Application of linear logic to simulation

Thomas L. Clarke

doi:10.1117/12.319347

24 August 1998 Application of linear logic to simulation

Thomas L. Clarke

Proceedings Volume 3369, Enabling Technology for Simulation Science II; (1998) https://doi.org/10.1117/12.319347
Event: Aerospace/Defense Sensing and Controls, 1998, Orlando, FL, United States

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 proportion 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 discuses 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 and its 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 eigen functions of dynamic differential operators. Particularly suggestive are possible relations between complexity result for linear logic and non-computability results for dynamical systems.

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Thomas L. Clarke "Application of linear logic to simulation", Proc. SPIE 3369, Enabling Technology for Simulation Science II, (24 August 1998); https://doi.org/10.1117/12.319347

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KEYWORDS

Logic

Quantum mechanics

Dynamical systems

Fuzzy logic

Quantum physics

Superposition

Computer programming

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