Open Access
2000 The Propositional Logic of Elementary Tasks
Giorgi Japaridze
Notre Dame J. Formal Logic 41(2): 171-183 (2000). DOI: 10.1305/ndjfl/1038234610

Abstract

The paper introduces a semantics for the language of propositional additive-multiplicative linear logic. It understands formulas as tasks that are to be accomplished by an agent (machine, robot) working as a slave for its master (user, environment). This semantics can claim to be a formalization of the resource philosophy associated with linear logic when resources are understood as agents accomplishing tasks. I axiomatically define a decidable logic TSKp and prove its soundness and completeness with respect to the task semantics in the following intuitive sense: ${\textbf{TSKp}}\vdash\alpha$ iff $\alpha$ can be accomplished by an agent who has nothing but its intelligence (that is, no physical resources or external sources of information) for accomplishing tasks.

Citation

Download Citation

Giorgi Japaridze. "The Propositional Logic of Elementary Tasks." Notre Dame J. Formal Logic 41 (2) 171 - 183, 2000. https://doi.org/10.1305/ndjfl/1038234610

Information

Published: 2000
First available in Project Euclid: 25 November 2002

zbMATH: 1015.03027
MathSciNet: MR1932228
Digital Object Identifier: 10.1305/ndjfl/1038234610

Subjects:
Primary: 03B47
Secondary: 03B70 , 68T27

Keywords: Game semantics , linear logic , substructural logics , tasks

Rights: Copyright © 2000 University of Notre Dame

Vol.41 • No. 2 • 2000
Back to Top