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Explore advanced concepts in quantitative logic through this Oxford seminar that delves into p-means as quantitative analogues of first-order quantifiers and their application in constructing hyperdoctrines valued in enriched graded preorders. Learn how p-means provide a mathematical framework for extending classical logical quantifiers into quantitative settings, offering new perspectives on logical reasoning with degrees rather than binary truth values. Discover the construction methodology for hyperdoctrines that serve as the intended semantics for first-order quantitative linear logic, bridging category theory, logic, and quantitative reasoning. Examine the theoretical foundations that connect enriched category theory with logical systems, particularly focusing on graded preorders and their role in semantic structures. Gain insights into how quantitative linear logic extends traditional linear logic by incorporating quantitative aspects while maintaining its resource-sensitive nature. Understand the mathematical machinery behind hyperdoctrines and their significance in providing semantic models for advanced logical systems that can handle both qualitative and quantitative information.
