T-rule

T-rules, or transformation rules, are rules that alter the state of the nodes. They are used for normalization, for syntactic analysis and for semantic interpretation. The set of the t-rules forms the Transformation grammar, or T-Grammar.

Syntax

The Transformation Rules follow the very general formalism

α:=β;

where the left side α is a condition statement, and the right side β is an action to be performed over α.

Types of Transformation Rules

Natural language sentences and UNL graphs are supposed to convey the same amount of information in different structures: whereas the former arranges data as an ordered list of words, the latter organizes it as a hypergraph. In that sense, translating from natural language into UNL and from UNL into natural language is ultimately a matter of transforming lists into networks and vice-versa.

The UNDLF generation and analysis tools assume that such transformation should be carried out progressively, i.e., through a transitional data structure: the tree, which could be used as an interface between lists and networks. Accordingly, the UNL Grammar states seven different types of rules (LL, TT, NN, LT, TL, TN, NT), as indicated below:

• ANALYSIS (NL-UNL)
  • LL - List Processing (list-to-list)
  • LT - Surface-Structure Formation (list-to-tree)
  • TT - Syntactic Processing (tree-to-tree)
  • TN - Deep-Structure Formation (tree-to-network)
  • NN - Semantic Processing (network-to-network)

• GENERATION (UNL-NL)
  • NN - Semantic Processing (network-to-network)
  • NT - Deep-Structure Formation (network-to-tree)
  • TT - Syntactic Processing (tree-to-tree)
  • TL - Surface-Structure Formation (tree-to-list)
  • LL - List Processing (list-to-list)

The NL original sentence is supposed to be preprocessed, by the LL rules, in order to become an ordered list. Next, the resulting list structure is parsed with the LT rules, so as to unveil its surface syntactic structure, which is already a tree. The tree structure is further processed by the TT rules in order to expose its inner organization, the deep syntactic structure, which is supposed to be more suitable to the semantic interpretation. Then, this deep syntactic structure is projected into a semantic network by the TN rules. The resultant semantic network is then post-edited by the NN rules in order to comply with UNL standards and generate the UNL Graph.

The reverse process is carried out during natural language generation. The UNL graph is preprocessed by the NN rules in order to become a more easily tractable semantic network. The resulting network structure is converted, by the NT rules, into a syntactic structure, which is still distant from the surface structure, as it is directly derived from the semantic arrangement. This deep syntactic structure is subsequently transformed into a surface syntactic structure by the TT rules. The surface syntactic structure undergoes many other changes according to the TL rules, which generate a NL-like list structure. This list structure is finally realized as a natural language sentence by the LL rules.

As sentences are complex structures that may contain nested or embedded phrases, both the analysis and the generation processes may be interleaved rather than pipelined. This means that the natural flow described above is only "normal" and not "necessary". During natural language generation, a LL rule may apply prior to a TT rule, or a NN rule may be applied after a TL rule. Rules are recursive and must be applied in the order defined in the grammar as long as their conditions are true, regardless of the state.

List-to-List Rules

The list-to-list (LL) rules are used for processing lists, both in analysis and in generation. In analysis, these rules are used for pre-editing the natural language sentence and preparing the input to the syntactic module; in generation, they are used for post-editing the output of the syntactic module and generating the natural language sentence.

There are 5 different subtypes of LL rules:

LL rules

ACTION	RULE	DESCRIPTION
ADD	(%x):=(%x)(%y);	The node %y is added to the right of the node %x
	(%x):=(%y)(%x);	The node %y is added to the left of the node %x
DELETE	(%x):=-(%x);	The node %x is deleted.
	(%x):=;
REPLACE	(%x):=(%y);	All the instances of the node %x will be replaced by the node %y
MERGE	(%x)(%y):=(%x&%y);	The nodes %x and %y will be merged

Where %x and %y are nodes.

