Related papers: A coalgebraic semantics for causality in Petri net…
Imagery is frequently used to model, represent and communicate knowledge. In particular, graphs are one of the most powerful tools, being able to represent relations between objects. Causal relations are frequently represented by directed…
We consider approaches for causal semantics of Petri nets, explicitly representing dependencies between transition occurrences. For one-safe nets or condition/event-systems, the notion of process as defined by Carl Adam Petri provides a…
Event structures have emerged as a foundational model for concurrent computation, explaining computational processes by outlining the events and the relationships that dictate their execution. They play a pivotal role in the study of key…
We provide a unified operational framework for the study of causality, non-locality and contextuality, in a fully device-independent and theory-independent setting. Our work has its roots in the sheaf-theoretic framework for contextuality…
Petri networks and network models are two frameworks for the compositional design of systems of interacting entities. Here we show how to combine them using the concept of a "catalyst": an entity that is neither destroyed nor created by any…
A causal-net is a finite acyclic directed graph. In this paper, we introduce a category, denoted by $\mathbf{Cau}$ and called causal-net category, whose objects are causal-nets and morphisms between two causal-nets are the functors between…
We provide a model independent construction of a net of C*-algebras satisfying the Haag-Kastler axioms over any spacetime manifold. Such a net, called the net of causal loops, is constructed by selecting a suitable base K encoding causal…
The execution of an event in a complex and distributed system where the dependencies vary during the evolution of the system can be represented in many ways, and one of them is to use Context-Dependent Event structures. Event structures are…
For one-safe Petri nets or condition/event-systems, a process as defined by Carl Adam Petri provides a notion of a run of a system where causal dependencies are reflected in terms of a partial order. Goltz and Reisig have generalised this…
Petri nets are a well-known model of concurrency and provide an ideal setting for the study of fundamental aspects in concurrent systems. Despite their simplicity, they still lack a satisfactory causally reversible semantics. We develop…
The operational semantics of interactive systems is usually described by labeled transition systems. Abstract semantics (that is defined in terms of bisimilarity) is characterized by the final morphism in some category of coalgebras. Since…
Causal nets (CNs) are Petri nets where causal dependencies are modelled via inhibitor arcs. They play the role of occurrence nets when representing the behaviour of a concurrent and distributed system, even when reversibility is considered.…
We present a categorical construction for modelling causal structures within a general class of process theories that include the theory of classical probabilistic processes as well as quantum theory. Unlike prior constructions within…
Modeling causal relationships in graph representation learning remains a fundamental challenge. Existing approaches often draw on theories and methods from causal inference to identify causal subgraphs or mitigate confounders. However, due…
Trace semantics has been defined for various kinds of state-based systems, notably with different forms of branching such as non-determinism vs. probability. In this paper we claim to identify one underlying mathematical structure behind…
The framework of causal models provides a principled approach to causal reasoning, applied today across many scientific domains. Here we present this framework in the language of string diagrams, interpreted formally using category theory.…
In this dissertation we develop a new formal graphical framework for causal reasoning. Starting with a review of monoidal categories and their associated graphical languages, we then revisit probability theory from a categorical perspective…
Discrete Bayesian Networks have been very successful as a framework both for inference and for expressing certain causal hypotheses. In this paper we present a class of graphical models called the chain event graph (CEG) models, that…
Knowledge graph embedding (KGE) focuses on representing the entities and relations of a knowledge graph (KG) into the continuous vector spaces, which can be employed to predict the missing triples to achieve knowledge graph completion…
The analysis of system reliability has often benefited from graphical tools such as fault trees and Bayesian networks. In this article, instead of conventional graphical tools, we apply a probabilistic graphical model called the chain event…