1,721,190 research outputs found
On The Spectrum of Countable MV-algebras
Full text linkIn this paper we consider MV-algebras and their prime spectrum. We show that there is an uncountable MV-algebra that has the same spectrum as the free MV-algebra over one element, that is, the MV-algebra of McNaughton functions from to , the continuous, piecewise linear functions with integer coefficients. The construction is heavily based on Mundici equivalence between MV-algebras and lattice ordered abelian groups with the strong unit. Also, we heavily use the fact that two MV-algebras have the same spectrum if and only if their lattice of principal ideals is isomorphic.As an intermediate step we consider the MV-algebra of continuous, piecewise linear functions with rational coefficients. It is known that contains , and that and are equispectral. However, is in some sense easy to work with than . Now, is still countable. To build an equispectral uncountable MV-algebra , we consider certain ``almost rational'' functions on , which are rational in every initial segment of , but which can have an irrational limit in .We exploit heavily, via Mundici equivalence, the properties of divisible lattice ordered abelian groups, which have an additional structure of vector spaces over the rational field
On modal mu-calculus over finite graphs with bounded strongly connected components.
No full textThere is a problem with corollaries 6.2 and 7.2. Their proofs
rely on the wrong assumption that the parity automata defined here
and the standard parity alternating automata coincide level by level.
So, the proofs of corollaries 6.2 and 7.2 are wrong and we do not know
whether the statements are true. The summary of the paper has to be
changed accordingly as follows.
Summary: For every positive integer k we consider the class SCCk of
all finite graphs whose strongly connected components have size at most
k. We show that for every k, the Modal mu-Calculus fixpoint hierarchy
on SCCk collapses to the level Delta_2; moreover, we introduce a
kind of automata analogous to Janin-Walukiewicz disjunctive formulas,
and we show that the mu-calculus in SCC1 does not collapse to weak
automata (as they are defined here)
On modal mu-calculus in S5 and application
No full textWe show that the vectorial mu-calculus model checking prob-
lem over arbitrary graphs reduces to the vectorial, existential -calculus model checking problem over S5 graphs.We also draw some consequencesof this fact. Moreover, we give a proof that satisability of -calculus in S5 is NP-complete, and by using S5 graphs we give a new proof that the
satisability problem of the existential mu-calculus is also NP-complete
Introducing Predicates into a Basic Theory for the Foundations of Mathematics
No full textPreprints di Matematica della
Scuola Normale Superior
ENTROPY OF MV-ALGEBRAIC DYNAMICAL SYSTEMS: AN EXAMPLE
No full textWe give examples showing that the Kolmogorov-Sinai entropy generator theorem is false for both upper and lower Riesz entropy of MV-Algebraic dynamical systems, both two sided (i.e., analogous to two sided Bernoulli shifts) and one sided (i.e., analogous to one sided Bernoulli shifts
The spectrum problem for Abelian l-groups and MV-algebras
No full textAbstract. This paper deals with the problem of characterizing those topological spaces which are homeomorphic to the prime spectra of MValgebras or Abelian l-groups. As a first main result, we show that a topological space X is the prime spectrum of an MV-algebra if and only if X is spectral, and the lattice K(X) of compact open subsets of X is a closed epimorphic image of the lattice of “cylinder rational polyhedra” (a natural generalization of rational polyhedra) of [0, 1]Y for some set Y . As a second main result we extend our results to Abelian -groups. That is, a topological space X is the prime spectrum of an Abelian l-group if and only if X is generalized spectral, and the lattice K(X) is a closed epimorphic image of the lattice of "cylinder rational cones" (a generalization of rational cones) in RY for some set Y . Finally, we axiomatize, in monadic second order logic, the Belluce lattices of free MV-algebras (equivalently, the lattice of cylinder rational polyhedra) of dimension 1, 2 and infinite, and we study the problem of describing Belluce lattices in certain fragments of second order logic
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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