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Explore quantitative logic through this Oxford seminar where judgments are valued in real numbers rather than traditional binary truth values. Discover how this approach, following Lawvere's framework, enables treating addition as an additive connective in Girard's sense while maintaining excellent structural properties. Learn about the approximation of 'hard' connectives with 'soft' ones using the full spectrum of sums that multiplication distributes over, with practical applications in machine learning. Examine a sequent calculus for a quantitative version of linear logic, presented as ongoing collaborative research with Atkey, Grellois, and Komendantskaya. Gain insights into how quantitative logic bridges theoretical foundations with computational applications, offering new perspectives on logical reasoning and its implementation in modern computational contexts.
