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  1. Resource Modalities in Tensor Logic.Paul-André Melliès & Nicolas Tabareau - 2010 - Annals of Pure and Applied Logic 161 (5):632-653.
    The description of resources in game semantics has never achieved the simplicity and precision of linear logic, because of the misleading conception that linear logic is more primitive than game semantics. Here, we defend the opposite view, and thus advocate that game semantics is conceptually more primitive than linear logic. This revised point of view leads us to introduce tensor logic, a primitive variant of linear logic where negation is not involutive. After formulating its categorical semantics, we interpret tensor logic (...)
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  • Computational Adequacy for Recursive Types in Models of Intuitionistic Set Theory.Alex Simpson - 2004 - Annals of Pure and Applied Logic 130 (1-3):207-275.
    This paper provides a unifying axiomatic account of the interpretation of recursive types that incorporates both domain-theoretic and realizability models as concrete instances. Our approach is to view such models as full subcategories of categorical models of intuitionistic set theory. It is shown that the existence of solutions to recursive domain equations depends upon the strength of the set theory. We observe that the internal set theory of an elementary topos is not strong enough to guarantee their existence. In contrast, (...)
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