Notre Dame Journal of Formal Logic

The Propositional Logic of Elementary Tasks

Giorgi Japaridze

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: $\mbox{\textbf{TSKp}}\vdash\alpha$ 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

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

Dates
First available: 25 November 2002

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

Subjects
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

Keywords
tasks game semantics linear logic substructural logics

Citation

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


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