** Matteo Mio **

*PhD, CNRS Researcher*

** PhD: ** I'm looking for PhD students at the moment.
- See list of topics below.
- Several PhD-scholarship opportunities are currently available at LIP, ENS-Lyon!
- If interested, send me an email.

** Master Internships: ** I'm happy to supervise the internship (*'Stage M1'* or *'Stage M2'* in the French system, read this) of master students.
- See list of topics below.
- Some scholarships (even for master students coming from abroad) are currently available at LIP, ENS-Lyon!
- If interested, send me an email.

** Topics: ** the research topics I currently propose aim at devoloping a mathematical theory of *quantitative modal and temporal logics*.
While in ordinary (Boolean) logics a formula is either *True* or *False*, in quantitative logics a formula has a * degree of truth* which is tipycally a real number. This number might, for example, represent the probability of the property expressed by the formula occuring after one experiment.
- Topic A, 'Proof Theory': develop axiomatizations and (sequent calculus based) proof systems for quantitative logics.
- Topic B. 'Model Theory': Investigate properties of models of quantitative logics. For example the 'universal model' of a certain quantitative logic (called
*Riesz Modal logic*) has been proved to be metrizable (see my LICS 2017 paper). Can we describe explicitly a compatible metric and investigate its properties?

The two topics are strongly intertwined but may suit different tastes. Research on Topic A typically requires a lot of syntactical arguments (nested inductions of formulas, proofs, etc) while research on Topic B requires some knowledge of algebra and topology.