422 research outputs found
Lukasiewicz logic and Riesz spaces
We initiate a deep study of {\em Riesz MV-algebras} which are MV-algebras
endowed with a scalar multiplication with scalars from . Extending
Mundici's equivalence between MV-algebras and -groups, we prove that
Riesz MV-algebras are categorically equivalent with unit intervals in Riesz
spaces with strong unit. Moreover, the subclass of norm-complete Riesz
MV-algebras is equivalent with the class of commutative unital C-algebras.
The propositional calculus that has Riesz MV-algebras as
models is a conservative extension of \L ukasiewicz -valued
propositional calculus and it is complete with respect to evaluations in the
standard model . We prove a normal form theorem for this logic,
extending McNaughton theorem for \L ukasiewicz logic. We define the notions of
quasi-linear combination and quasi-linear span for formulas in and we relate them with the analogue of de Finetti's coherence
criterion for .Comment: To appear in Soft Computin
Layers of zero probability and stable coherence over Łukasiewicz events
The notion of stable coherence has been recently introduced to characterize coherent assignments to conditional many-valued events by means of hyperreal-valued states. In a nutshell, an assignment, or book, β on a finite set of conditional events is stably coherent if there exists a coherent variant β of β such that β maps all antecedents of conditional events to a strictly positive hyperreal number, and such that β and β differ by an infinitesimal. In this paper, we provide a characterization of stable coherence in terms of layers of zero probability for books on Łukasiewicz logic events. © 2016, Springer-Verlag Berlin Heidelberg.The authors would like to thank there referee for the valuable comments that considerably improved the presentation of this paper. Flaminio has been funded by the Italian project FIRB 2010 (RBFR10DGUA_002). Godo has been also funded by the MINECO/FEDER Project TIN2015-71799-C2-1-P.Peer Reviewe
Betting on Quantum Objects
Dutch book arguments have been applied to beliefs about the outcomes of
measurements of quantum systems, but not to beliefs about quantum objects prior
to measurement. In this paper, we prove a quantum version of the probabilists'
Dutch book theorem that applies to both sorts of beliefs: roughly, if ideal
beliefs are given by vector states, all and only Born-rule probabilities avoid
Dutch books. This theorem and associated results have implications for
operational and realist interpretations of the logic of a Hilbert lattice. In
the latter case, we show that the defenders of the eigenstate-value orthodoxy
face a trilemma. Those who favor vague properties avoid the trilemma, admitting
all and only those beliefs about quantum objects that avoid Dutch books.Comment: 26 pages, 3 figures, 1 table; improved operational semantics, results
unchange
Английский язык
Практическое пособие предназначено для студентов 2 курса филологического факультета. Пособие составлено в соответствии с программой по данному курсу и включает в себя тексты для чтения и упражнения к ним. Упражнения содержат задания, направленные на развитие навыков различных видов чтения, понимания и перевода, навыков монологической и диалогической речи
Geometrical aspects of possibility measures on finite domain MV-clans
In this paper, we study generalized possibility and necessity measures on MV-algebras of [0, 1]-valued functions (MV-clans) in the framework of idempotent mathematics, where the usual field of reals ℝ is replaced by the max-plus semiring ℝ max We prove results about extendability of partial assessments to possibility and necessity measures, and characterize the geometrical properties of the space of homogeneous possibility measures. The aim of the present paper is also to support the idea that idempotent mathematics is the natural framework to develop the theory of possibility and necessity measures, in the same way classical mathematics serves as a natural setting for probability theory. © 2012 Springer-Verlag.The authors would like to thank the anonymous referees for their relevant suggestions and helpful remarks They also acknowledge partial support from the Spanish projects TASSAT (TIN2010- 20967-C04-01), Agreement Technologies (CONSOLIDER CSD2007-0022, INGENIO 2010) and ARINF (TIN2009-14704-C03-03), as well as the ESF Eurocores-Log ICCC/MICINN project (FFI2008-03126-E/FILO). Flaminio and Marchioni acknowledge partial support from the Juan de la Cierva Program of the Spanish MICINN.Peer Reviewe
Paraconsistent probabilities: consistency, contradictions and bayes' theorem
2010/51038-0sem informaçãoThis paper represents the first steps towards constructing a paraconsistent theory of probability based on the Logics of Formal Inconsistency (LFIs). We show that LFIs encode very naturally an extension of the notion of probability able to express sophisticated probabilistic reasoning under contradictions employing appropriate notions of conditional probability and paraconsistent updating, via a version of Bayes' theorem for conditionalization. We argue that the dissimilarity between the notions of inconsistency and contradiction, one of the pillars of LFIs, plays a central role in our extended notion of probability. Some critical historical and conceptual points about probability theory are also reviewed.This paper represents the first steps towards constructing a paraconsistent theory of probability based on the logics of formal inconsistency (LFIs). We show that LFIs encode very naturally an extension of the notion of probability able to express sophisticated probabilistic reasoning under contradictions employing appropriate notions of conditional probability and paraconsistent updating, via a version of Bayes' theorem for conditionalization. We argue that the dissimilarity between the notions of inconsistency and contradiction, one of the pillars of LFIs, plays a central role in our extended notion of probability. Some critical historical and conceptual points about probability theory are also reviewed.189FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTIFICO E TECNOLOGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTIFICO E TECNOLOGICO2010/51038-0sem informaçã
Coherence in the aggregate: a betting method for belief functions on many-valued events
Betting methods, of which de Finetti's Dutch Book is by far the most well-known, are uncertainty modelling devices which accomplish a twofold aim. Whilst providing an (operational) interpretation of the relevant measure of uncertainty, they also provide a formal definition of coherence. The main purpose of this paper is to put forward a betting method for belief functions on MV-algebras of many-valued events which allows us to isolate the corresponding coherence criterion, which we term coherence in the aggregate. Our framework generalises the classical Dutch Book method
State morphism MV-algebras
We present a complete characterization of subdirectly irreducible MV-algebras
with internal states (SMV-algebras). This allows us to classify subdirectly
irreducible state morphism MV-algebras (SMMV-algebras) and describe single
generators of the variety of SMMV-algebras, and show that we have a continuum
of varieties of SMMV-algebras
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