Perspectives for proof unwinding by programming languages techniques

In this chapter, we propose some future directions of work, potentially beneficial to Mathematics and its foundations, based on the recent import of methodology from the theory of programming languages into proof theory. This scientific essay, written for the audience of proof theorists as well as the working mathematician, is not a survey of the field, but rather a personal view of the author who hopes that it may inspire future and fellow researchers

Groupoid Semantics for Thermal Computing

A groupoid semantics is presented for systems with both logical and thermal degrees of freedom. We apply this to a syntactic model for encryption, and obtain an algebraic characterization of the heat produced by the encryption function, as predicted by Landauer's principle. Our model has a linear representation theory that reveals an underlying quantum semantics, giving for the first time a functorial classical model for quantum teleportation and other quantum phenomena.Comment: We describe a groupoid model for thermodynamic computation, and a quantization procedure that turns encrypted communication into quantum teleportation. Everything is done using higher category theor

Bounded Rationality and Heuristics in Humans and in Artificial Cognitive Systems

In this paper I will present an analysis of the impact that the notion of “bounded rationality”, introduced by Herbert Simon in his book “Administrative Behavior”, produced in the field of Artificial Intelligence (AI). In particular, by focusing on the field of Automated Decision Making (ADM), I will show how the introduction of the cognitive dimension into the study of choice of a rational (natural) agent, indirectly determined - in the AI field - the development of a line of research aiming at the realisation of artificial systems whose decisions are based on the adoption of powerful shortcut strategies (known as heuristics) based on “satisficing” - i.e. non optimal - solutions to problem solving. I will show how the “heuristic approach” to problem solving allowed, in AI, to face problems of combinatorial complexity in real-life situations and still represents an important strategy for the design and implementation of intelligent systems

The Knowledge Level in Cognitive Architectures: Current Limitations and Possible Developments

In this paper we identify and characterize an analysis of two problematic aspects affecting the representational level of cognitive architectures (CAs), namely: the limited size and the homogeneous typology of the encoded and processed knowledge. We argue that such aspects may constitute not only a technological problem that, in our opinion, should be addressed in order to build articial agents able to exhibit intelligent behaviours in general scenarios, but also an epistemological one, since they limit the plausibility of the comparison of the CAs' knowledge representation and processing mechanisms with those executed by humans in their everyday activities. In the final part of the paper further directions of research will be explored, trying to address current limitations and future challenges