Related papers: Classical realizability as a classifier for nondet…
This paper proposes new semantics for nondeterministic program execution, replacing the standard relational semantics for propositional dynamic logic (PDL). Under these new semantics, program execution is represented as fundamentally…
We present a new partial order reduction method for reachability analysis of nondeterministic labeled transition systems over metric spaces. Nondeterminism arises from both the choice of the initial state and the choice of actions, and the…
This paper investigates stochastic nondeterminism on continuous state spaces by relating nondeterministic kernels and stochastic effectivity functions to each other. Nondeterministic kernels are functions assigning each state a set o…
The problem of emergence of classicality from quantum mechanics has been addressed over time through numerous frameworks, from Bohr's correspondence principle to quantum Darwinism. Traditional approaches associate the emergence of…
We describe a mathematical language for determining all possible patterns of contextuality in the dependence of stochastic outputs of a system on its deterministic inputs. The central notion is that of all possible couplings for…
We develop techniques at the interface between differential algebra and model theory to study the following problems of exponential algebraicity: Does a given algebraic differential equation admits an exponentially algebraic solution, that…
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…
I generalize acyclic deterministic structural causal models to the nondeterministic case and argue that this offers an improved semantics for counterfactuals. The standard, deterministic, semantics developed by Halpern (and based on the…
We investigate how to model exchangeability with choice functions. Exchangeability is a structural assessment on a sequence of uncertain variables. We show how such assessments are a special indifference assessment, and how that leads to a…
We introduce a version of probabilistic Kleene algebra with angelic nondeterminism and a corresponding class of automata. Our approach implements semantics via distributions over multisets in order to overcome theoretical barriers arising…
In this paper we consider a nondeterministic computation by deterministic multi-head 2-way automata having a read-only access to an auxiliary memory. The memory contains additional data (a guess) and computation is successful iff it is…
Interactive theorem provers based on dependent type theory have the flexibility to support both constructive and classical reasoning. Constructive reasoning is supported natively by dependent type theory and classical reasoning is typically…
Every computable function has to be continuous. To develop computability theory of discontinuous functions, we study low levels of the arithmetical hierarchy of nonuniformly computable functions on Baire space. First, we classify…
In (Beckers, 2025) I introduced nondeterministic causal models as a generalization of Pearl's standard deterministic causal models. I here take advantage of the increased expressivity offered by these models to offer a novel definition of…
We present a family of paraconsistent counterparts of the constructive modal logic CK. These logics aim to formalise reasoning about contradictory but non-trivial propositional attitudes like beliefs or obligations. We define their…
We give a general notion of combinatory completeness with respect to a faithful cartesian club and use it systematically to obtain characterisations of a number of different kinds of applicative system. Each faithful cartesian club…
Consider a decision problem whose instance is a function. Its degree of undecidability, measured by the corresponding class of the arithmetic (or Kleene-Mostowski) hierarchy hierarchy, may depend on whether the instance is a partial…
We demonstrate the simple and deep equivalence between quantum coherence and nonclassicality and the definite way in which they determine metrological resolution. Moreover, we define a coherence observable consistent with a classical…
In order to reason about effects, we can define quantitative formulas to describe behavioural aspects of effectful programs. These formulas can for example express probabilities that (or sets of correct starting states for which) a program…
We present here three different approaches to the problem of modeling mathematically the concept of a non-deterministic mechanism. Each of these three approaches leads to a mathematical definition. We then show that all the three…