An Introduction to Effectus Theory

Understand

Effectus theory is a new branch of categorical logic that aims to capture the essentials of quantum logic, with probabilistic and Boolean logic as special cases.

• Predicates in effectus theory are not subobjects having a Heyting algebra structure, like in topos theory, but `characteristic' functions, forming effect algebras.
• Such effect algebras are algebraic models of quantitative logic, in which double negation holds.
• Effects in quantum theory and fuzzy predicates in probability theory form examples of effect algebras.