Mathematical foundations of Representing Knowledge

1. Mathematical foundations of Representing Knowledge Investigators: Robert H. Sloan, Computer Science, Gy. Turan, Mathematics Prime Grant Support: National Science Foundation (grant # CCF-0431059) • All “intelligent systems” (artificial intelligence–AI) rely on large quantities of knowledge. • Knowledge representation is an old area of study in AI that saw great progress in last dozen years or so • Similarly (machine) learning is old area of AI that is absolutely critical for building modern systems, and that has had great progress in last dozen or so years. • BUT little study of interaction between them; little recent study of foundations of knowledge representation • Precisely determine expressiveness of basic representation formalisms (e.g., decision trees, Disjunctive Normal Forms) • Complexity theory and combinatorics are the key mathematical tools • Develop algorithms for learning important representations that have no learning algorithms, such as modal logic • Recent new results on k-Disjunctive Normal Forms • “3 SAT” sentence solvers have been one of the great areas of progress recently, but Horn sentences are widely used in AI applications. Currently working on detailed analysis of properties of Horn sentence (figure in opposite corner). • Also completing study of the revision of Horn sentences–it’s easiest to learn when you have a “pretty good” starting point