Title:Probabilistically Quantitative Logic and its Applications

Speaker: Prof. Hongjun Zhou, College of Mathematics and Information Science, Shaanxi Normal University, China

Date: October 13, 2016

Time:10:00 am-11:00 am

Location: Room B1032, Tenth Floor, Zhixin Building, Central Campus

Abstract: In this talk we provide a brief introduction to Probabilistically Quantitative Logic from four viewpoints of its research approaches and applications. The outline of this talk is as follows:

1. Semantic quantification

1.1 Probabilistic truth degrees of propositions

1.2 Axiomatic definition of probabilistic truth degree function and its representation

1.3 Choquet type truth degree of propositions

1. Modal formalization

In this section we review a modal-like logic system for reasoning about truth degrees of propositions, through abstracting as a modality P the probabilistic truth degree function in n-valued Lukasiewicz propositional logic, and as axioms of modal formulas some basic identities of truth degree functions, which provides a logic foundation for semantic quantification.

1. Algebraic axiomatization

The state theory is closely related to the theory of probabilistic truth degree of propositions, and it shows that there is a one-to-one correspondence between state operators on the Lukasiewicz Lindenbaum algebra and the probabilistic truth degree functions in Lukasiewicz propositional logic. In short words, the former is a generalized and axiomatized version of the latter, while the latter is a semantic analyzed version. In general, they are different from each other. In this section we review the theory of generalized states which has the most general framework.

1. Applications and extensions

4.1 Consistency degrees of logic theories

4.2 Three methods of graded reasoning

4.3 Characterizations of maximally consistent theories

4.4 Three-valued Stone representations in R0-algebras

4.5 Similarity Cauchy completion of residuated lattices w.r.t. order-preserving type I states

Bio:Hongjun Zhou is now a professor at College of Mathematics and Information Science of Shaanxi Normal University (SNNU for short), China. He received his bachelor’s degree in Mathematics and Applied Mathematics and Ph.D degree in Pure Mathematics under the supervision of Prof. Guojun Wang both from SNNU in July of 2003 and in June of 2009, respectively. After graduation, he found a teaching and research position at SNNU. He was exceptionally promoted to an associative professor in December of 2010 and normally promoted to a professor in December of 2015. He was a postdoctoral researcher under the direction of Prof. Constantine Tsinakis at Vanderbilt University sponsored by China Scholarship Council from August 28, 2013 to August 30, 2014.

His research interests include Non-classical Logics, Quantitative Logic, Ordered Algebra and Logic, and Fuzzy Aggregation Operators. His main contributions are that he established the whole framework of Probabilistically Quantitative Logic from four aspects of semantic quantification, modal formalization, algebraic axiomatization and applications. He has published two treatises at Science Press, Beijing, and more than 30 academic papers. He is now chairing his third National Science Foundation grant, and the previous two and one more Doctoral Research Program from the Ministry of Education of China were already finished. His dissertation was recommended in 2012 as an Excellent Doctoral Dissertation of Shaanxi province and he was selected in 2015 as a Youth Science and Technology Star of Shaanxi province. He serves now as a reviewer for Mathematical Reviews, a member of the Fundamental Division of Chinese Association for Artificial Intelligence, and a member of Division of Many-valued Logic and Fuzzy Logic of China Computer Federation.