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.
Domaines
Logique en informatique [cs.LO] Informatique et langage [cs.CL] Algèbres quantiques [math.QA] Géométrie algébrique [math.AG] Informatique et théorie des jeux [cs.GT] Logiciel mathématique [cs.MS] Théorie et langage formel [cs.FL] Langage de programmation [cs.PL] Catégories et ensembles [math.CT] Logique [math.LO] Topologie algébrique [math.AT]
Origine : Fichiers produits par l'(les) auteur(s)
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