  Logic can define how agents are provided or denied access to resources, how
to interlink resources using mining processes and provide users with choices
for possible next steps in a workflow. These decisions are for the most part
hidden, internal to machines processing data. In order to exchange this
internal logic a portable Web logic is required which the Semantic Web could
provide. Combining logic and data provides insights into the reasoning process
and creates a new level of trust on the Semantic Web. Current Web logics
carries only a fragment of first-order logic (FOL) to keep exchange languages
decidable or easily processable. But, this is at a cost: the portability of
logic. Machines require implicit agreements to know which fragment of logic is
being exchanged and need a strategy for how to cope with the different
fragments. These choices could obscure insights into the reasoning process. We
created RDF Surfaces in order to express the full expressivity of FOL including
saying explicitly `no'. This vision paper provides basic principles and
compares existing work. Even though support for FOL is semi-decidable, we argue
these problems are surmountable. RDF Surfaces span many use cases, including
describing misuse of information, adding explainability and trust to reasoning,
and providing scope for reasoning over streams of data and queries. RDF
Surfaces provide the direct translation of FOL for the Semantic Web. We hope
this vision paper attracts new implementers and opens the discussion to its
formal specification.
