I will present a simple(!) categorical framework for Logic Programming that gives a syntax, and semantics for logic programs defined over a category. This framework captures constraints, state-change and the use of different logical extensions.The semantics includes generalized “Herbrand-style” interpretations as well as more operational notions of model. A completeness theorem will be sketched using bottom-up semantics and fixed points. I will give some monad examples as well.

The results presented are from a joint paper with Amato and McGrail, joint work in progress with Ed Morehouse, and from earlier work with Krishnan, Freyd and Finkelstein.

Categorical foundations for logic programming started with work by Burstall, Asperti, Corradini, Montanari, Goguen, Power and others. I will briefly sketch the development of some of the main ideas over the years.