Mulgara

MulgaraOpen Source Semantic Web

Paul Gearon

[email protected]

mailto:[email protected]


Mulgara

RDF Database

Open Source

Written in Java

Over 320,000 lines of code

Math in MulgaraGraphs and Trees (Chapter 5)

Recursive Algorithms (Chapter 2)

Functions (Chapter 4)

Formal Languages and Algebras (Chapter 8)

Graph Algorithms (Chapter 6)

Prolog, Rules, Logic (Chapter 1)

Sets (Chapter 3)

Math in MulgaraGraphs and Trees (Chapter 5)

Recursive Algorithms (Chapter 2)

Functions (Chapter 4)

Formal Languages and Algebras (Chapter 8)

Graph Algorithms (Chapter 6)

Prolog, Rules, Logic (Chapter 1)

Sets (Chapter 3)

All programming uses Boolean Logic (Chapter 7)

RDF

A simple Description Logic (Chapter 1)

Provides structure for data in the Semantic Web

Simple data format of binary predicates, or Triples

Triples combine to form a directed graph

RDF

Simple

Describes schemas, ontologies, and instance data

Foundation for complex logic systems like OWL

Describes relationships between arbitrary things

Forms a graph (Chapter 5)

Can be used to describe anything

RDF Triples

:David :knows :Paul

:knows(:David, :Paul)

:Paul:David

:knows

RDF Graph

:David

:Person

:Paul

Dr David Smith


:knows

rdf:typerdf:type

:email

:fullname:title

mailto:david@e

mailto:david@e





RDF Graph

:David

:Person

:Paul

Dr David Smith


:knows

rdf:typerdf:type

:email

:fullname:title

:knows

:email

:fullname

:title

rdfs:domainrdfs:range

rdfs:domain

rdfs:domain

rdfs:domain

mailto:david@e

mailto:david@e





Storage

Speed

Fast storage

Quickly find what we want

Storage

Speed

Fast storage

Quickly find what we want

Index the data

Persistent Storage

Must be efficient in space

Smaller means more data

Smaller means faster read/write

Must support re-writable data

Indexed, rewritable data usually means regular sized data blocks

One Approach

Map URIs and strings to numbers

Map numbers back to URIs and strings

Store a triple as 3 numbers

see Adjacency Matrix (page 418)and Adjacency List (page 420)

:David :Paul

:Person

rdf:typerdf:type

:knows

Representation

:David rdf:type :Person:Paul rdf:type :Person:David :knows :Paul

3 4

5

11

2

rdf:type:knows:David:Paul:Person

1 2 3 4 5

3 1 5 4 1 5 3 2 4

Representation

:David rdf:type :Person:Paul rdf:type :Person:David :knows :Paul

Finding Triples

Sort by columns

3 1 5 3 2 4 4 1 5

3 1 5 4 1 5 3 2 4

3 2 4 3 1 5 4 1 5

S P O

S then P then O

P then O then S

O then S then P

Disk Structure

Linear layouts do not scale

Disk Structure

Linear layouts do not scale

Trees scale well

Trees

Scale well

Basis of every major database

Fast writing

Fast reading

Can be split over a network

Index Searches

Use a binary tree search on the trees (page 456)

Logarithmic complexity

Blocks of data stored in tree nodes as stored data

Use a binary search on sorted data blocks (page 138)

Logarithmic complexity

Why Binary?

Wider trees have identical complexity (logarithmic)

Wider trees have fewer disk seeks

Linear effect on complexity, which has no effect

Wider trees have complex rebalancing

Better than Trees?

Hash Tables (pages 362-366)

Better than Trees?


Have constant complexity, BUT:

Use too much space (scaling issues)

Need to be expanded when they get too full

Great for smaller data sets in RAM

Better than Trees?


Have constant complexity, BUT:

Use too much space (scaling issues)

Need to be expanded when they get too full

Great for smaller data sets in RAM

Poor for disk usage - Good for clusters

Mapping

Bijective Function (page 339)

Store key/value pair, indexed by key

Trees order by keyDatatype ordering (lexical, numerical, dates, etc)

Can find ranges of dataFind all students enrolled between 1-1-2010 and 31-12-2010

Hashmaps have no ordering

Real Data Searches

Combination searches

“The list of people who know :Paul”

The list of people

AND

Things that know :Paul

Constraints

Bind a variable with a constraint

?x rdf:type :Person

?x :knows :Paul

Describe requirements with a formal language

Tucana Query Language (TQL)

SPARQL Protocol and RDF Query Language (SPARQL)

Query Languages

Formal language

Context Free Grammar

Chapter 8, section 8.4

SPARQL example:

SELECT ?personWHERE { ?person a :Person . ?person :knows :Paul}

Algebra

Formal language converted to an Algebra (Section 8.1)

Constraints are combined and manipulated algebraically

Optimization through algebraic manipulation

Example:

before optimization: ~600 seconds

after optimization: 0.8 seconds

Algebraic Operations

AND operations (Conjunctions)

Mergesort (page 179)

OR operations (Disjunctions)

Union then sort (Chapter 2)

Others

Filter, Minus, LeftJoin, Datatype, etc...

Graph Operations

List operations

Graph traversal

Transitivity (page 289)

Distance between nodes

Algorithm similar to Euler Path (page 490) on constrained graph

Ontologies

Formal representation of knowledge

Set of concepts in a domain

Relationship between concepts

Vocabularies for building ontologies expressed in RDF

RDF Schema (RDFS)Simple Knowledge Organization System (SKOS)Web Ontology Language (OWL)

Rules

RDF has few semantics

Support for higher languages through Rules (page 72)

Uses Prolog style language (page 64-71) to express Horn clauses (page 66), and therefore modus ponens (page 23)

RDFS, SKOS and most of OWL all supported through Rules

Rule Examples

P(B,X) :- owl:sameAs(A,B), P(A,X).

P(B,A) :- owl:SymmetricProperty(P), P(A,B).

owl:SymmetricProperty(owl:sameAs).

if A is the same as B (owl:sameAs), and A relates to X, then B relates to X the same way.

if P is a symmetric property (owl:SymmetricProperty), and P relates A to B, then P also relates B to A

owl:sameAs is a symmetric property

OWL Properties

Transitive Properties (page 289)

Symmetric/Asymmetric Properties (page 289)

Reflexive/Irreflexive Properties (page 289)

Functional/Inverse-Functional Properties (page 341)

Property inverses (page 342)

Disjoint properties (page 195)

OWL Classes

Defined with Set semantics (Chapter 3, section 3.1)

Handles both instance data (set membership, pg 187) and set descriptions

Types described with a Unary Predicate (pg 36, 188)RDF represents this with predicate of rdf:type

Existential (pg 36), Universal (pg 35), Complementary (pg 195), Cardinality (pg 320), and Datatype operations

OWL in Use

Represent schemas, similar to database schemas

Automated research for candidate drug treatments

NASA inventories

Mulgara

Documents

Transcript of Mulgara