Much of modern logic originates in work on the foundations of mathematics. My talk reports on work in logic that has a different goal, the study of inference in language. This study leads to what I will call "natural logic", the enterprise of studying logical inference in languages that look more like natural language than standard logical systems.

By now there is a growing body of work which presents logical systems that differ from first-order logic in various ways. Most of the systems are complete and decidable. Some are modern versions of syllogistic logic, but with additional features. Some are fragments of first-order logic. But there are also flavors of logic which look rather far from either traditional or modern logic. For example, some of the logics are reminiscent of description logics, and there are new typed lambda calculi designed to help with monotonicity reasoning.

The talk will be programmatic and far-ranging rather than detailed. I hope to touch on connections to natural language semantics and processing, computer implementations of natural logics, teaching materials on this topic, and interactions of logic and cognitive science.