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We present a formal semantics and proof of soundness for shapes schemas, anexpressive schema language for RDF graphs that is the foundation of ShapeExpressions Language 2.0. It can be used to describe the vocabulary and thestructure of an RDF graph, and to constrain the admissible properties andvalues for nodes in that graph. The language defines a typing mechanism calledshapes against which nodes of the graph can be checked. It includes analgebraic grouping operator, a choice operator and cardinality constraints forthe number of allowed occurrences of a property. Shapes can be combined usingBoolean operators, and can use possibly recursive references to other shapes.  We describe the syntax of the language and define its semantics. Thesemantics is proven to be well-defined for schemas that satisfy a reasonablesyntactic restriction, namely stratified use of negation and recursion. Wepresent two algorithms for the validation of an RDF graph against a shapesschema. The first algorithm is a direct implementation of the semantics,whereas the second is a non-trivial improvement. We also briefly giveimplementation guidelines.

Semantics and Validation of Shapes Schemas for RDF