What is the problem?
The Web of Data (WOD) connects data in a similar way as the WWW connects documents. Atomic data-units called resources are connected via typed links with arbitrary resources anywhere on the Web, and together these RDF triples form a gigantic graph of linked data. The meaning of the types can be fixed using standardised schema and ontology languages such as RDFS and OWL. The semantics of these languages are based on logical paradigms that were designed for small and hand-made knowledge bases, and come with a classical model-theory assigning truth to formulae, and entailment based on this truth. In a highly complex, dynamic, context-dependent, opinionated, contradictory and multi-dimensional semantic network as the WOD, these Semantics are insufficient, as they are one-dimensional, often prone to logical fallacies, and usually intractable.
On the Web in general, and the Web of Data in particular, almost every bit of information is context-dependent, biased towards a particular viewpoint, opinionated, dated, uncertain or vague. The WOD is a market-place of ideas, not a database, and has to be dealt with accordingly. As making the representational languages more complex is not an option, we have to adapt the formal semantics of existing formalisms to the new requirements.
Pragmatic semantics integrate different world-views instead of defining meaning with respect to a single one. The idea is to make as much information in the data explicit, and turn it into first-class semantics citizens. First, it allows integrating classic model-theoretic notions of truth with explicit knowledge about the structure of the knowledge base. But also semantic meta-data, such as popularity, scarcity, abnormality, etc., and even background knowledge from other sources, can be integrated.
Interoperability is then achieved by enriching an ontology with meta-information about semantic orderings, as well as agreement on the weighting of orderings. As there are possibly several pragmatic closures (different solutions on the Pareto-front) also agreement on the weighting of features is required. We will refer to the entailment induced by a given set of orderings as an instantiation of the family of pragmatic semantics.