Light, elementary and soft linear logics are formal systems derived from Linear Logic, enjoying remarkable normalization properties. In this paper we prove decidability of Elementary A ne Logic, EAL. The result is obtained by semantical means, first defining a class of phase models for EAL and then proving soundness and (strong) completeness, following Okada s technique. Phase models for Light A ne Logic and Soft Linear Logic are also defined and shown complete.
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