The propositional logic of elementary tasks. (English) Zbl 1015.03027

Japaridze, Giorgi

Notre Dame J. Formal Logic 41, No. 2, 171-183 (2000).

Summary: 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: \(\mathbf{TSKp}\vdash \alpha\) 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.

MSC:

03B47	Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
03B70	Logic in computer science
68T27	Logic in artificial intelligence

Keywords:

game semantics; linear logic

References:

[1]	Blass, A., ”A game semantics for linear logic”, Annals of Pure and Applied Logic , vol. 56 (1992), pp. 183–220. · Zbl 0763.03008
[2]	Girard, J.-Y., ”Linear logic”, Theoretical Computer Science , vol. 50 (1987), pp. 1–102. · Zbl 0625.03037
[3]	Japaridze, G., ”A constructive game semantics for the language of linear logic”, Annals of Pure and Applied Logic , vol. 85 (1997), pp. 87–156. · Zbl 0882.03057