Related papers: Testing Probabilistic Processes: Can Random Choice…
The central question of this paper is: are deterministic and indeterministic descriptions observationally equivalent in the sense that they give the same predictions? I tackle this question for measure-theoretic deterministic systems and…
The Born's rule introduces intrinsic randomness to the outcomes of a measurement performed on a quantum mechanical system. But, if the system is prepared in the eigenstate of an observable then the measurement outcome of that observable is…
Temporal logics over finite traces have recently seen wide application in a number of areas, from business process modelling, monitoring, and mining to planning and decision making. However, real-life dynamic systems contain a degree of…
We tackle the problem of conditioning probabilistic programs on distributions of observable variables. Probabilistic programs are usually conditioned on samples from the joint data distribution, which we refer to as deterministic…
We show that many bounded rationality patterns of choice can be alternatively represented as testable models of limited consideration, and we elicit the features of the associated unobserved consideration sets from the observed choice.…
In this paper we work on (bi)simulation semantics of processes that exhibit both nondeterministic and probabilistic behaviour. We propose a probabilistic extension of the modal mu-calculus and show how to derive characteristic formulae for…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
Probabilistic specifications are fast gaining ground as a tool for statistical modeling of probabilistic systems. One of the main goals of formal methods in this domain is to ensure that specific behavior is present or absent in the system,…
Bayesian inference is often utilized for uncertainty quantification tasks. A recent analysis by Xu and Raginsky 2022 rigorously decomposed the predictive uncertainty in Bayesian inference into two uncertainties, called aleatoric and…
We present a domain-theoretic framework for probabilistic programming that provides a constructive definition of conditional probability and addresses computability challenges previously identified in the literature. We introduce a novel…
In this work, we develop a formal system of inductive logic. It uses an infinitary language that allows for countable conjunctions and disjunctions. It is based on a set of nine syntactic rules of inductive inference, and contains classical…
Opacity is a general language-theoretic framework in which several security properties of a system can be expressed. Its parameters are a predicate, given as a subset of runs of the system, and an observation function, from the set of runs…
In this PhD thesis the ancient question of determinism ('Does every event have a cause ?') will be re-examined. In the philosophy of science and physics communities the orthodox position states that the physical world is indeterministic:…
Theory of quantum measurements is often classified as decision theory. An event in decision theory corresponds to the measurement of an observable. This analogy looks clear for operationally testable simple events. However, the situation is…
Probabilistic programming languages allow programmers to write down conditional probability distributions that represent statistical and machine learning models as programs that use observe statements. These programs are run by accumulating…
One fundamental problem in studying dynamical process is whether it is possible and how to construct prediction model for an unknown system via sampled time series, especially in the modern big data era. The research in this area is…
We study monads resulting from the combination of nondeterministic and probabilistic behaviour with the possibility of termination, which is essential in program semantics. Our main contributions are presentation results for the monads,…
We give extensional and intensional characterizations of functional programs with nondeterminism: as structure preserving functions between biorders, and as nondeterministic sequential algorithms on ordered concrete data structures which…
Physical theories must stem from observation. The possibility that perceived events are simulated, not real, raises a crucial dilemma about the credibility of known physics, known as the simulation hypothesis. To analyze this hypothesis in…
Probabilistic operational semantics for a nondeterministic extension of pure lambda calculus is studied. In this semantics, a term evaluates to a (finite or infinite) distribution of values. Small-step and big-step semantics are both…