509 research outputs found
An introduction to DSmT
The management and combination of uncertain, imprecise, fuzzy and even
paradoxical or high conflicting sources of information has always been, and
still remains today, of primal importance for the development of reliable
modern information systems involving artificial reasoning. In this
introduction, we present a survey of our recent theory of plausible and
paradoxical reasoning, known as Dezert-Smarandache Theory (DSmT), developed for
dealing with imprecise, uncertain and conflicting sources of information. We
focus our presentation on the foundations of DSmT and on its most important
rules of combination, rather than on browsing specific applications of DSmT
available in literature. Several simple examples are given throughout this
presentation to show the efficiency and the generality of this new approach
Activating Generalized Fuzzy Implications from Galois Connections
This paper deals with the relation between fuzzy implications and Galois connections, trying to raise the awareness that the fuzzy implications are indispensable to generalise Formal Concept Analysis. The concrete goal of the paper is to make evident that Galois connections, which are at the heart of some of the generalizations of Formal Concept Analysis, can be interpreted as fuzzy incidents. Thus knowledge processing, discovery, exploration and visualization as well as data mining are new research areas for fuzzy implications as they are areas where Formal Concept Analysis has a niche.F.J. Valverde-Albacete—was partially supported by EU FP7 project LiMoSINe, (contract 288024). C. Peláez-Moreno—was partially supported by the Spanish Government-CICYT project 2011-268007/TEC.Publicad
Faculty of Sciences
A comprehensive study of fuzzy rough sets and their application in data reductio
Compatible Quantum Theory
Formulations of quantum mechanics can be characterized as realistic,
operationalist, or a combination of the two. In this paper a realistic theory
is defined as describing a closed system entirely by means of entities and
concepts pertaining to the system. An operationalist theory, on the other hand,
requires in addition entities external to the system. A realistic formulation
comprises an ontology, the set of (mathematical) entities that describe the
system, and assertions, the set of correct statements (predictions) the theory
makes about the objects in the ontology. Classical mechanics is the prime
example of a realistic physical theory. The present realistic formulation of
the histories approach originally introduced by Griffiths, which we call
'Compatible Quantum Theory (CQT)', consists of a 'microscopic' part (MIQM),
which applies to a closed quantum system of any size, and a 'macroscopic' part
(MAQM), which requires the participation of a large (ideally, an infinite)
system. The first (MIQM) can be fully formulated based solely on the assumption
of a Hilbert space ontology and the noncontextuality of probability values,
relying in an essential way on Gleason's theorem and on an application to
dynamics due in large part to Nistico. The microscopic theory does not,
however, possess a unique corpus of assertions, but rather a multiplicity of
contextual truths ('c-truths'), each one associated with a different framework.
This circumstance leads us to consider the microscopic theory to be physically
indeterminate and therefore incomplete, though logically coherent. The
completion of the theory requires a macroscopic mechanism for selecting a
physical framework, which is part of the macroscopic theory (MAQM). Detailed
definitions and proofs are presented in the appendice
Inadequacy of Modal Logic in Quantum Settings
We test the principles of classical modal logic in fully quantum settings.
Modal logic models our reasoning in multi-agent problems, and allows us to
solve puzzles like the muddy children paradox. The Frauchiger-Renner thought
experiment highlighted fundamental problems in applying classical reasoning
when quantum agents are involved; we take it as a guiding example to test the
axioms of classical modal logic. In doing so, we find a problem in the original
formulation of the Frauchiger-Renner theorem: a missing assumption about
unitarity of evolution is necessary to derive a contradiction and prove the
theorem. Adding this assumption clarifies how different interpretations of
quantum theory fit in, i.e., which properties they violate. Finally, we show
how most of the axioms of classical modal logic break down in quantum settings,
and attempt to generalize them. Namely, we introduce constructions of trust and
context, which highlight the importance of an exact structure of trust
relations between agents. We propose a challenge to the community: to find
conditions for the validity of trust relations, strong enough to exorcise the
paradox and weak enough to still recover classical logic.Comment: In Proceedings QPL 2018, arXiv:1901.0947
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