У среду 11.09.2019. у сали 401 Машинског факултета са почетком у 11 часова
Центар за примењену математику Машинског факултета у Нишу, CAM –FMEN
У оквиру серије
Примењене конструктивне и класичне семигрупе CAM-FMEN: ACaCS
Workshop “Substructural Logics and their algebraic models“
Department of Information engineering and mathematics, University of Siena, Italija
11-11:50 PART I
12:10- 13 PART II
Abstract. The aim of these lectures is to get a glimpse at Substructural Logics, their motivations and the way they can be investigated and understood through their natural algebraic models. The study of Substructural Logics is a relatively young field; one of the first conference on the topic was held in October 1990 in Tubingen, as “Logics with Restricted Structural Rules”. During the conference Kosta Došen proposed the term substructural logics, which is now in use today. Any system that it is worth calling a logic must have some form of entailment, which is usually represented by a binary connective →, called the implication. Among all the possible rules that implication can satisfy the following are know as the structural rules
x→ (y→x) (weakening)
(x→ (x→y)) → (x→y) (contraction)
Any logic lacking at least one of these rules for implication is called substructural; for simplicity’s sake we will deal only with logics lacking the contraction rule.
In Part I of this lecture, we will introduce the main concepts and we will explain haw it make sense to consider a rich enough logic as the logic of a variety of algebras; this variety, called, the equivalent algebraic semantics of the logic plays a very important role in understanding the behavior of the logic and the properties of the implication. The link between a logic and its equivalent algebraic semantics can be used to transfer algebraic concepts into logic and viceversa.
In Part II we will concentrate more on a particular class of substructural logics, i.e. the Fuzzy Logics in their various incarnations (Many-Valued Logic, Basic Logic and so on). In particular we will show how it makes sense to construct a logic from a (possibly infinite) set of truth values and how this constructions allow us to deal woth vague concepts in a mathematically rigorous way. The algebraic models of these logic are particularly interesting, since they belong to the huge and widely investigated family of partially ordered residuated monoids.
др Меланија Митровић, ред. проф.