All in Logic
Here's a short movie by Martha Goddard. It features the logician Gödel... one of the most important mathematicians of the 20th century. The title: "Gödel, incomplete." Gödel's most famous results were his "incompleteness" theorems. These theorems demonstrated limits of formal systems. At the same time, Gödel himself, as a person, is incomplete, and defined not only by what he is, but by what he is not... by his empty spaces, his desires. Which include love.
My PhD dissertation showed “why logic works,” gave a pattern for creating new techniques for building models of consequence, and developed ways of comparing the relative power of different modeling techniques. It showed how to understand logic as a tool we use for the construction of knowledge, and how design choices in the construction of the semantic model lead to different properties of the resulting system. A new set of techniques, ones more appropriate for modeling the meaning of object-oriented data, were created and analyzed.
My adviser Jon Barwise was a world-famous logician, a founder of the Center for the Study of Language and Information at Stanford, a professor of Mathematics, Philosophy, and Computer Science, and editor of the Handbook of Mathematical Logic. He wrote: “I think what you have done in your dissertation is quite interesting and makes a real contribution to the program of understanding what we mean by logical consequence.”
An exploration of why logic works and how to create new approaches to logical semantics. It explains Tarski's model-theoretic semantics which were created to model the meaning of sentences. It further defines and describes new approaches to logical semantics which have certain advantages for the modeling the meaning of object-oriented data.
