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

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
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### 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
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