Related papers: Philosophy-Guided Mathematical Formalism for Compl…
Active learning algorithms have been an integral part of recent advances in artificial intelligence. However, the research in the field is widely varying and lacks an overall organizing leans. We outline a Markovian formalism for the field…
We propose the concepts of philomatics and psychomatics as hybrid combinations of philosophy and psychology with mathematics. We explain four motivations for this combination which are fulfilling the desire of analytical philosophy,…
Logic has proved essential for formally modeling software based systems. Such formal descriptions, frequently called specifications, have served not only as requirements documentation and formalisation, but also for providing the…
We introduce Metatheory.jl: a lightweight and performant general purpose symbolics and metaprogramming framework meant to simplify the act of writing complex Julia metaprograms and to significantly enhance Julia with a native term rewriting…
Automata learning is a technique that has successfully been applied in verification, with the automaton type varying depending on the application domain. Adaptations of automata learning algorithms for increasingly complex types of automata…
This paper proposes a functional foundation for model driven engineering that unifies model construction, metamodels, templates, and transformations under a single formalism: the model expression algebra. In this algebra, models are values,…
Despite the recent success of neural network models in mimicking animal performance on visual perceptual tasks, critics worry that these models fail to illuminate brain function. We take it that a central approach to explanation in systems…
Recent studies have highlighted the limitations of large language models in mathematical reasoning, particularly their inability to capture the underlying logic. Inspired by meta-learning, we propose that models should acquire not only…
A multi-decade exploration into the theoretical foundations of artificial and natural general intelligence, which has been expressed in a series of books and papers and used to guide a series of practical and research-prototype software…
The expansion of a classical Hamilton formalism consisting in adaptation of it to describe the nonequilibrium systems is offered. Expansion is obtained by construction of formalism on the basis of the dynamics equation of the equilibrium…
Since the early twentieth century, it has been understood that mathematical definitions and proofs can be represented in formal systems systems with precise grammars and rules of use. Building on such foundations, computational proof…
This paper motivates the need for a formalism for the modelling and analysis of dynamic reconfiguration of dependable real-time systems. We present requirements that the formalism must meet, and use these to evaluate well established…
Complex systems thinking is applied to a wide variety of domains, from neuroscience to computer science and economics. The wide variety of implementations has resulted in two key challenges: the progenation of many domain-specific…
We take a fresh look at analogue-digital systems focussing on their physical behaviour. We model a general analogue-digital system as a physical process controlled by an algorithm by viewing the physical process as physical oracle to the…
In recent years, the idea of formalising and modelling fairness for algorithmic decision making (ADM) has advanced to a point of sophisticated specialisation. However, the relations between technical (formalised) and ethical discourse on…
Formal methods apply algorithms based on mathematical principles to enhance the reliability of systems. It would only be natural to try to progress from verification, model checking or testing a system against its formal specification into…
In this article one introduces a formalism of classical mechanics where complex Lagrangian functions are admitted. The results include complex versions of the Lagrangian function, of the Euler-Lagrange equation, of the Hamilton principle, a…
We examine the practicality for a user of using Answer Set Programming (ASP) for representing logical formalisms. Our example is a formalism aiming at capturing causal explanations from causal information. We show the naturalness and…
We introduce a meta-model based on formal languages, dubbed formal choreographic languages, to study message-passing systems. Our framework allows us to generalise standard constructions from the literature and to compare them. In…
We argue that explanations for "algorithmic decision-making" (ADM) systems can profit by adopting practices that are already used in the learning sciences. We shortly introduce the importance of explaining ADM systems, give a brief overview…