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Despite ample evidence that our concepts, our cognitive architecture, and mathematics itself are all deeply compositional, few models take advantage of this structure. We therefore propose a radically compositional approach to computational…
Cantor's diagonal method is traditionally used to prove the uncountability of the set of all infinite binary sequences. This paper analyzes the expressive limits of this method. It is shown that under any constructive application --…
The concept of intelligent software is flawed. The behaviour of software is determined by the hardware that "interprets" it. This undermines claims regarding the behaviour of theorised, software superintelligence. Here we characterise this…
In the last years many accurate decision support systems have been constructed as black boxes, that is as systems that hide their internal logic to the user. This lack of explanation constitutes both a practical and an ethical issue. The…
If an active citizen should increasingly be a computationally enlightened one, replacing the autonomy of reason with the heteronomy of algorithms, then I argue in this article that we must begin teaching the principles of critiquing the…
Making a linguistic theory is like making a programming language: one typically devises a type system to delineate the acceptable utterances and a denotational semantics to explain observations on their behavior. Via this connection, the…
Envy-freeness is one of the most prominent fairness concepts in the allocation of indivisible goods. Even though trivial envy-free allocations always exist, rich literature shows this is not true when one additionally requires some…
The current paper offers a perspective on what we term conceptive intelligence - the capacity of an agent to continuously think of new object definitions (tasks, problems, physical systems, etc.) and to look for methods to realize them. The…
Creativity is individual, and it is social. The social aspects of creativity have become of increasing interest as systems have emerged that mobilize large numbers of people to engage in creative tasks. We examine research related to…
Compositionality is one of the fundamental abilities of the human reasoning process, that allows to decompose a complex problem into simpler elements. Such property is crucial also for neural networks, especially when aiming for a more…
In domains with high knowledge distribution a natural objective is to create principle foundations for collaborative interactive learning environments. We present a first mathematical characterization of a collaborative learning group, a…
In part one of the Critique of Judgment, Immanuel Kant wrote that "the judgment of taste...is not a cognitive judgment, and so not logical, but is aesthetic."\cite{Kant} While the condition of aesthetic discernment has long been the subject…
This article redefines arbitrariness not as a normative flaw or a symptom of domination, but as a foundational functional mechanism structuring human systems and interactions. Diverging from critical traditions that conflate arbitrariness…
Generative AI presents a profound challenge to traditional notions of human uniqueness, particularly in creativity. Fueled by neural network based foundation models, these systems demonstrate remarkable content generation capabilities,…
Natural language semantics has recently sought to combine the complementary strengths of formal and distributional approaches to meaning. More specifically, proposals have been put forward to augment formal semantic machinery with…
Humans have the innate capability to answer diverse questions, which is rooted in the natural ability to correlate different concepts based on their semantic relationships and decompose difficult problems into sub-tasks. On the contrary,…
It is shown that, in certain circumstances, systems of cultural rules may be represented by doubly stochastic matrices denoted called possibility transforms, and by certain real valued possibility densities with inner product. Using such…
Interpretability of machine learning models has gained more and more attention among researchers in the artificial intelligence (AI) and human-computer interaction (HCI) communities. Most existing work focuses on decision making, whereas we…
This paper delves into the intersection of computational theory and music, examining the concept of undecidability and its significant, yet overlooked, implications within the realm of modern music composition and production. It posits that…
A perceived limitation of evolutionary art and design algorithms is that they rely on human intervention; the artist selects the most aesthetically pleasing variants of one generation to produce the next. This paper discusses how computer…