Tree-to-Tree Rules

The tree-to-tree rules (TT) are used for processing trees, both in analysis and in generation. During analysis, these rules are used for revealing the deep structure out of the surface structure; in generation, they are used for transforming the deep into the surface syntactic structure.

Syntactic relations are n-ary: they can have as many arguments (nodes) as necessary.

There are 3 different subtypes of TT rules:

TT rules

ACTION	RULE	DESCRIPTION
ADD RELATION	SYN1(%x;%y):=+SYN2(%w;%z);	The relation SYN2 between the nodes %w and %z will be added to the graph containing the relation SYN1 between the nodes %x and %y
DELETE RELATION	SYN(%x;%y):=-SYN(%x;%y);	The relation SYN between the nodes %x and %y will be deleted (the nodes %x and %y will not be deleted)
	SYN(%x;%y)=;
REPLACE RELATION	SYN1(%x;%y):=SYN2(%w;%z);	The relation SYN1 between the nodes %x and %y will be replaced by the relation SYN2 between the nodes %w and %z

Where SYN is a syntactic relation, and %x, %y, %z and %w are nodes.

As syntactic relations are n-ary, the REPLACE RELATION may also be used to ADD or DELETE nodes.

Special types of TT replace relations

ACTION	RULE	DESCRIPTION
ADD NODE	SYN(%x;%y):=SYN(%x;%y;%z);	The binary relation SYN between the nodes %x and %y is replaced by a ternary relation SYN between the nodes %x, %y and %z
DELETE NODE	SYN(%x;%y):=SYN(%y);	The binary relation SYN between the nodes %x and %y is replaced by a unary relation SYN with the node %y

Where SYN is a syntactic relation, and %x, %y and %z are nodes.

Network-to-Network Rules

The network-to-network rules (NN) are used for processing networks, both in analysis and in generation. During analysis, these rules are used for post-editing the semantic network structure derived from the syntactic module in order to generate the UNL graph; in generation, they are used for pre-editing the UNL graph, transforming it into a semantic network that would be more appropriate for sentence generation.

There are 3 different subtypes of NN rules:

NN rules

ACTION	RULE	DESCRIPTION
ADD RELATION	SEM1(%x;%y):=+SEM2(%w;%z);	The relation SEM2 between the nodes %w and %z will be added to the graph containing the relation SEM1 between the nodes %x and %y
DELETE RELATION	SEM(%x;%y):=-SEM(%x;%y);	The relation SEM between the nodes %x and %y will be deleted (the nodes %x and %y will not be deleted)
	SEM(%x;%y)=;
REPLACE RELATION	SEM1(%x;%y):=SEM2(%w;%z);	The relation SEM1 between the nodes %x and %y will be replaced by the relation SEM2 between the nodes %w and %z

Where SEM is any of the existing UNL relations, and %x, %y, %z and %w are nodes.

List-to-Tree Rules

The list-to-tree (LT) rules are used to parse the list structure into a tree structure.
There are 2 different subtypes of LT rules:

LT rule

ACTION	RULE	DESCRIPTION
ADD	(%x)(%y):=+SYN(%x;%y);	The relation SYN is created between the nodes %x and %y if there is a linear relation between them (the linear relation is not deleted)
REPLACE	(%x)(%y):=SYN(%x;%y);	The linear relation between %x and %y is replaced by the relation SYN between the same nodes (i.e., the linear relation is deleted)

Where SYN is a syntactic relation, and %x and %y are nodes.

Tree-to-List Rules

The tree-to-list (TL) rules are used to linearize the tree structure into a list structure. There is one single type of TL rule:

There is a single type of TL rule:

TL rule

ACTION	RULE	DESCRIPTION
REPLACE	SYN(%x;%y):=(%x)(%y);	The relation SYN between %x and %y is replaced by a linear relation between %x and %y

Where SYN is a syntactic relation and %x and %y are nodes.

