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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… (More)

Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic, but also in probabilistic and classical logic. This relation is presented by a long series of examples, some of them… (More)

Coinductive predicates express persisting " safety " specifications of transition systems. Previous observations by Hermida and Jacobs identify coinductive predicates as suitable final coalgebras in a fibration—a categorical abstraction of predicate logic. In this paper we follow the spirit of a seminal work by Worrell and study final sequences in a… (More)

We present a model of Selinger and Valiron's quantum lambda calculus based on von Neumann algebras, and show that the model is adequate with respect to the operational semantics. 1 Introduction In 1925, Heisenberg realised, pondering upon the problem of the spectral lines of the hydrogen atom, that a physical quantity such as the x-position of an electron… (More)

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