Finite Algebras and AI: From Matrix Semantics to Stochastic Local Search

Universal algebra has underpinned the modern research in formal logic since Garrett Birkoff’s pioneering work in the 1930’s and 1940’s. Since the early 1970’s, the entanglement of logic and algebra has been successfully exploited in many areas of computer science from the theory of computation to Artificial Intelligence (AI). The scientific outcome of the interplay between logic and universal algebra in computer science is rich and vast (cf. [2]). In this presentation I shall discuss some applications of universal algebra in AI with an emphasis on Knowledge Representation and Reasoning (KRR). A brief survey, such as this, of possible ways in which the universal algebra theory could be employed in research on KRR systems, has to be necessarily incomplete. It is primarily for this reason that I shall concentrate almost exclusively on propositional KRR systems. But there are other reasons too. The outburst of research activities on stochastic local search for propositional satisfiability that followed the seminal paper A New Method for Solving Hard Satisfiability Problems by Selman, Levesque, and Mitchel (cf. [11]), provides some evidence that propositional techniques could be surprisingly effective in finding solutions to ‘realistic’ instances of hard problems.