Related papers: Quantitative Behavioural Reasoning for Higher-orde…
Quasi-probabilities appear across diverse areas of physics, but their conceptual foundations remain unclear: they are often treated merely as computational tools, and operations like conditioning and Bayes' theorem become ambiguous. We…
Agent-based models (ABMs) are valuable for modelling complex, potentially out-of-equilibria scenarios. However, ABMs have long suffered from the Lucas critique, stating that agent behaviour should adapt to environmental changes.…
The bisimulation metric (BSM) is a powerful tool for computing state similarities within a Markov decision process (MDP), revealing that states closer in BSM have more similar optimal value functions. While BSM has been successfully…
Higher-order abstract GSOS is a recent extension of Turi and Plotkin's framework of Mathematical Operational Semantics to higher-order languages. The fundamental well-behavedness property of all specifications within the framework is that…
Quantifying the similarity between mathematical expressions is a fundamental problem in computational mathematics, symbolic reasoning, and scientific discovery. While behavioral notions of similarity have previously been explored in the…
We introduce a framework for estimating causal effects of binary and continuous treatments in high dimensions. We show how posterior distributions of treatment and outcome models can be used together with doubly robust estimators. We…
In randomized clinical trials, adjusting for baseline covariates can improve credibility and efficiency for demonstrating and quantifying treatment effects. This article studies the augmented inverse propensity weighted (AIPW) estimator,…
Relational properties describe multiple runs of one or more programs. They characterize many useful notions of security, program refinement, and equivalence for programs with diverse computational effects, and they have received much…
Research in analogical reasoning suggests that higher-order cognitive functions such as abstract reasoning, far transfer, and creativity are founded on recognizing structural similarities among relational systems. Here we integrate theories…
The recently introduced framework of Graded Quantitative Rewriting is an innovative extension of traditional rewriting systems, in which rules are annotated with degrees drawn from a quantale. This framework provides a robust foundation for…
Plausibility measures are structures for reasoning in the face of uncertainty that generalize probabilities, unifying them with weaker structures like possibility measures and comparative probability relations. So far, the theory of…
This paper defines a new pseudometric for binary relations between finite sets that measures consensus among subsets. The main results are (1) a concise restatement of this pseudometric with an intuitively appealing interpretation via a…
We explore a fuzzy modal logic that can formalise probabilistic reasoning about actions and knowledge. In particular, we deal with contexts involving statements about events expressed via modal formulas, e.g., "after doing $a$, the…
In this paper we demonstrate that a well known linear inequality method developed for rational Chebyshev approximation is equivalent to the application of the bisection method used in quasiconvex optimisation. Although this correspondence…
We consider the asymptotic behaviour of the fluctuation process for large stochastic systems of interacting particles driven by both idiosyncratic and common noise with an interaction kernel \(k \in L^2(\R^d) \cap L^\infty(\R^d)\). Our…
Bisimulation metrics provide a robust and accurate approach to study the behavior of nondeterministic probabilistic processes. In this paper, we propose a logical characterization of bisimulation metrics based on a simple probabilistic…
The motivation of this paper is the development of an optimisation method for solving optimisation problems appearing in Chebyshev rational and generalised rational approximation problems, where the approximations are constructed as ratios…
This paper shows a novel fuzzy approximate reasoning method based on the least common multiple (LCM). Its fundamental idea is to obtain a new fuzzy reasoning result by the extended distance measure based on LCM between the antecedent fuzzy…
Bounded fitting is an attractive paradigm for learning logical formulas from labeled data examples that offers PAC-style generalization guarantees and can often be implemented leveraging SAT solvers. It has been successfully applied to…
We introduce a two-sort weighted modal logic for possibilistic reasoning with fuzzy formal contexts. The syntax of the logic includes two types of weighted modal operators corresponding to classical necessity ($\Box$) and sufficiency…