HyperGraphDb

HyperGraphDB Motivation, Architecture and Applications

From Graph to HyperGraphs In a graph G=(V, E), V is a set and E a set of pairs e={v 1 , v 2 } from V . Take e to be any subset {v 1 ,…, v n } of V and you get a hypergraph. Study: set combinatorics, Claude Berge Applications: machine learning, database indexing and optimization, SAT

Directed Hypergraphs Type 1: partition a hyperedge into a head and a tail Type 2: make the hyperedge a tuple

HyperGraphDB Model Type 2 directed edges by default Support of Type 1 directed edges Undirected edges – maybe in the future V (nodes) + E (edges) = A (atoms) Care about set theoretic foundation? Look at Peter Aczel Non-well-founded sets Invented by Dr. Ben Goertzel et al. for an AGI system.

Benefits All representations automatically reified Higher-order logic Recursive buildup of structures: levels of abstraction contextualization N-ary relations lead to more compact and natural representations Example: between(New Jersey, New York, Boston)

Applications Artificial Intelligence: Ben Goertzel et al. – OpenCog AI (http://www.opencog.org) Harold Boley and Directed Recursive Labelnode Hypergraphs, circa 1977 Freebase is a 4-unform hypergraph Relational algebra: HyperGraphDB is essentially a dynamic schema relational DB. Computational Biology, see “Hypergraphs and Cellular Networks” by Steffen Klamt et al.

More Applications RDF – triple stores are conceptually hypergraphs Named RDF – quadruple stores, hypergraphs too General (type 2) directed hypergraphs proposed to the RDF community as well. Efficient RDF representation: System ∏ Topic Maps – perfect marriage OO Database

Architecture Model Layer Key-value Store Caching Primitive Storage Layer Indexing Querying & Graph Algorithms Events P2P Distribution Framework Applications: Topic Maps, WordNet, XSD, RDF Sail, OWL, Prolog, Neural Nets, Distributed Dataflow Processing Type System

HyperGraphDB Concepts Atom – links 0 or more other atoms, carries strongly typed value Value – arbitrary, doesn’t participate in linkage Type – a special kind of atom that manages value storage and interpretation Target Set – the set of atoms that an atom points to. Arity – size of the target set Incidence Set – the set of atoms pointing to an atom. Node – an atom with arity 0 (doesn’t point to anything) Link – an atom with arity > 0 (points to something)

Storage Architecture Two layers – primitive and model layer Primitive Layer – a low-level graph of identities and raw data Mode layer – a layout for representing typed hypergraph atoms

Primitive Layer A graph of identities and raw, byte[] data LinkStore ID -> [ID, …., ID] DataStore ID -> byte[] Current IDs are type 4 UUID

Model Layer Formalizes layout of primitives: AtomID -> [TypeID, ValueID, TargetID, ..., TargetID] TypeID := AtomID TargetID := AtomID ValueID -> [ID, …, ID] | byte[] A set of predefined indices: IncidenceIndex: AtomID -> SortedSet<AtomID> TypeIndex: TypeID -> SortedSet<AtomID> ValueIndex: ValueID -> SortedSet<AtomID>

Type System: Why types? Meaningful interpretation of data. Ensure integrity and consistency. Customized storage model They are a dynamic database schema

Type System : Types Are Atoms So an application domain model is directly represented, augmented and programmed against So new ones can be dynamically added So type constructors (= types of types) will cover any type systems of any programming language Reflectivity is good any way you look at it

Typing Bootstrap:Predefined Types Stored at database creation time … more added any time later Handle primitive types such as numbers, strings etc. Other standard types: lists, maps etc. Type constructors for structured records (e.g. Java beans), strongly type relationships and more. Any domain/application specific custom type implementations

Working with HyperGraphDB Embedded, Java-based (C++ version planned) Store any object as an atom value and create arbitrary n-ary relationships b/w any objects The object structure is a graph at runtime, but it can be represented in many ways: As a serialized blob. As a primitive value graph. As an atom graph.

Indexing Associate indexes with atom types – then indexing is automatic Out-of-box + custom indexing possible Out-of-box implementations: object property -> atom target -> atom target -> another target target tuple -> atom multikey: compose any of the above

Querying Traversals – API for standard graph traversals. Hyper-traversals by jumping levels Constrained Atom Sets (SQL style) – API to retrieve sets of atoms based on constraining conditional expressions. (Vaporware) Graph patterns - a new comprehensive query language, coming up, looking for help to do it!

Distribution Build on ACL (Agent Communication Language) foundation Pluggable presence&communication layer – XMPP (default), JXTA (available) or your own Nested workflows framework for agent (i.e. DB instance) conversations Primitive conversations such as subgraph transfer available Eventually consistent replication at model layer level.

API Highlights HGHandle – universal reference to atoms HyperGraph – a database instance add, remove, replace, define atoms access to high-level objects: type system, transaction, primitive store etc. HGTypeSystem – manage types, mapping b/w HGDB types and Java classes etc. HGQuery.hg – create and execute queries

More API Highlights HGEventManager – track and/or prevent every database atom operation HGTraversal – breadth-first, depth-first, user-defined adjancy lists HGIndexManager –arbitrary indexing of atoms HGStore – primitive storage layer HGIndex – use the key-value store directly HyperGraphPeer/ActivityManager – manage P2P activities

API –Interfaces HGLink getArity(), getTargetAt(i) HGAtomType make runtime object from storage add, remove value from storage subsumes(X, Y) HGAtomPredicate/HGQueryCondition Plug into querying facilities

API – More Interfaces HGALGenerator – generate a list of atoms adjacent to a given atom HGIndexer - index an atom by an arbitrary key derived somehow from it Activity/FSMActivity – implement P2P conversation workflow

HyperGraphDb

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HyperGraphDb