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Effect algebras were introduced in order to describe the structure of effects, i.e. events in quantum mechanics. They are partial algebras describing the logic behind the corresponding events. It is natural to ask how to introduce the…
Monotone co-design enables compositional engineering design by modeling components through feasibility relations between required resources and provided functionalities. However, its standard boolean formulation cannot natively represent…
In order to study quantum measurement theory, sequential product defined for any two quantum effects is introduced. Physically motivated conditions ask the sequential product to be continuous with respect to the strong operator topology. In…
A sequential effect algebra (SEA) is an effect algebra on which a sequential product is defined. We present examples of effect algebras that admit a unique, many and no sequential product. Some general theorems concerning unique sequential…
In all our well-established theories, it is assumed that events are embedded in a global causal structure such that, for every pair of events, the causal order between them is always fixed. However, the possible interplay between quantum…
In this paper we study the problem of a possibility to use quantum observables to describe a possible combination of the order effect with sequential reproducibility for quantum measurements. By the order effect we mean a dependence of…
In this paper, we consider event structures and their probabilistic and quantum extensions as originally defined by Winskel. If these structures have already been part of sophisticated computational models, they have rarely been directly…
Causal models capture cause-effect relations both qualitatively - via the graphical causal structure - and quantitatively - via the model parameters. They offer a powerful framework for analyzing and constructing processes. Here, we…
Effectus theory is a new branch of categorical logic that aims to capture the essentials of quantum logic, with probabilistic and Boolean logic as special cases. Predicates in effectus theory are not subobjects having a Heyting algebra…
Type-and-effect systems help the programmer to organize data and computational effects in a program. While for traditional type systems expressive variants with sophisticated inference algorithms have been developed and widely used in…
A quantum effect is an operator $A$ on a complex Hilbert space $H$ that satisfies $0\leq A\leq I$, ${\cal E} (H)$ is the set of all quantum effects on $H$. In 2001, Professor Gudder and Nagy studied the sequential product $A\circ…
We propose the concept of a system algebra with a parallel composition operation and an interface connection operation, and formalize composition-order invariance, which postulates that the order of composing and connecting systems is…
The partial (ceteris paribus) effects of interest in nonlinear and interactive linear models are heterogeneous as they can vary dramatically with the underlying observed or unobserved covariates. Despite the apparent importance of…
Sequential modelling entails making sense of sequential data, which naturally occurs in a wide array of domains. One example is systems that interact with users, log user actions and behaviour, and make recommendations of items of potential…
A quantum effect is an operator on a complex Hilbert space $H$ that satisfies $0\leq A\leq I$. We denote the set of all quantum effects by ${\cal E}(H)$. In this paper we prove, Theorem 4.3, on the theory of sequential product on ${\cal…
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…
Quantum causality extends the conventional notion of fixed causal structure by allowing channels and operations to act in an indefinite causal order. The importance of such an indefinite causal order ranges from the foundational---e.g.…
Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory,…
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…
We develop a new interpretation of quantum theory by combining insights from extended Wigner's friend scenarios and quantum causal modelling. In this interpretation, which synthesizes ideas from relational quantum mechanics and consistent…