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We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…

This paper presents n-coding, a theoretical model of multiple internal mental representations. The n-coding construct is developed from a review of cognitive and imaging studies suggesting the independence of information processing along…

In these lecture notes, we give a brief introduction to some elements of category theory. The choice of topics is guided by applications to functional programming. Firstly, we study initial algebras, which provide a mathematical…

Predicting a label correctly does not necessarily require representing the operation that produces it. Transformer representations are known to carry label-level information, but whether they encode semantic operations producing those…

This literature review discovers an implementation of formal logic systems in cyber security by enhancing access control models. We explore the characteristics of the existing access control theories, their limitations and how classical…

The use of argumentation in education has been shown to improve critical thinking skills for end-users such as students, and computational models for argumentation have been developed to assist in this process. Although these models are…

Neural networks excel at pattern recognition but struggle with reliable logical reasoning, often violating basic logical principles during inference. We address this limitation by developing a categorical framework that systematically…

Recently, high-performing code generation systems based on large language models have surfaced. They are trained on massive corpora containing much more natural text than actual executable computer code. This work shows that current code…

A probabilistic model describes a system in its observational state. In many situations, however, we are interested in the system's response under interventions. The class of structural causal models provides a language that allows us to…

This paper presents equational-based logics for proving first order properties of programming languages involving effects. We propose two dual inference system patterns that can be instanciated with monads or comonads in order to be used…

We describe a representation and a set of inference methods that combine logic programming techniques with probabilistic network representations for uncertainty (influence diagrams). The techniques emphasize the dynamic construction and…

We show an approach to automated control of machine vision systems based on incremental creation and evaluation of a particular family of influence diagrams that represent hypotheses of imagery interpretation and possible subsequent…

When trained on language data, do transformers learn some arbitrary computation that utilizes the full capacity of the architecture or do they learn a simpler, tree-like computation, hypothesized to underlie compositional meaning systems…

The software patterns provide building blocks to the design and implementation of a software system, and try to make the software engineering to progress from experience to science. The software patterns were made famous because of the…

Combining local exceptions and first class continuations leads to programs with complex control flow, as well as the possibility of expressing powerful constructs such as resumable exceptions. We describe and compare games models for a…

We revisit the problem of computing (robust) controlled invariant sets for discrete-time linear systems. Departing from previous approaches, we consider implicit, rather than explicit, representations for controlled invariant sets.…

We introduce structured active inference, a large generalization and formalization of active inference using the tools of categorical systems theory. We cast generative models formally as systems "on an interface", with the latter being a…

Interventional causal models describe several joint distributions over some variables used to describe a system, one for each intervention setting. They provide a formal recipe for how to move between the different joint distributions and…

In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…

We propose a method for inferring \emph{parameterized regular types} for logic programs as solutions for systems of constraints over sets of finite ground Herbrand terms (set constraint systems). Such parameterized regular types generalize…