Lecture by Prof. P. Johnstone

Prof. P. Johnstone will give a lecture on Friday 23 at 11:00 in Sala del Consiglio, at the Department of Mathematics and Computer Science. “Toposes as higher-order theories” Abstract. The elementary reformulation of topos theory by Lawvere and Tierney allowed scope for the interpretation not only of first-order but also of higher-order logic; in particular, it allows one to construct a topos which is the “embodiment” of an arbitrary higher-order theory.Of particular interest is the Read more

Semiring and semimodule issues in MV-algebras

by A. Di Nola, C. Russo In this paper we propose a new perspective on the theory of MV-algebras based on the connection between such algebras and idempotent semirings. Such a viewpoint yields, among other results, interesting representation theorems. We also present some results of more general interest, such as a matrix-based characterization of finitely generated projective semimodules over any semiring and, consequently, the functorial character of the construction of the Grothendieck group of a Read more

Quantale modules and their operators, with applications

by C. Russo Journal of Logic and Computation (2010), 20(4): 917-946.Advance access December 2008.doi:10.1093/logcom/exn088 The central topic of this work is the categories of modules over unital quantales. The main categorical properties are established and a special class of operators, called Q-module transforms, is defined. Such operators – that turn out to be precisely the homomorphisms between free objects in those categories – find concrete applications in two different branches of image processing, namely fuzzy Read more

A fuzzified BRAIN algorithm for learning DNF from incomplete data

by S. Rampone, C. Russo Aim of this paper is to address the problem of learning Boolean functions from training data with missing values. We present an extension of the BRAIN algorithm, called U-BRAIN (Uncertainty-managing Batch Relevance-based Artificial INtelligence), conceived for learning DNF Boolean formulas from partial truth tables, possibly with uncertain values or missing bits. Such an algorithm is obtained from BRAIN by introducing fuzzy sets in order to manage uncertainty. In the case Read more

PhD Course by Prof. Tsinakis at the DMI

On March 15, 16 and 17, at 11:00 in “aula del consiglio” DMI, Prof. C. Tsinakis (Vanderbilt University, U.S) wil give the folowing PhD course “Residuated Structures: Algebraic and Logical Perspectives” Contents of the course:Algebraic logic studies classes of algebras that are related to logical systems, as well as the process by which a class of algebras becomes the “algebraic counterpart (semantics)” of a logical system. A field practitioner usually approaches the solution of a Read more