David Corfield continuous logic, probability, quantum

• Successive enrichment + symmetrisation from different quantales.

• $[0, \infty]$ as metric space

• Three quantales on $[0, 1]$ (pair). One from reflection, one from mapping exp(-p).

• Partial entailment, etc. Is there anything like the triangle inequality for this?

• What does continuous logic do beyond other $[0,1]$ logics? All continuous connectives.

• Continuous logic for SymMet. Nice category. Is this why Cho finds a continuous subobject classifier?

• If (co)completeness of metric space brings in monoidal mutliplication and actions, what of space of models? What is a locally finitely presented metric space? Is it that a Lewisian metric space of worlds appears?

• Dubois and Prade, possibility logic.

• Counterfactuals, like predictions. Metric space for Lewis. Counterfactual probability, Had you taken an aspirin, there’s a 60% chance…

• Dependency: Had jack fallen down, Jill would have come tumbling after. Had I bought a goldfish, there’s a 50% chance I would have killed it by now.

• Duality theorems for various doctrines.

• What happens when Bohrification meets linear DTT? Discussion

• What would it be to ‘sugar’ linear DTT?

• $D(\sum_{x:A}B(x))$ and $\prod_{x:A}D(B(x))$, disintegration discussion.