Numerate Web components for RDF4J

This is an RDF4J SAIL implementation for mathematical computations with RDF.

Numerate Web is based on OpenMath to define formulas for running spreadsheet-like calculations on RDF data. These formulas can be expressed in POPCORN-LD, a simple human-friendly syntax for mathematical objects that is also compatible with RDF. For example, a simple formula for the area of a rectangle with the sides a and b can be expressed as:

@a * @b

The area of a triangle can be calculated using its semi perimeter $s via:

$s := (@a + @b + @c) / 2; root($s * ($s - @a) * ($s - @b) * ($s - @c), 2)

The formulas can be defined in Numerate Web rules files .nwrules using a Manchester inspired syntax:

polygons.nwrules

Prefix: : <http://example.org/>

Class: Rectangle
  Constraint:
    area = @a * @b

Class: Triangle
  Constraint:
    area = $s := @semiPerimeter; root($s * ($s - @a) * ($s - @b) * ($s - @c), 2),
    semiPerimeter = (@a + @b + @c) / 2

Alternatively, the rules can be represented in RDF as shown in the following example:

polygons.ttl

@prefix :       <http://example.org/> .
@prefix mathrl: <http://numerateweb.org/vocab/math/rules#> .
@prefix sh:     <http://www.w3.org/ns/shacl#> .
@prefix owl:    <http://www.w3.org/2002/07/owl#> .

: sh:declare [
  sh:prefix "" ; sh:namespace "http://example.org/"^^xsd:anyURI ;
] .

:Rectangle a owl:Class ; mathrl:constraint [
  a mathrl:Constraint ; sh:prefixes : ;
  mathrl:onProperty :area ;
  mathrl:expressionString  "@a * @b"
] .

:Triangle a owl:Class ; mathrl:constraint [
  a mathrl:Constraint ; sh:prefixes : ;
  mathrl:onProperty :area ;
  mathrl:expressionString "$s := @semiPerimeter; root($s * ($s - @a) * ($s - @b) * ($s - @c), 2)"
], [
  a mathrl:Constraint ; sh:prefixes : ;
  mathrl:onProperty :semiPerimeter ;
  mathrl:expressionString
  "(@a + @b + @c) / 2"
] .

Features

• ✓ RDF4J stackable SAIL

• ✓ incremental recomputation

  • changes to property values

  • schema changes

• ✓ named graphs support

  • use owl:imports to define readable graphs

  • new triples for resources are stored in same graph as their rdf:type declarations

• ✓ express formulas in:

  • POPCORN-LD

  • OpenMath-RDF

• ✓ planned:

  • ❏ support quantities and units (QUDT and others)

  • ❏ bi-directional conversion between OpenMath-RDF and POPCORN-LD

Structure of the repository

examples

Example programs and resources for using the Numerate Web RDF4J SAIL.

sail

Implementation and tests of the Numerate Web RDF4J SAIL.

Usage

The class NumerateWebSail is a stackable RDF4J SAIL. It can be combined with an RDF4J store implementing the NotifyingSail interface as follows:

import org.eclipse.rdf4j.repository.Repository;
import org.eclipse.rdf4j.repository.RepositoryConnection;
import org.eclipse.rdf4j.repository.sail.SailRepository;
import org.eclipse.rdf4j.sail.memory.MemoryStore;
import org.numerateweb.rdf4j.NumerateWebSail;

// ...

MemoryStore store = new MemoryStore();
NumerateWebSail sail = new NumerateWebSail(store);
// enable or disable incremental inference; default is enabled
sail.setIncrementalInference(true);
Repository repository = new SailRepository(sail);

Building all modules

• This is a plain Maven project.

• A full build can be executed via mvn package