Abstract
Fuzzy programming languages, such as the Fuzzy Arden Syntax (FAS), are used to describe behaviours which evolve in a fuzzy way and thus cannot be characterized neither by a Boolean outcome nor by a probability distribution. This paper introduces a semantics for FAS, focusing on the weighted parallel interpretation of its conditional statement. The proposed construction is based on the notion of a fuzzy multirelation which associates with each state in a program a fuzzy set of weighted possible evolutions. The latter is parametric on a residuated lattice which models the underlying semantic 'truth space'. Finally, a family of dynamic logics, equally parametric on the residuated lattice, is introduced to reason about FAS programs.

Abstract
Often in Software Engineering a modelling formalism has to support scenarios of inconsistency in which several requirements either reinforce or contradict each other. Paraconsistent transition systems are proposed in this paper as one such formalism: states evolve through two accessibility relations capturing weighted evidence of a transition or its absence, respectively. Their weights come from a specific residuated lattice. A category of these systems, and the corresponding algebra, is defined providing a formal setting to model different application scenarios. One of them, dealing with the effect of quantum decoherence in quantum programs, is used for illustration purposes.

Abstract
Variational quantum circuits are being used as versatile quantum machine learning models. Some empirical results exhibit an advantage in supervised and generative learning tasks. However, when applied to reinforcement learning, less is known. In this work, we considered a variational quantum circuit composed of a low-depth hardware-efficient ansatz as the parameterized policy of a reinforcement learning agent. We show that an epsilon-approximation of the policy gradient can be obtained using a logarithmic number of samples concerning the total number of parameters. We empirically verify that such quantum models behave similarly to typical classical neural networks used in standard benchmarking environments and quantum control, using only a fraction of the parameters. Moreover, we study the barren plateau phenomenon in quantum policy gradients using the Fisher information matrix spectrum.

Abstract
The development of more flexible and robust models for reasoning about systems in environments with potentially conflicting information is becoming more and more relevant in different contexts. In this direction, we recently introduced paraconsistent transition systems, i.e. transition systems whose transitions are tagged with a pair of weights, one standing for the degree of evidence that the transition exists, another weighting its potential non existence. Moreover, these structures were endowed with a modal logic [3] that was further formalised as an institution in [5]. This paper goes a step further, proposing an approach for the structured specification of paraconsistent transition processes, i.e. paraconsistent transition systems with initial states. The proposed approach is developed along the lines of [12], which introduced a complete methodology for (standard) reactive systems development building on the Sannella and Tarlecki stepwise implementation process. For this, we enrich the logic with dynamic modalities and hybrid features, and provide a pallet of constructors and abstractors to support the development process of paraconsistent processes along the entire design cycle.

Abstract

Abstract
MathIS is a new project that aims to reinvigorate secondary-school mathematics by exploiting insights of the dynamics of algorithmic problem solving. This paper describes the main ideas that underpin the project. In summary, we propose a central role for formal logic, the development of a calculational style of reasoning, the emphasis on the algorithmic nature of mathematics, and the promotion of self-discovery by the students. These ideas are discussed and the case is made, through a number of examples that show the teaching style that we want to introduce, for their relevance in shaping mathematics training for the years to come. In our opinion, the education of software engineers that work effectively with formal methods and mathematical abstractions should start before university and would benefit from the ideas discussed here.