Tree-to-Network Rules

The tree-to-network (TN) rules derive a semantic network out of a syntactic tree.

There are 2 types of TN rules:

TN rule

ACTION	RULE	DESCRIPTION
ADD	SYN(%x;%y):=+SEM(%w;%x);	The semantic relation SEM between the nodes %w and %x is created if there is a syntactic relation SYN between the nodes %x and %y
REPLACE	SYN(%x;%y):=SEM(%x;%y);	The syntactic relation SYN between the nodes %x and %y is replaced by the semantic relation SEM between the same nodes.

Where SYN is a syntactic relation, SEM is a semantic relation, and %x, %y, %w and %z are nodes.

Network-to-Tree Rules

The network-to-tree (NT) rules reorganizes the network structure as a deep tree structure.

There are two types of TN rules:

NT rule

ACTION	RULE	DESCRIPTION
ADD	SEM(%x;%y):=+SYN(%w;%x);	The syntactic relation SYN between the nodes %w and %x is created if there is a semantic relation SEM between the nodes %x and %y
REPLACE	SEM(%x;%y):=SYM(%x;%y);	The semantic relation SEM between the nodes %x and %y is replaced by the syntactic relation SYN between the same nodes.

Where SYN is a syntactic relation, SEM is a semantic relation, and %x, %y, %w and %z are nodes.

Transformations over nodes

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

Altering elements of nodes

Any changes to the elements of nodes must be stated in the right side of rules. Changes affect only the elements explicitly indicated in rules:

("a",[a],[[a]],A):=("b"); (only the string is affected by the rule; all other elements are preserved. The resulting node is ("b",[a],[[a]],A) )

"Strings"

Nodes may have one single string. This value is set through the operator "+", reset through the operator "-", or modified through A-rules. The operator "+" may be omitted. Changes to strings do not affect any other element (headwords, UWs and features)

• (""):=(+"a"); (the string of the node is set from "" to "a")
• (""):=("a"); (the same as above)
• ():=("a"); (the same as above)
• ("a"):=(+"b"); (the string of the node is set from "a" to "b")
• ("a"):=("b"); (the same as above)
• ("a"):=(-"a"); (the string of the node is reset, i.e., it changes from "a" to "")
• ("a"):=(""); (the same as above)
• ("a"):=("x"<0,0>"y"); (the string of the node is modified from "a" to "xay")

[headwords]

Nodes may have one single headword. This value is set through the operator "+" and reset through the operator "-". The operator "+" may be omitted. Headwords may not be modified through A-rules. Changes to headwords do not affect any other element (strings, UWs and features)

• ([]):=(+[a]); (the headword of the node is set from [] to [a])
• ([]):=([a]); (the same as above)
• ():=([a]); (the same as above)
• ([a]):=(+[b]); (the headword of the node is set from [a] to [b])
• ([a]):=([b]); (the same as above)
• ([a]):=(-[a]); (the headword of the node is reset, i.e., it changes from [a] to [])
• ([a]):=([]); (the same as above)
• ([a]):=("x"<0,0>"y"); (it is not possible to modify headwords through A-rules.

[[UWs]]

Nodes may have one single UW. This value is set through the operator "+" and reset through the operator "-". The operator "+" may be omitted. UWs may not be modified through A-rules. Changes to UWs do not affect any other element (strings, headwords and features)

• ([[]]):=(+[[a]]); (the UW of the node is set from [[]] to [[a]])
• ([[]]):=([[a]]); (the same as above)
• ():=([[a]]); (the same as above)
• ([[a]]):=(+[[b]]); (the UW of the node is set from [[a]] to [[b]])
• ([[a]]):=([[b]]); (the same as above)
• ([[a]]):=(-[[a]]); (the UW of the node is reset, i.e., it changes from [[a]] to [[]])
• ([[a]]):=([[]]); (the same as above)
• ([a]):=("x"<0,0>"y"); (it is not possible to modify UWs through A-rules.

