The Propositional Logic of Elementary Tasks

Notre Dame Journal of Formal Logic 41 (2):171-183 (2000)
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.
Keywords tasks   game semantics   linear logic   substructural logics
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DOI 10.1305/ndjfl/1038234610
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Giorgi Japaridze (2003). Introduction to Computability Logic. Annals of Pure and Applied Logic 123 (1-3):1-99.

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