CATEGORICAL SEMANTICS OF METRIC SPACES AND CONTINUOUS LOGIC

Monitoring Dense-Time, Continuous-Semantics, Metric Temporal Logic

Quantum Computation, Categorical Semantics and Linear Logic

We develop a type theory and provide a denotational semantics for a simple fragment of the quantum lambda calculus, a formal language for quantum computation based on linear logic. In our semantics, variables inhabit certain Hilbert bundles, and computations are interpreted as the appropriate inner product preserving maps between Hilbert bundles. These bundles and maps form a symmetric monoidal...

Categorical semantics of non-commutative logic

Previous work [9, 1, 10] was devoted to proof nets and sequent calculus for NL. Here we study the categorical semantics of NL. One can say that proof nets constitute already a semantics of proofs of NL, but on one hand the extension to non-multiplicative connectives is delicate (boxes) and on the other hand one would like to have a semantics that is more general than syntax (correctness) and cl...

Relating Categorical Semantics for Intuitionistic Linear Logic

There are several kinds of linear typed calculus in the literature, some with their associated notion of categorical model. Our aim in this paper is to systematise the relationship between three of these linear typed calculi and their models. We point out that mere soundness and completeness of a linear typed calculus with respect to a class of categorical models are not sufficient to identify ...

A categorical semantics for fuzzy predicate logic

Fuzzy Sets and Systems 161 (2010) 412-432 Elsevier www.elsevier.com/locate/fss A Categorical Semantics for Fuzzy Predicate Logic