45,295 research outputs found
Finite-Degree Predicates and Two-Variable First-Order Logic
We consider two-variable first-order logic on finite words with a fixed
number of quantifier alternations. We show that all languages with a neutral
letter definable using the order and finite-degree predicates are also
definable with the order predicate only. From this result we derive the
separation of the alternation hierarchy of two-variable logic on this
signature
Web and Semantic Web Query Languages
A number of techniques have been developed to facilitate
powerful data retrieval on the Web and Semantic Web. Three categories
of Web query languages can be distinguished, according to the format
of the data they can retrieve: XML, RDF and Topic Maps. This article
introduces the spectrum of languages falling into these categories
and summarises their salient aspects. The languages are introduced using
common sample data and query types. Key aspects of the query
languages considered are stressed in a conclusion
Semantics and Validation of Shapes Schemas for RDF
We present a formal semantics and proof of soundness for shapes schemas, an
expressive schema language for RDF graphs that is the foundation of Shape
Expressions Language 2.0. It can be used to describe the vocabulary and the
structure of an RDF graph, and to constrain the admissible properties and
values for nodes in that graph. The language defines a typing mechanism called
shapes against which nodes of the graph can be checked. It includes an
algebraic grouping operator, a choice operator and cardinality constraints for
the number of allowed occurrences of a property. Shapes can be combined using
Boolean operators, and can use possibly recursive references to other shapes.
We describe the syntax of the language and define its semantics. The
semantics is proven to be well-defined for schemas that satisfy a reasonable
syntactic restriction, namely stratified use of negation and recursion. We
present two algorithms for the validation of an RDF graph against a shapes
schema. The first algorithm is a direct implementation of the semantics,
whereas the second is a non-trivial improvement. We also briefly give
implementation guidelines
Named Models in Coalgebraic Hybrid Logic
Hybrid logic extends modal logic with support for reasoning about individual
states, designated by so-called nominals. We study hybrid logic in the broad
context of coalgebraic semantics, where Kripke frames are replaced with
coalgebras for a given functor, thus covering a wide range of reasoning
principles including, e.g., probabilistic, graded, default, or coalitional
operators. Specifically, we establish generic criteria for a given coalgebraic
hybrid logic to admit named canonical models, with ensuing completeness proofs
for pure extensions on the one hand, and for an extended hybrid language with
local binding on the other. We instantiate our framework with a number of
examples. Notably, we prove completeness of graded hybrid logic with local
binding
Equational reasoning with context-free families of string diagrams
String diagrams provide an intuitive language for expressing networks of
interacting processes graphically. A discrete representation of string
diagrams, called string graphs, allows for mechanised equational reasoning by
double-pushout rewriting. However, one often wishes to express not just single
equations, but entire families of equations between diagrams of arbitrary size.
To do this we define a class of context-free grammars, called B-ESG grammars,
that are suitable for defining entire families of string graphs, and crucially,
of string graph rewrite rules. We show that the language-membership and
match-enumeration problems are decidable for these grammars, and hence that
there is an algorithm for rewriting string graphs according to B-ESG rewrite
patterns. We also show that it is possible to reason at the level of grammars
by providing a simple method for transforming a grammar by string graph
rewriting, and showing admissibility of the induced B-ESG rewrite pattern.Comment: International Conference on Graph Transformation, ICGT 2015. The
final publication is available at Springer via
http://dx.doi.org/10.1007/978-3-319-21145-9_
- …