Commonsense temporal reasoning is full of situations that require drawing default conclusions, since we rarely have all the information available. Unfortunately, most modal temporal logics cannot accommodate default reasoning, since they typically deal with a monotonic inference relation. On the other hand, non-monotonic approaches are very expensive and their treatment of time is not so well delimited and studied as in modal logic.

Temporal Equilibrium Logic [Cabalar and Pérez, 2007] (TEL) is the first non-monotonic temporal logic which fully covers the syntax of some standard modal temporal approach without requiring further constructions. TEL shares the syntax of Linear-time Temporal Logic (LTL) (first proposed by Arthur Prior and later extended by Hans Kamp) which has become one of the simplest, most used and best known temporal logics in Theoretical Computer Science.

The development of TEL and its application to real problems has been the core of my PhD and Postoctoral work. In this talk I will go through several results and applications of TEL in which I participated during my career as a researcher.