Related papers: Knowledge and simplicial complexes
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
We construct a model structure on the category of ordered simplicial complexes, Quillen equivalent to the standard model structure on simplicial sets. This shows that simplicial complexes, which are fully combinatorial in nature, provide a…
In most current applications of belief networks, domain knowledge is represented by a single belief network that applies to all problem instances in the domain. In more complex domains, problem-specific models must be constructed from a…
In this paper, we generalize epistemic logic so that it can help reason about ways of combining common knowledge and distributed knowledge such as "common distributed knowledge", "distributed common knowledge", "distributed common…
There is no single definition of complexity (Edmonds 1999; Gershenson 2008; Mitchell 2009; De Domenico, et al., 2019), as it acquires different meanings in different contexts. A general notion is the amount of information required to…
We define a modular multi-concept extension of the lexicographic closure semantics for defeasible description logics with typicality. The idea is that of distributing the defeasible properties of concepts into different modules, according…
Complex system simulation has been playing an irreplaceable role in understanding, predicting, and controlling diverse complex systems. In the past few decades, the multi-scale simulation technique has drawn increasing attention for its…
An epistemic ensemble is composed of knowledge-based agents capable of retrieving and sharing knowledge and beliefs about themselves and their peers. These agents access a global knowledge state and use actions to communicate and cooperate,…
A simple model for the formation of a complex organism is introduced. Individuals can communicate and specialize, leading to an increase in productivity. If there are limits to the capacity of individuals to communicate with other…
The aim of these notes is to introduce the intuition motivating the notion of a "complicial set", a simplicial set with certain marked "thin" simplices that witness a composition relation between the simplices on their boundary. By varying…
Let $G$ be a finite group. In 2024, Cameron introduced two different concepts of independence (namely independence and strong independence) for the subsets of $G$, yielding to the definition of two simplicial complexes whose vertices are…
In this paper we study the notion of knowledge from the positions of universal algebra and algebraic logic. We consider first order knowledge which is based on first order logic. We define categories of knowledge and knowledge bases. These…
The data of a physical experiment can be represented as a presheaf of probability distributions. A striking feature of quantum theory is that those probability distributions obtained in quantum mechanical experiments do not always admit a…
In the last years complex networks tools contributed to provide insights on the structure of research, through the study of collaboration, citation and co-occurrence networks. The network approach focuses on pairwise relationships, often…
A general notion of information-related complexity applicable to both natural and man-made systems is proposed. The overall approach is to explicitly consider a rational agent performing a certain task with a quantifiable degree of success.…
The standard assumptions that underlie many conceptual and quantitative frameworks do not hold for many complex physical, biological, and social systems. Complex systems science clarifies when and why such assumptions fail and provides…
This is an expository introduction to simplicial sets and simplicial homotopy theory with particular focus on relating the combinatorial aspects of the theory to their geometric/topological origins. It is intended to be accessible to…
The computability power of a distributed computing model is determined by the communication media available to the processes, the timing assumptions about processes and communication, and the nature of failures that processes can suffer. In…
We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for which many important results…
In this paper we consider a family of abstract simplicial complexes which we call immediate snapshot complexes. Their definition is motivated by theoretical distributed computing. Specifically, these complexes appear as protocol complexes…