Features

Nodes may have as many features as necessary. Features may come isolated in a list (POS,NOU,GEN,MCL,NUM,SNG) or as pairs of attribute=value (POS=NOU,GEN=MCL,NUM=SNG). Changes to features do not affect any other element (strings, headwords and UWs)

• Adding features to nodes

  Features are added through the operator + (add). The operator "+" may be omitted.

  • ():=(+B); (add the feature B to the node)
  • ():=(B); (the same as above)

  Rules are recursive: the feature will be added to the node while the condition is true.

  • ():=(+B); (the resulting node is (B,B,B,...), i.e., this is an infinite loop)
  • (^B):=(+B); (the resulting node is (B), i.e., the feature B is added only if the node does not contain it yet)

  The operator + (add) does not create attribute=value pairs automatically (it simply adds features to the nodes)

  • (%x,^POS,^NOU):=(%x,+NOU); (the resulting node is (NOU) and not (POS=NOU) because POS has not been added)
  • (%x,^POS,^NOU):=(%x,+POS,+NOU); (the resulting node is (POS,NOU) and not (POS=NOU) because there was no assignment POS=NOU)
  • (%x,POS,^NOU):=(%x,+NOU); (the resulting node is (POS,NOU) because there was no assignment POS=NOU)
  • (%x,^POS,^NOU):=(%x,+POS=NOU); (the resulting node is (POS=NOU))
  • (%x,POS,^NOU):=(%x,+POS=NOU); (the resulting node is (POS, POS=NOU) because the feature POS has been duplicated)

• Deleting features from nodes

  Features are deleted through the operator - (delete).

  ():=(-B); (delete the feature B from the node)

  Rules are recursive: the feature will be deleted from the node while the condition is true.

  ():=(-B); (the rule will delete all instances of the feature B from the node, i.e., the node (B,B,B,B,B) will become ()

  The operator "-" may also be used to reset attributes:

  • (%x,POS,NOU):=(%x,-NOU); (the resulting node is (POS) because the feature POS was not deleted)
  • (%x,POS,NOU):=(%x,-POS,-NOU); (the resulting node is () because both features POS and NOU were deleted)
  • (%x,POS=NOU):=(%x,-NOU); (the resulting node is (POS) because only the value of the attribute POS was deleted)
  • (%x,POS=NOU):=(%x,-POS); (the resulting node is () because the attribute POS was deleted with all its values)

• Copying features

  Features can be copied from one to another node through indexes

  • (%x,GEN)(%y,^GEN):=(%x)(%y,GEN=%x); (the value of the attribute GEN is copied from the node %x to %y);

Indexes

Indexes are used to make reference to the whole node instead of its elements. Any change in the index means a completely new node, and no element is preserved.

• (%x,"a"):=(%x,"b"); (the string of the node %x is set from "a" to "b"; all the other elements of the node %x are preserved)
• (%x,"a"):=(%y,"b"); (the whole node %x is replaced by a new node %y whose string is "b"; no element from %x is copied to %y)

Deleting nodes

In linear rules, nodes are deleted if they are not repeated (co-indexed) in the right side:

• (%x)(%y):=(%x); (the node %y will be deleted)

In other rules, nodes are deleted if they are not repeated (co-indexed) in the right side and are not part of any other relation:

• rel(%x;%y):=rel(%x); (the node %y will be deleted if, and only if, it is not part of any other relation)

Creating nodes

Nodes are created through the use of new indexes in the right side:

• ("a",%x)("b",%y):=(%x)(%y)("c",%z); (the node %z will be created)
• ("a",%x)("b",%y):=(%x)("c",%z); (the node %z will be created, and %y will be deleted)

Duplicating (cloning) nodes

Nodes may be duplicated by repeating indexes on the right side along with the command #CLONE:

• ("a",^CLONED,%x):=(%x,+CLONED)(%x,+CLONED,#CLONE);

