# Hyper-relation

(Redirected from Hyper-Relation)

Hyper-relation is a relation between relations, or between relations and nodes.

## Basic Symbols

Basic symbols used in the UNL framework
Symbol Definition Example
( ) node (%a)
" " string "went"
[ ] natural language entry (headword) [go]
[[ ]] UW [[to go(icl>to move)]]
// regular expression /a{2,3}/ = aa,aaa
rel(x;y) relation agt(kill;Peter)
^ not ^a = not a
{ | } or {a|b} = a or b
% index for nodes, attributes and values %x
: scope ID :01
# index for sub-NLWs #01
= attribute-value assignment POS=NOU
! rule trigger !PLR
& merge operator %x&%y
? dictionary lookup operator ?[a]

## Basic Concepts

Node
A node is the most elementary unit in the graph. It is the result of the tokenization process, and corresponds to the notion of "lexical item". At the surface level, a natural language sentence is considered a list of nodes, and a UNL graph a set of relations between nodes.
Relation
In order to form a natural language sentence or a UNL graph, nodes are inter-related by relations. In the UNL framework, there are three different types of relations: the linear (list) relation, syntactic relations and semantic relations.
Hyper-Node
A hyper-node is a sub-graph, i.e., a scope: a node containing relations between nodes.
Hyper-Relation
A hyper-relation is a relation between relations.

## Notation

Hyper-relations and relations are represented in the same way, i.e.,

```rel:scope(arg1;arg2;...;argn)
```

where:

• rel is the name of the hyper-relation
• scope is the scope of the hyper-relation
• arg1, arg2, ... are the arguments of the hyper-relation

The only difference between relations and hyper-relations is that the latter has at least one relation as one of its arguments, e.g.:

• rel(rel1(arg1;arg2);arg3;...;argn)

For better readability, inner relations are normally replaced by relation ID's, to be represented by :XX, where XX is a two-digit string

• rel(rel1(arg1;arg2);arg3;...;argn) is the same as rel(:01;arg3;...;argn)rel1:01(arg1;arg2)

## Properties

A hyper-relation may have one single relation as each argument
• XP(XB(%a;%b);%c) - the source argument of the hyper-relation XP is a relation
• XP(%a;XB(%b;%c)) - the target argument of the hyper-relation XP is a relation
• XP(VC(%a;%b);VA(%a;%c)) - the source and the target argument of the hyper-relation XP are relations
• XP(VC(%a;%b)VA(%a;%c);VS(%a;%d)) - a hyper-relation may not have more than one relation as one single argument (in this case, the hyper-relation XP contained two relations as the source argument)
Differently from nodes, relations do not have elements (strings, headwords, features and indexes)
• XP(XB(%a;%b),"ab",[ab],[[ab]],A,B;%c) (the relation XB(%a;%b) may not have strings, UWs, headwords or any features)

## Examples

Examples of hyper-relations

• XP(XB(%a;%b);%c) - a syntactic relation XP between the syntactic relation XB(%a;%b) and the node %c
• and(agt([a];[b]);agt([a];[c])) - a semantic relation "and" between the semantic relations agt([a];[b]) AND agt([a];[c])

## Transformations

Hyper-relations are altered, replaced, created and deleted by T-rules:

### Creating hyper-relations

Hyper-relations are created through encapsulating relations:

• rel1(%x;%y)rel2(%x;%z):=rel1(rel2(%x;%z);%y); (the relation rel1 between %x and %y becomes a hyper-relation between the relation rel2(%x;%z) and the node %y.)

### Transforming hyper-relations into simple relations

Hyper-relations are transformed into simple relations by removing their internal relations:

• rel1(rel2(%x;%z);%y):=rel1(%x;%y)rel2(%x;%z); (the hyper-relation rel1 between the relation rel2(%x;%z) and the node %y is transformed into a simple relation between the nodes %x and %y; the relatin rel2(%x;%z) is not affected.)