Lax Liftings and Lax Distributive Laws

Lax Distributive Laws for Topology, Ii

For a small quantaloid Q we consider four fundamental 2-monads T on Q-Cat, given by the presheaf 2-monad P and the copresheaf 2-monad P†, as well as their two composite 2-monads, and establish that they all laxly distribute over P. These four 2-monads therefore admit lax extensions to the category Q-Dist of Q-categories and their distributors. We characterize the corresponding (T,Q)-categories ...

Lax Distributive Laws for Topology, I

For a quantaloid Q, considered as a bicategory, Walters introduced categories enriched in Q. Here we extend the study of monad-quantale-enriched categories of the past fifteen years by introducing monad-quantaloid-enriched categories. We do so by making lax distributive laws of a monad T over the discrete presheaf monad of the small quantaloid Q the primary data of the theory, rather than the l...

Propositional Lax Logic Propositional Lax Logic

We investigate a peculiar intuitionistic modal logic, called Propositional Lax Logic (PLL), which has promising applications to the formal veri cation of computer hardware. The logic has emerged from an attempt to express correctness `up to' behavioural constraints | a central notion in hardware veri cation | as a logical modality. As a modal logic it is special since it features a single modal...

Patterns and Lax Lambda Laws for Relational and Imperative Programming

Quantiied Lax Logic Quantiied Lax Logic

Lax Logic is an intuitionistic modal logic which has so far been investigated at the propositional level. It has shown itself to have applications in the formal veriication of hardware|a logical modality is used to capture and express the correctness of speciicationsùp to' behavioural constraints. A translation from Quantiied Lax Logic to a quantiied classical modal logic is presented which ena...