Notre Dame Journal of Formal Logic

The Propositional Logic of Elementary Tasks

Giorgi Japaridze


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.

Article information

Notre Dame J. Formal Logic, Volume 41, Number 2 (2000), 171-183.

First available in Project Euclid: 25 November 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52}
Secondary: 03B70: Logic in computer science [See also 68-XX] 68T27: Logic in artificial intelligence

tasks game semantics linear logic substructural logics


Japaridze, Giorgi. The Propositional Logic of Elementary Tasks. Notre Dame J. Formal Logic 41 (2000), no. 2, 171--183. doi:10.1305/ndjfl/1038234610.

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