Explore the foundations of tensorial logic and its relationship to dialogue games and categories in this 33-minute lecture by Paul Andre Mellies. Delve into a primitive logic of tensor and negation that refines linear logic by relaxing the hypothesis of involutive linear negation. Discover how tensorial logic provides a proof-theoretic and algebraic account of the dialogical interpretation of proofs and programs, while examining the mechanisms at work in double negation translations. Gain insights into the connections between tensorial logic, dialogue games, and dialogue categories. For those interested in further exploration, additional resources on tensorial logic and related topics are provided.