Related papers: Quantitative Logics for Equivalence of Effectful P…
We investigate quantitative extensions of modal logic and the modal mu-calculus, and study the question whether the tight connection between logic and games can be lifted from the qualitative logics to their quantitative counterparts. It…
Possibilistic logic has been proposed as a numerical formalism for reasoning with uncertainty. There has been interest in developing qualitative accounts of possibility, as well as an explanation of the relationship between possibility and…
In probabilistic transition systems, behavioural metrics provide a more fine-grained and stable measure of system equivalence than crisp notions of bisimilarity. They correlate strongly to quantitative probabilistic logics, and in fact the…
Logic programs, more specifically, Answer-set programs, can be annotated with probabilities on facts to express uncertainty. We address the problem of propagating weight annotations on facts (eg probabilities) of an ASP to its standard…
In computer science, various logical languages are defined to analyze properties of systems. One way to pinpoint the essential differences between those logics is to compare their expressivity in terms of distinguishing power and expressive…
Recent works have shown that defining a behavioural equivalence that matches the observational properties of a quantum-capable, concurrent, non-deterministic system is a surprisingly difficult task. We explore coalgebras over distributions…
Various effects in human cognition, often considered `non-classical', have been argued to be most naturally modelled by quantum-like models of decision making. We extend this approach to describe models of cognition and decision-making in…
To support the understanding of declarative probabilistic programming languages, we introduce a lambda-calculus with a fair binary probabilistic choice that chooses between its arguments with equal probability. The reduction strategy of the…
The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In…
Inspired by the seminal work of Hyland, Plotkin, and Power on the combination of algebraic computational effects via sum and tensor, we develop an analogous theory for the combination of quantitative algebraic effects. Quantitative…
Given a set of several inputs into a system (e.g., independent variables characterizing stimuli) and a set of several stochastically non-independent outputs (e.g., random variables describing different aspects of responses), how can one…
Cognitive theories for reasoning are about understanding how humans come to conclusions from a set of premises. Starting from hypothetical thoughts, we are interested which are the implications behind basic everyday language and how do we…
Probabilistic applicative bisimulation is a recently introduced coinductive methodology for program equivalence in a probabilistic, higher-order, setting. In this paper, the technique is applied to a typed, call-by-value, lambda-calculus.…
We provide here a computational interpretation of first-order logic based on a constructive interpretation of satisfiability w.r.t. a fixed but arbitrary interpretation. In this approach the formulas themselves are programs. This contrasts…
Quantitative logic reasons about the degree to which formulas are satisfied. This paper studies the fundamental reasoning principles of higher-order quantitative logic and their application to reasoning about probabilistic programs and…
We study bisimulation and context equivalence in a probabilistic $\lambda$-calculus. The contributions of this paper are threefold. Firstly we show a technique for proving congruence of probabilistic applicative bisimilarity. While the…
Within the possibilistic approach to uncertainty modeling, the paper presents a modal logical system to reason about qualitative (comparative) statements of the possibility (and necessity) of fuzzy propositions. We relate this qualitative…
Probabilistic programs are a powerful and convenient approach to formalise distributions over system executions. A classical verification problem for probabilistic programs is temporal inference: to compute the likelihood that the execution…
Based on ideas of quantum theory of open systems we propose the consistent approach to the formulation of logic of plausible propositions. To this end we associate with every plausible proposition diagonal matrix of its likelihood and…
Modal logics for reasoning about the power of coalitions capture the notion of effectivity functions associated with game forms. The main goal of coalition logics is to provide formal tools for modeling the dynamics of a game frame whose…