present a natural way to cover an Archimedean directed ordered vector
space by Banach spaces and extend the notion of Bochner integrability to
functions with values in . 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
Let be a length function on a group , and let denote the
operator of pointwise multiplication by on \bell^2(G). Following
Connes, can be used as a ``Dirac'' operator for . It
defines a Lipschitz seminorm on , which defines a metric on the state
space of . 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 when
is a word-length, or the restriction to of a norm on
. This works for 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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