We study thorn forking and rosiness in the context of continuous logic. We prove that the Urysohn sphere is rosy (with respect to finitary imaginaries), providing the first example of an essentially continuous unstable theory with a nice notion of independence. In the process, we show that a real rosy theory which has weak elimination of finitary imaginaries is rosy with respect to finitary ima...

The ultraproduct construction is generalized to $p$-ultramean constructions ($1\leqslant p<\infty$) by replacing ultrafilters with finitely additive measures. These correspond the linear fragments $\mathscr L^p$ of continuous logic. A powermean variant Keisler-Shelah isomorphism theorem proved for L^p$. It then that L^p$-sentences (and their approximations) are exactly those sentences logic whi...

Continuous logic extends the multi-valued Lukasiewicz logic by adding a halving operator on propositions. This extension is designed to give a more satisfactory model theory for continuous structures. The semantics of these logics can be given using specialisations of algebraic structures known as hoops and coops. As part of an investigation into the metatheory of propositional continuous logic...

We define an invariant of a multi-valued logic gate by considering the number of certain threshold functions associated with the gate. We call this invariant the continuous sensitivity of the gate. We discuss a method for analysing continuous sensitivity of a multi-valued logic gate by using experimental data about the gate. In particular, we will show that this invariant provides a lower bound...

Article history: Available online xxxx We present a novel temporal logic for expressing properties of behaviour in context. The logic is applied to models of continuous processes, specifically using the continuous π-calculus as a modelling language for biochemical systems. The logic allows the expression of the temporal behaviour of a system when placed in the context of another system. Here we...

Hybrid systems are real-time systems consisting of both continuous and discrete components. This thesis presents deductive and diagrammatic methodologies for proving point-based and intervalbased properties of hybrid systems, where the hybrid system is modeled in either a sampling semantics or a continuous semantics. Under a sampling semantics the behavior of the system consists of a discrete n...