Intuitionistic Basis for Input/Output Logic

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Abstract

It is shown that I/O logic can be based on intuitionistic logic instead of classical logic. More specifically, it is established that, when going intuitionistic, a representation theorem is still available for three of the four (unconstrained) original I/O operations. The trick is to see a maximal consistent set as a saturated one. The axiomatic characterization is as in the classical case. Therefore, the choice between the two logics does not make any difference for the resulting framework.

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Parent, X., Gabbay, D., & Torre, L. van der. (2014). Intuitionistic Basis for Input/Output Logic. In Outstanding Contributions to Logic (Vol. 3, pp. 263–286). Springer. https://doi.org/10.1007/978-94-007-7759-0_13

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