Abstract
The need for more flexible and robust models to reason about systems in the presence of conflicting information is becoming more and more relevant in different contexts. This has prompted the introduction of paraconsistent transition systems, where transitions are characterized by two pairs of weights: one representing the evidence that the transition effectively occurs and the other its absence. Such a pair of weights can express scenarios of vagueness and inconsistency. . This paper establishes a foundation for a compositional and structured specification approach of paraconsistent transition systems, framed as paraconsistent institution. . The proposed methodology follows the stepwise implementation process outlined by Sannella and Tarlecki.

Abstract
Modelling complex information systems often entails the need for dealing with scenarios of inconsistency in which several requirements either reinforce or contradict each other. This lecture summarises recent joint work with Juliana Cunha, Alexandre Madeira and Ana Cruz on a variant of transition systems endowed with positive and negative accessibility relations, and a metric space over the lattice of truth values. Such structures are called paraconsistent transition systems, the qualifier stressing a connection to paraconsistent logic, a logic taking inconsistent information as potentially informative. A coalgebraic perspective on this family of structures is also discussed.

Abstract

Abstract
Discerning between quantum and classical correlations is of great importance. Bell polytopes are well established as a fundamental tool for such a purpose. In this paper, we extend this line of inquiry by applying resource theory within the context of network scenarios, to a Quantum Key Distribution (QKD) protocol, BBM92. To achieve this, we consider the causal structure P3 to describe the protocol, and we aim to develop useful statistical tests to assess it. Our objectives are twofold: firstly, to utilise the underlying causal structure of the QKD protocol to produce a geometrical analysis of the resulting nonconvex polytope, with a focus on the classical behaviours, and secondly to devise a test within this framework to evaluate the distance between any two behaviours within the generated polytope. This approach offers a unique perspective, linking deviations from expected behaviour directly to the quality of the quantum resource involved or the residual nonclassicality in protocol execution.

Abstract