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Communication Dans Un Congrès Année : 2018

Ribbon Tensorial Logic

Résumé

We introduce a topologically-aware version of tensorial logic, called ribbon tensorial logic. To every proof of the logic, we associate a ribbon tangle which tracks the flow of tensorial negations inside the proof. The translation is functorial: it is performed by exhibiting a correspondence between the notion of dialogue category in proof theory and the notion of ribbon category in knot theory. Our main result is that the translation is also faithful: two proofs are equal modulo the equational theory of ribbon tensorial logic if and only if the associated ribbon tangles are equal up to topological deformation. This “proof-as-tangle” theorem may be understood as a coherence theorem for balanced dialogue categories, and as a mathematical foundation for topological game semantics.
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Dates et versions

hal-02436302 , version 1 (12-01-2020)

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Paul-André Melliès. Ribbon Tensorial Logic. Thirty-Third Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2018), Jul 2018, Oxford, United Kingdom. ⟨10.1145/3209108.3209129⟩. ⟨hal-02436302⟩
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