My Work

My field of research is Logic, specifically Modal Logic. I am interested in what we call ``non classical'' modal logics, i.e. modal logic different from the standard Diamonds and Boxes. In the last years, an important number of these new systems have seen the light: Arrow Logics, Propositional Dynamic Logic, Since/Until Logics, the Universal Modality, the Difference Operator, Hybrid Logics, Interpretability Logics, etc.

At the momment, I am studing the issue of how to define modal operators to capture different subset of First Order Logic and how these new modalities behave. For example, in which cases do we have a "nice" model theory? When can we obtain characterizations via bisimulations? How does all these relate to complexity issues?

We will pay attention specially to two important topics:

• Expressive Power, and
• Interpolation.

Suppose we want to design a new language to tackle a particular problem at hand. The first requisite is that the language should provide the needed expressive power to describe all the issues related to the problem. The second requisite is that it should be ``well behaved'' (i.e., decidable and with good metalogical properties). From a syntactic point of view, the interpolation property is considered a sign of a well defined proof system.

In this engineering approach to modal logic, we look for general results on expressive power and interpolation. How do they interact? How does expressive power determine presence or absence of interpolation? And if interpolation fails, can we obtain hints on how to strengthen expressiveness to recover it?

As you can see, at the momment I have many, many more questions than answers.

If you are interested, you can download a slightly more detailed description of my research topic.