Critical theories of varieties of semigroups satisfying a permutation identity.
In [6] da Costa has introduced a new hierarchy , of logics that are both paraconsistent and paracomplete. Such logics are now known as non-alethic logics. In this article we present an algebraic version of the logics and study some of their properties.
The resemblance relation is used to reflect some real life situations for which a fuzzy equivalence is not suitable. We study the properties of cuts for such relations. In the case of a resemblance on a real line we show that it determines a special family of crisp functions closely connected to its cut relations. Conversely, we present conditions which should be satisfied by a collection of real functions in in order that this collection determines a resemblance relation.
We give a new proof of the fact that finite bipartite graphs cannot be axiomatized by finitely many first-order sentences among finite graphs. (This fact is a consequence of a general theorem proved by L. Ham and M. Jackson, and the counterpart of this fact for all bipartite graphs in the class of all graphs is a well-known consequence of the compactness theorem.) Also, to exemplify that our method is applicable in various fields of mathematics, we prove that neither finite simple groups, nor the...
Proponiamo in questa Nota un quadro assiomatico aperto e non riduzionista, che si basa sulle idee primitive di qualità e relazione, in cui speriamo sia possibile innestare i concetti fondamentali della Matematica, della Logica e dell’Informatica (di cui diamo solo alcuni primissimi esempi). Auspichiamo che sviluppando liberamente tale quadro sia possibile giungere ad un fruttuoso confronto critico delle idee fondamentali delle diverse discipline scientifiche ed umanistiche, non ristretto agli «specialisti...