Title

Application of linear logic to simulation

Abstract

Linear logic, since its introduction by Girard in 1987 has proven expressive and powerful. Linear logic has provided natural encodings of Turing machines, Petri nets and other computational models. Linear logic is also capable of naturally modeling resource dependent aspects of reasoning. The distinguishing characteristic of linear logic is that it accounts for resources; two instances of the same variable are considered differently from a single instance. Linear logic thus must obey a form of the linear superposition principle. A proposition can be reasoned with only once, unless a special operator is applied. Informally, linear logic distinguishes two kinds of conjunction, two kinds of disjunction, and also introduces a modal storage operator that explicitly indicates propositions that can be reused. This paper discusses the application of linear logic to simulation. A wide variety of logics have been developed; in addition to classical logic, there are fuzzy logics, affine logics, quantum logics, etc. All of these have found application in simulations of one sort or another. The special characteristics of linear logic andits benefits for simulation will be discussed. Of particular interest is a connection that can be made between linear logic and simulated dynamics by using the concept of Lie algebras and Lie groups. Lie groups provide the connection between the exponential modal storage operators of linear logic and the eigenfunctions of dynamic differential operators. Particularly suggestive are possible relations between complexity results for linear logic and non-computablity results for dynamical systems.

Publication Date

12-1-1998

Publication Title

Proceedings of SPIE - The International Society for Optical Engineering

Volume

3369

Number of Pages

314-318

Document Type

Article; Proceedings Paper

Personal Identifier

scopus

DOI Link

https://doi.org/10.1117/12.319347

Socpus ID

0032404505 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0032404505

This document is currently not available here.

Share

COinS