The success of the Web of Data (WOD) is based on the thorough understanding of, and agreement upon, the semantics of data and ontologies. But the Web of Data as a whole is complex, and inherently messy, contextualised, opinionated, in short: the Web of Data is a market-place of ideas, rather than a database. Existing paradigms are inappropriate for dealing with this new type of knowledge structure. The urgency of dealing with the non-standard characteristics of the Web of Data has been recognised, and separate initiatives try to tackle its individual manifestations, e.g. inconsistencies, contexts, vagueness, provenance, etc. Tomorrow?s Web requires novel semantics with efficient (generic) implementations to ensure semantic clarity, reuse and interoperability. We recently introduced pragmatic semantics [29] as a new semantic paradigm integrating elements from market theory and classical semantics into a framework of optimisation over partial truth functions, each representing a particular world-view. We propose nature-based algorithms to implement those semantics. The main results will be 1) Well-understood formalisms for pragmatically interpreting semantic data on the Web. 2) Algorithms to calculate the related inferences, such as entailment and truth, and guidelines for using the new paradigm in application domains. 3) A system integrating various implementations of generic and specific multi-optimisation methods, implementations of a variety of partial truth-functions, and representation standards for semantic meta-data. 4) A thorough analytic and empirical evaluation of the proposed semantic paradigm.