Related papers: Coalgebraic Trace Semantics for Continuous Probabi…
The partial trace is commonly introduced in quantum mechanics as an algebraic operation used to define reduced states of composite systems. However, the probabilistic origin of this operation goes systematically unnoticed in the literature.…
This paper presents equational-based logics for proving first order properties of programming languages involving effects. We propose two dual inference system patterns that can be instanciated with monads or comonads in order to be used…
This paper presents a categorical account of conditional probability, covering both the classical and the quantum case. Classical conditional probabilities are expressed as a certain "triangle-fill-in" condition, connecting marginal and…
Coalgebras for an endofunctor provide a category-theoretic framework for modeling a wide range of state-based systems of various types. We provide an iterative construction of the reachable part of a given pointed coalgebra that is inspired…
A point process on a space is a random bag of elements of that space. In this paper we explore programming with point processes in a monadic style. To this end we identify point processes on a space X with probability measures of bags of…
We consider a bag (multiset) monad on the category of standard Borel spaces, and show that it gives a free measurable commutative monoid. Firstly, we show that a recent measurability result for probabilistic database queries (Grohe and…
We consider a system of weak* closed sets of finite-dimensional distributions. We show that a corresponding system of random variables can be defined on a probability space with a probability measure determined up to some set of measures,…
It came to the attention of myself and the coauthors of (S., Rozowski, Silva, Rot, 2022) that a number of process calculi can be obtained by algebraically presenting the branching structure of the transition systems they specify. Labelled…
We first define the coarse-graining of probability measures in terms of stochastic kernels. We define when a probability measure is part of another probability measure and say that two probability measures coexist if they are both parts of…
Quasi-trees generalize trees in that the unique "path" between two nodes may be infinite and have any countable order type. They are used to define the rank-width of a countable graph in such a way that it is equal to the least upper-bound…
In the first part of the paper we recall the coalgebraic approach to handling the so-called invisible transitions that appear in different state-based systems semantics. We claim that these transitions are always part of the unit of a…
Probability monads on categories of topological spaces are classical objects of study in the categorical approach to probability theory, with important applications in the semantics of probabilistic programming languages. We construct a…
State-based models of concurrent systems are traditionally considered under a variety of notions of process equivalence. In the particular case of labelled transition systems, these equivalences range from trace equivalence to (strong)…
Lecture notes as per the title. In the first part, the concepts of a measurable space, measurable maps between measurable spaces and that of a measure on a measurable space are introduced, after which the fundamentals of the theory of…
Labeled transition systems are typically used to represent the behavior of nondeterministic processes, with labeled transitions defining a one-step state to-state reachability relation. This model has been recently made more general by…
This article proposes a category-theoretic formalization of Greimasian narrative programs (NPs) that makes their compositional structure mathematically precise. Building on a reconstruction of the actantial model as a categorical schema, we…
An a priori semimeasure (also known as "algorithmic probability" or "the Solomonoff prior" in the context of inductive inference) is defined as the transformation, by a given universal monotone Turing machine, of the uniform measure on the…
We provide sufficient conditions for the existence of a trace on the essential $\mathrm{C}^\ast$-algebra of a (not necessarily Hausdorff) \'etale groupoid $G$ which extends an invariant measure $\mu$ on the unit space of $G$. In particular,…
In this paper we use topological techniques to construct generalized trace and modified dimension functions on ideals in certain ribbon categories. Examples of such ribbon categories naturally arise in representation theory where the usual…
CSP-Agda is a library, which formalises the process algebra CSP in the interactive theorem prover Agda using coinductive data types. In CSP-Agda, CSP processes are in monadic form, which sup- ports a modular development of processes. In…