Real-Valued Modal Logics

Real-valued modal logics address the limitations of classical modal logic for reasoning about modal notions such as necessity, belief, and spatio-temporal relations in the presence of uncertainty, possibility, or vagueness, by allowing modalities and operations defined over sets of real numbers. They also provide a basis for defining description logics that model vague or uncertain concepts, and useful and computationally feasible fragments of corresponding first-order logics.

Abstracts and Slides

Towards a Proof Theory of the Riesz Modal Logic

Christophe Lucas

It has recently been shown that two Riesz-modal-logic formulas are semantically equivalent if and only if they are equivalent when interpreted in all "modal Riesz spaces". In this talk we will introduce a hyper-sequent calculus for the theory of "modal lattice-ordered abelian groups" which builds on previous work of Metcalfe, Olivetti and Gabbay. It is our hope to eventually extend this work to the theory of modal Riesz spaces.

An Abelian Modal Logic

George Metcalfe

In this talk, I will describe recent axiomatization and complexity results (obtained in joint work with D. Diaconescu and L. Schnüriger) for a many-valued modal logic equipped with the usual group and lattice operations over the real numbers that extends Meyer and Slaney's Abelian Logic. These results also provide a first step towards solving open axiomatization and complexity problems for a many-valued modal logic based on the semantics of Lukasiewicz infinite-valued logic.

The Riesz Modal Logic

Matteo Mio

In this talk I will introduce the Riesz modal logic, a recently introduced real-valued (fuzzy) temporal logic specifically designed to express properties of Markov chains and present some results about it.

The Proof Theory of Modal Fixed Point Logics

Thomas Studer

We present a survey of deductive systems for the modal mu-calculus and we discuss the problem of syntactic cut-elimination for this logic.