This paper outlines the Chinese research on mathematical logic and foundations of mathematics. Firstly, it presents introduction spread in China, especially teaching translation initiated by Bertrand Russell’s lectures country. Secondly, after founding People’s Republic China. The this period experienced a short revival under criticism Soviet Union, explorations heavy influence Cultural Revolut...

Kleene’s well-known strong three-valued logic is shown to be one of a family of logics with similar mathematical properties. These logics are produced by an intuitively natural construction. The resulting logics have direct relationships with bilattices. In addition they possess mathematical features that lend themselves well to semantical constructions based on fixpoint procedures, as in logic...

We discuss how concepts and methods introduced in mathematical logic can be used to support the engineering and deployment of life science ontologies. The required applications of mathematical logic are not straighforward and we argue that such ontologies provide a new and rich family of logical theories that wait to be explored by logicians.

This is a set of lecture notes used in a course on model theory at Virginia Commonwealth University (Math 591 Topics: Logic and Mathematical Structures), which I taught jointly with Sean Cox in the spring of 2014. Most of the material contained in these notes can be found in the following sources. References: • Chang and Keisler. Model Theory, Studies in Logic and the Foundations of Mathematics...

Cut-elimination, introduced by Gentzen, plays an important role in automating the analysis of mathematical proofs. The removal of cuts corresponds to the elimination of intermediate statements (lemmas), resulting in an analytic proof. CERes is a method of cut-elimination by resolution that relies on global proof transformations, in contrast to reductive methods, which use local proof-rewriting ...