Related papers: An Invitation to Higher Arity Science

The double slit experiment provides a clear demarcation between classical and quantum theory, while multi-slit experiments demarcate quantum and higher-order interference theories. In this work we show that these experiments pertain to a…

Studying how we explore the world in search of novelties is key to understand the mechanisms that can lead to new discoveries. Previous studies analyzed novelties in various exploration processes, defining them as the first appearance of an…

Artificial intelligence is often measured by the range of tasks it can perform. Yet wide ability without depth remains only an imitation. This paper proposes a Structural-Generative Ontology of Intelligence: true intelligence exists only…

Research in Artificial Intelligence (AI) has focused mostly on two extremes: either on small improvements in narrow AI domains, or on universal theoretical frameworks which are usually uncomputable, incompatible with theories of biological…

We extend the theory (formal part only} of algebras with one binary operation (our paper arXiv:math/0110333v1 [math.RA] 31 Oct 2001) to algebras with several operations of any arity.

The notion of (symmetric) coloured operad or "multicategory" can be obtained from the notion of commutative algebra through a certain general process which we call "theorization" (where our term comes from an analogy with William Lawvere's…

In this paper, I develop a novel version of the multiverse theory of sets called hierarchical pluralism by introducing the notion of `degrees of intentionality' of theories. The presented view is articulated for the purpose of reconciling…

This book is concerned with the various aspects of hierarchical collective behaviour which is manifested by most complex systems in nature. From the many of the possible topics, we plan to present a selection of those that we think are…

Query answering under existential rules -- implications with existential quantifiers in the head -- is known to be decidable when imposing restrictions on the rule bodies such as frontier-guardedness [BLM10, BLMS11]. Query answering is also…

Identifying central entities and interactions is a fundamental problem in network science. While well-studied for graphs (pairwise relations), many biological and social systems exhibit higher-order interactions best modeled by hypergraphs.…

In this work, a novel quaternary algebra has been proposed that can be used to implement an arbitrary quaternary logic function in more than one systematic ways. The proposed logic has evolved from and is closely related to the Boolean…

Hierarchy is one of the most conspicuous features of numerous natural, technological and social systems. The underlying structures are typically complex and their most relevant organizational principle is the ordering of the ties among the…

We show that each irreducible tensor representation of weight 2 of the rotation group of three-dimensional space in the space of rank 3 covariant tensors gives rise to an associative algebra with unity. We find the algebraic relations that…

This letter seeks to illuminate the profound connection between complexity, self-organization, emergent behaviour, pattern formation, and entropy concepts that are foundational to understanding our universe. By examining these ideas through…

Science is built on the scholarly consensus that shifts with time. This raises the question of how new and revolutionary ideas are evaluated and become accepted into the canon of science. Using two recently proposed metrics, we identify…

Creative thought is conventionally believed to involve searching memory and generating multiple independent candidate ideas followed by selection and refinement of the most promising. Honing theory, which grew out of the quantum approach to…

This note presents a method of interpreting the tree adjoining languages as the natural third step in a hierarchy that starts with the regular and the context-free languages. The central notion in this account is that of a higher-order…

The ascent of scaling in artificial intelligence research has revolutionized the field over the past decade, yet it presents significant challenges for academic researchers, particularly in computational social science and critical…

Although algebraic structures are frequently analyzed using unary and binary operations, they can also be effectively defined and unified through ternary operations. In this context, we introduce structures that contain two constants and a…

What do societies, the Internet, and the human brain have in common? They are all examples of complex relational systems, whose emerging behaviours are largely determined by the non-trivial networks of interactions among their constituents,…