102 research outputs found
Stable non-standard imprecise probabilities
Stability arises as the consistency criterion in a betting interpretation for hyperreal imprecise previsions, that is imprecise previsions (and probabilities) which may take infinitesimal values. The purpose of this work is to extend the notion of stable coherence introduced in [8] to conditional hyperreal imprecise probabilities. Our investigation extends the de Finetti-Walley operational characterisation of (imprecise) prevision to conditioning on events which are considered "practically impossible" but not "logically impossible"
A representation theorem for MV-algebras
An {\em MV-pair} is a pair where is a Boolean algebra and is
a subgroup of the automorphism group of satisfying certain conditions. Let
be the equivalence relation on naturally associated with . We
prove that for every MV-pair , the effect algebra is an MV-
effect algebra. Moreover, for every MV-effect algebra there is an MV-pair
such that is isomorphic to
Electron-hole asymmetry in two-terminal graphene devices
A theoretical model is proposed to describe asymmetric gate-voltage
dependence of conductance and noise in two-terminal ballistic graphene devices.
The model is analyzed independently within the self-consistent Hartree and
Thomas-Fermi approximations. Our results justify the prominent role of metal
contacts in recent experiments with suspended graphene flakes. The
contact-induced electrostatic potentials in graphene demonstrate a power-law
decay with the exponent varying from -1 to -0.5. Within our model we explain
electron-hole asymmetry and strong Fabri-Perot oscillations of the conductance
and noise at positive doping, which were observed in many experiments with
submicrometer samples. Limitations of the Thomas-Fermi approximation in a
vicinity of the Dirac point are discussed.Comment: 7 pages, 8 figure
Proof Theory and Ordered Groups
Ordering theorems, characterizing when partial orders of a group extend to
total orders, are used to generate hypersequent calculi for varieties of
lattice-ordered groups (l-groups). These calculi are then used to provide new
proofs of theorems arising in the theory of ordered groups. More precisely: an
analytic calculus for abelian l-groups is generated using an ordering theorem
for abelian groups; a calculus is generated for l-groups and new decidability
proofs are obtained for the equational theory of this variety and extending
finite subsets of free groups to right orders; and a calculus for representable
l-groups is generated and a new proof is obtained that free groups are
orderable
Sharp and fuzzy observables on effect algebras
Observables on effect algebras and their fuzzy versions obtained by means of
confidence measures (Markov kernels) are studied. It is shown that, on effect
algebras with the (E)-property, given an observable and a confidence measure,
there exists a fuzzy version of the observable. Ordering of observables
according to their fuzzy properties is introduced, and some minimality
conditions with respect to this ordering are found. Applications of some
results of classical theory of experiments are considered.Comment: 23 page
Semiring and semimodule issues in MV-algebras
In this paper we propose a semiring-theoretic approach to MV-algebras based
on the connection between such algebras and idempotent semirings - such an
approach naturally imposing the introduction and study of a suitable
corresponding class of semimodules, called MV-semimodules.
We present several results addressed toward a semiring theory for
MV-algebras. In particular we show a representation of MV-algebras as a
subsemiring of the endomorphism semiring of a semilattice, the construction of
the Grothendieck group of a semiring and its functorial nature, and the effect
of Mundici categorical equivalence between MV-algebras and lattice-ordered
Abelian groups with a distinguished strong order unit upon the relationship
between MV-semimodules and semimodules over idempotent semifields.Comment: This version contains some corrections to some results at the end of
Section
Hyperstates of Involutive MTL-Algebras that Satisfy
States of MV-algebras have been the object of intensive study and attempts of
generalizations. The aim of this contribution is to provide a preliminary
investigation for states of prelinear semihoops and hyperstates of algebras in
the variety generated by perfect and involutive MTL-algebras (IBP0-algebras for
short). Grounding on a recent result showing that IBP0-algebras can be
constructed from a Boolean algebra, a prelinear semihoop and a suitably defined
operator between them, our first investigation on states of prelinear semihoops
will support and justify the notion of hyperstate for IBP0- algebras and will
actually show that each such map can be represented by a probability measure on
its Boolean skeleton, and a state on a suitably defined abelian l-group.Comment: 12 page
Fuzzy Propositional Logic Associated with Quantum Computational Gates
We apply residuated structures associated with fuzzy logic to develop certain
aspects of information processing in quantum computing from a logical
perspective. For this purpose, we introduce an axiomatic system whose natural
interpretation is the irreversible quantum Poincare structure.Comment: 41 pages, no figure
A modal theorem-preserving translation of a class of three-valued logics of incomplete information
International audienceThere are several three-valued logical systems that form a scattered landscape, even if all reasonable connectives in three-valued logics can be derived from a few of them. Most papers on this subject neglect the issue of the relevance of such logics in relation with the intended meaning of the third truth-value. Here, we focus on the case where the third truth-value means unknown, as suggested by Kleene. Under such an understanding, we show that any truth-qualified formula in a large range of three-valued logics can be translated into KD as a modal formula of depth 1, with modalities in front of literals only, while preserving all tautologies and inference rules of the original three-valued logic. This simple information logic is a two-tiered classical propositional logic with simple semantics in terms of epistemic states understood as subsets of classical interpretations. We study in particular the translations of Kleene, Gödel, ᴌukasiewicz and Nelson logics. We show that Priest’s logic of paradox, closely connected to Kleene’s, can also be translated into our modal setting, simply by exchanging the modalities possible and necessary. Our work enables the precise expressive power of three-valued logics to be laid bare for the purpose of uncertainty management
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