## 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: ${\textbf{TSKp}}\vdash\alpha$ 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 in Project Euclid: 25 November 2002

https://projecteuclid.org/euclid.ndjfl/1038234610

Digital Object Identifier
doi:10.1305/ndjfl/1038234610

Mathematical Reviews number (MathSciNet)
MR1932228

Zentralblatt MATH identifier
1015.03027

#### Citation

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