数学研究所
中科院管理、决策和信息系统重点实验室
学术报告会
报告人:Prof. Antonio Di Nola (Department of Mathematics, University of Salerno, Italy)
题 目:Infinitary Riesz Logic: a logical approach to Functional Analysis
时 间:2017.10.07(星期六),09:30-10:30
地 点:数学院南楼N205室
摘要:
Rieszz Spaces have had a predominant position in the development of functional analysis over ordered structures. They have a widespread of applications related to lattice-ordered vec- tor spaces (vector lattices) and complete normed vector lattices (Banach lattices). Not very known is the role that vector lattices play in logic. Given any positive element u of a riesz Space the interva l[0, u] can be endowed with a stucture of Riesz MV-algebra. These structures have been defined in the setting of Lukasiewicz logic, as expansion of MValgebras the standard semantics of the infinite valued Lukasiewicz logic. It is proved that Riesz MV-algebras are categorical equivalent to Riesz Spaces with a strong unit. Henceforth, vector lattices and logic are closely related. Many results from the theory of Riesz Spaces have facilitated the growth of Lukasiewicz logic and MV-algebras and we will show how Lukasiewicz logic could be an important tool in functional analysis, via Riesz MV-algebras.
简历:
Antonio Di Nola is Full Professor of Mathematical Logic and Director of the Department of Mathematics of the University of Salerno. Since the nineties he has been a leading proponent of the study of algebraic models of Lukasiewicz logic (MV-algebras), the most important among the many-valued logics. His contribution to the study of MV-algebras, witnessed by the seventeen citations of his works in the fundamental monograph "Algebraic foundations of many-valued reasoning", includes: a functional representation theorem for all MV-algebras (aka Di Nola's Representation Theorem); the discovery of categorical equivalences between categories of MV-algebras and categories of groups, rings, and semi-rings, profitably used in the literature of MV-algebras, the discovery of an equational axiomatisation of all varieties of MV-algebras, and a normal form theorem for Lukasiewicz logic. Today is actively committed to apply ideas from algebraic geometry in the MV-algebra and in the study of probability which admit infinitesimal values. He is author/coauthor of more than 150 scientific works, published on international journals of logic, algebra and computer science.
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