## Logic and Computation

Qualitative and quantitative notions of consistency and contradiction.

*Walter Carnielli*, CLE - Universidade Estadual de Campinas, Brazil.

## Abstract

Possibility and necessity theories rival with probability in representing uncertain knowledge, while offering a more qualitative view of uncertainty. Moreover, necessity and possibility measures constitute, respectively, lower and upper bounds for probability measures, with the advantage of avoiding the complications of the notion of probabilistic independence.

On the other hand, paraconsistent formal systems, especially the Logics of Formal Inconsistency, are capable of quite carefully expressing the circumstances of reasoning with contradictions. The aim of this talk is to merge these ideas, by precisely defining new notions of possibility and necessity theories involving the concept of consistency (generalizing the proposal by (Besnard & Lang 1994)) based on connecting them to the notion of partial and conclusive evidence. This combination permits a whole treatment of contradictions, both local and global, including a gradual handling of the notion of contradiction, thus obtaining a really useful tool for AI and machine learning, with potential applications in logic programming via appropriate resolution rules.

## Partial Differential Equations

To be announced.

*Heinrich Freistühler*, University of Konstanz.

## Analysis, Geometry, and Dynamical Systems

To be announced.

*Adriana Neumann*, Universidade Federal do Rio Grande do Sul.

## Analysis, Geometry, and Dynamical Systems

To be announced.

*David Krejciric*, Czech Technical University.

## Analysis, Geometry, and Dynamical Systems

To be announced.

*Daniel Rodrigues*, University of Groningen.

## Analysis, Geometry, and Dynamical Systems

A random particle system and nonentropy solutions of the Burgers equation on the circle.

*Alexandre Boritchev*, Institut Camille Jordan, Université Lyon 1.

## Abstract

We consider a particle system which is equivalent to a process valued on the space of nonentropy solutions of the inviscid Burgers equation. Such solutions are conjectured to be relevant for the study of the KPZ fixed point. We prove ergodicity and obtain some properties of the stationary measure.

Joint work with C.-E. Bréhier (Lyon) and M. Mariani (Rome).