The aim of the paper is to work towards a generalisation of coalgebraic logic enriched over a commutative quantale. Previous work has shown how to dualise the coalgebra type functor T : Ω-Cat //Ω-Cat in order to obtain the modal operators and axioms describing transitions of type T . Here we give a logical description of the dual of Ω-Cat.

This paper is about omitting types in logic of metric structures introduced by Ben Yaacov, Berenstein, Henson and Usvyatsov. While a complete type is omissible in some model of a countable complete theory if and only if it is not principal, this is not true for the incomplete types by a result of Ben Yaacov. We prove that there is no simple test for determining whether a type is omissible in a ...

A finite metric tree is a finite connected graph that has no cycles, endowed with an edge weighted path metric. Finite metric trees are known to have strict 1-negative type. In this paper we introduce a new family of inequalities (1) that encode the best possible quantification of the strictness of the non trivial 1-negative type inequalities for finite metric trees. These inequalities are suff...

In recent years, quadratic weighted kappa has been growing in popularity in the machine learning community as an evaluation metric in domains where the target labels to be predicted are drawn from integer ratings, usually obtained from human experts. For example, it was the metric of choice in several recent, high profile machine learning contests hosted on Kaggle : www.kaggle.com/c/asap-aes , ...

The aim of this paper is twofold: to characterize contextual logic programs by means of metric semantics and to argue the usefulness of metric characterizations for formally reasoning about program properties. A new denotational semantics of contextual logic programs is proposed. It is deened compositionally, without any help of any declarative paradigm and of any transition system. Following t...

Metric Temporal Logic (MTL) is a widely-studied real-time extension of Linear Temporal Logic. In this paper we survey results about the complexity of the satisfiability and model checking problems for fragments of MTL with respect to different semantic models. We show that these fragments have widely differing complexities: from polynomial space to non-primitive recursive and even undecidable. ...

Current approaches to monitoring real-time properties suffer either from unbounded space requirements or lack of expressiveness. In this paper, we adapt a separation technique enabling us to rewrite arbitrary MTL formulas into LTL formulas over a set of atoms comprising bounded MTL formulas. As a result, we obtain the first trace-length independent online monitoring procedure for full MTL.

Program execution traces can be so large in practical testing and monitoring applications that it would be very expensive, if not impossible, to store them for detailed analysis. Monitoring execution traces without storing them, can be a nontrivial matter for many specification formalisms, because complex formulae may require a considerable amount of information about the past. Metric temporal ...

We study translations from Metric Temporal Logic (MTL) over the natural numbers to Linear Temporal Logic (LTL). In particular, we present two approaches for translating from MTL to LTL which preserve the EXPSPACE complexity of the satisfiability problem for MTL. Our translations, thus, allow us to utilise LTL provers to solve MTL satisfiability problems.

GEOMETRIES TOPOLOGICAL SPACES RELATIONS SETS METRIC SPACES Add open set axioms MEASURABLE SPACES LOWER PREDICATE CALCULUS