The Propositional Logic of Elementary Tasks
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: iff 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.
Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1038234610
Digital Object Identifier: doi:10.1305/ndjfl/1038234610
Mathematical Reviews number (MathSciNet): MR1932228
Zentralblatt MATH identifier: 1015.03027