A semantics and a logic for Fuzzy Arden Syntax

Abstract

Fuzzy programming languages, such as the Fuzzy Arden Syntax (FAS), are used to describe behaviours which evolve in a fuzzy way and thus cannot be characterized neither by a Boolean outcome nor by a probability distribution. This paper introduces a semantics for FAS, focusing on the weighted parallel interpretation of its conditional statement. The proposed construction is based on the notion of a fuzzy multirelation which associates with each state in a program a fuzzy set of weighted possible evolutions. The latter is parametric on a residuated lattice which models the underlying semantic 'truth space'. Finally, a family of dynamic logics, equally parametric on the residuated lattice, is introduced to reason about FAS programs.

Weighted synchronous automata

“…This paper was born out of a challenge: having previously worked with the Fuzzy Arden Syntax (FAS) (Gomes et al 2021), a fuzzy, imperative language used for medical diagnosis and prescription of medical procedures, our aim was to introduce a specific kind of automata, and corresponding languages, are able to express the behaviour of the underlying fuzzy systems.…”

Special issue “International Symposium on Molecular Logic and Computational Synthetic Biology: MLCSB18”

“…This special issue includes seven peer-reviewed articles about synthetic biology, whose aim is to develop formal models for biological-like phenomena, specially in the context of molecular logic (Djordević and Silva 2019;Nemati and Torres 2020;Santiago et al 2020;Braccini et al 2020;Moreira et al 2020;Tavares et al 2021;Veloz and Flores 2021). Molecular logic focuses on understanding logical and operational aspects on molecules and their interactions, providing a fruitful conceptual crossover between chemistry and computation with unsuspected applications.…”

“…The aim of MLSCB18 was harnessing logical and algebraic methods for modeling and verifying systems on the interaction of Nature and Computation, around two main themes, which can also serve to split the list of articles published in this special issue: The development of biological computation models and devices (Djordević and Silva 2019;Braccini et al 2020;Tavares et al 2021;Veloz and Flores 2021), and the application of new computing paradigms to the design of biological systems (Nemati and Torres 2020;Santiago et al 2020;Moreira et al 2020).…”