A Hybrid Linear Logic for Constrained Transition Systems

TL;DR

This paper introduces a hybrid linear logic framework that incorporates constraints into the logical representation of transition systems, enabling modeling of complex systems like stochastic processes.

Contribution

It presents a modal extension of intuitionistic linear logic with constraint indexing and hybrid connectives, along with a focused sequent calculus for constrained transition systems.

Findings

Provides an encoding of the synchronous stochastic pi-calculus

Enables internalization of transition system rules within the logic

Supports modeling of temporal, stochastic, and probabilistic constraints

Abstract

Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal extension of intuitionistic linear logic where logical truth is indexed by constraints and hybrid connectives combine constraint reasoning with logical reasoning. The logic has a focused cut-free sequent calculus that can be used to internalize the rules of particular constrained transition systems; we illustrate this with an adequate encoding of the synchronous stochastic pi-calculus.