Rensselaer Department of Cognitive Science

Research

Much of my research is fundamental and pre-experimental, pushing fundamental concepts and ideas. With my research I always keeps an eye on education: many projects are designed to provide thought-provoking and educational material that complements and adds to my courses. I also design my research projects so that motivated and interested undergraduate students can join at any time and gain some valuable experience in undergraduate research. I encourage students interested in joining my research groups to contact me directly.

Existential Graphs -	Existential Graphs is a graphical system of logic developed by the American philosopher Charles S. Peirce about 100 years ago. Peirce hoped that the visual nature of Existential Graphs would be more transparent and user-friendly. In order to investigate this claim, I am developing interfaces for the use of Existential Graphs. I am also investigating the use of Existential Graphs for Automated Theorem Proving.
Busy Beaver -	The Busy Beaver function was formulated and shown to be Turing-uncomputable by Tibor Rado in 1962. However, for low values of n, BB(n) can be found. To find these values poses an interesting engineering challenge, but I am mostly interested in the fundamental philosophical questions this search raises regarding the nature of computation and demonstration.
Grid Logic -	I am working on developing logics for various related 'grid logic puzzles' such as Battleship, Tree Tent, and the currently wildly popular Sudoku. These logics will become 'modules' that can be inserted into a general grid logic inference engine that allows the user to solve puzzles of these various types, while indicating their reasoning. I plan to eventually use this engine in my Introduction to Logic course, in the hopes that it will be a bit more interesting than working with P's and Q's.