CAISL: Simplification Logic for Conditional Attribute Implications

In this work, we present a sound and complete axiomatic system for conditional attribute implications (CAIs) in Triadic Concept Analysis (TCA). Our approach is strongly based on the Simplification paradigm which offers a more suitable way for automated reasoning than the one based on Armstrong’s Axioms. We also present an automated method to prove the derivability of a CAI from a set of CAI s.

On the existence of right adjoints for surjective mappings between fuzzy structures0

En este trabajo los autores continúan su estudio de la caracterización de la existencia de adjunciones (conexiones de Galois isótonas) cuyo codominio no está dotado de estructura en principio. En este artículo se considera el caso difuso en el que se tiene un orden difuso R definido en un conjunto A y una aplicación sobreyectiva f:A-> B compatible respecto de dos relaciones de similaridad definidas en el dominio A y en el condominio B, respectivamente. Concretamente, el problema es encontrar un orden difuso S en B y una aplicación g:B-> A compatible también con las correspondientes similaridades definidas en A y en B, de tal forma que el par (f,g) constituya un adjunción.

Nature of the spin-glass phase in dense packings of Ising dipoles with random anisotropy axes

By Monte Carlo simulations, we study the character of the spinglass (SG) phase in dense disordered packings of magnetic nanoparticles (NPs). We focus on NPs which have large uniaxial anisotropies and can be well represented as Ising dipoles. Dipoles are placed on SC lattices and point along randomly oriented axes. From the behaviour of a SG correlation length we determine the transition temperature Tc between the paramagnetic and a SG phase. For temperatures well below Tc we find distributions of the SG overlap parameter q that are strongly sample-dependent and exhibit several spikes. We find that the average width of spikes, and the fraction of samples with spikes higher than a certain threshold does not vary appreciably with the system sizes studied. We compare these results with the ones found previously for 3D site-diluted systems of parallel Ising dipoles and with the behaviour of the Sherrington-Kirkpatrick model.