AUC Logic Lectures: Logic, the Art of Walking at Interfaces
Our walk starts with quantifier expressions like "all", "some" which underlie both ordinary language and the mathematical language of science. We look at the history of logical systems for quantifiers, flagging some issues that very much alive today, such as the interplay of formal and natural languages, fast practical quantifier inference versus slow conscious deductive proof, compositionality and recursion, and interfaces with probability. These topics show logic as a design lab, but also as a cross-roads where many academic disciplines meet and interact.
Prof. Dr. Johan van Benthem is a University Professor emeritus of pure and applied logic, University of Amsterdam; Henry Waldgrave Stuart Professor of philosophy, Stanford University (philosophy and CSLI); Changjiang Professor, Chinese Ministry of Education, Tsinghua University, Beijing; Co-director, UvA-Tsinghua joint research center in logic. He was awarded the Spinozapremie in 1996 and elected a Foreign Fellow of the American Academy of Arts & Sciences in 2015. Van Benthem is known for his research in the area of modal logic. He has also been active in the fields of philosophy of science, logical structures in natural language (generalised quantifiers, categorial grammar, substructural proof theory), dynamic logic and update logic, and applications of logic to game theory as well as applications of game theory to logic (game semantics).