  ("a") becomes ("a")("a")
  

In order to avoid infinite recursion, it is important to change the condition on the right side (in the example above, the feature +CLONED, assigned to all instances of the clone, prevents the rule from applying indefinitely)
Clones contain the same elements of the original nodes, unless they are explicitly altered during the cloning:

• ("a",[a],[[a]],A,^CLONED,%x):=(%x,+CLONED)(%x,+CLONED,#CLONE);

  ("a",[a],[[a]],A) becomes ("a",[a],[[a]],A,CLONED)("a",[a],[[a]],A,CLONED)

• (A,^CLONED,%x):=(%x,-A,+B,+CLONED)(%x,-A,+C,+CLONED,#CLONE);

  (A) becomes (B,CLONED)(C,CLONED)

Splitting nodes

One node may be split into two or more nodes through the use of splitting rules. Consider, for instance, the cases below:

Splitting rules deal only with strings and apply only to nodes with the feature TEMP.

Original node: ("abc",TEMP)

Split rule: ("abc"):=("ab")("c");

Resulting nodes: ("ab",TEMP)("c",TEMP);

However, if the original node was ("abc"), without TEMP, the rule would not have been applied (i.e., it is necessary to assign the feature TEMP to the node before splitting it)

Splitting rules are conservative: the elements of the original node, except the string, will be preserved unless explicitly altered.

Original node: ("abc",[abc],[[abc]],A,B,C,TEMP)

Split rule: ("abc"):=("ab")("c");

Resulting nodes: ("ab",[abc],[[abc]],A,B,C,TEMP)("c",[abc],[[abc]],A,B,C,TEMP) (i.e., the elements of the original node will be copied to the new nodes)

However, if the rule was: ("abc"):=("ab",-A,-B,-C,-TEMP,+AB)("c",-TEMP);

The result would be: ("ab",[abc],[[abc]],AB)("c",[abc],[[abc]],A,B,C)

Merging nodes (&)

Two or more nodes may be merged by the command &:

• (%x)(%y)(%z):=(%x&%y&%z);

In the example above("a")("b")("c") becomes ("abc")

Merge operations concatenate headwords and UWs, and join features

("hw1",[[uw1]],F1,%x)("hw2",[[uw2]],F2,%y)("hw3",[[uw3]],F3,%z):=(%x&%y&%z);
The resulting node is ("hw1hw2hw3",[[uw1uw2uw3]],F1,F2,F3)

Compare the difference

• (%x)(%y):=(%z); (the nodes %x and %y are replaced by %z, and their features are lost unless explicitly included in %z)
• (%x)(%y):=(%x&%y); (the nodes %x and %y are merged)

Retrieving entries in the dictionary after tokenization (?)

During transformation (i.e., after tokenization), dictionary entries may be accessed from transformation rules by the command "?"

• (?[headword]) retrieves the first entry in the dictionary with the headword "headword"
• (?[[uw]]) retrieves the first entry in the dictionary with the UW "uw"
• (?[headword],?[[uw]],?feature) retrieves the first entry in the dictionary with the headword "headword", the UW "uw" and the feature "feature"

Regular expressions, variables and disjunction may also be used in dictionary search

• (?[/abcd./]) retrieves the first entry in the dictionary whose headword has 5 characters and begins with "abcd" (this works only in natural language generation)
• (?[[/abcd./]]) retrieves the first entry in the dictionary whose UW has 5 characters and begins with "abcd" (this works only in natural language analysis)

Obligatory parameters

Due to the indexation algorithm, the headword is obligatory in IAN and the UW is obligatory in EUGENE:

• (?[headword]) will work only in IAN
• (?[[uw]]) will work only in EUGENE
• (?feature) will not work in IAN or EUGENE

Variables

In order to avoid repetition, dictionary look-up may use the values of indexed nodes in the left side

• (?[%x]) retrieves the first entry in the dictionary with the same headword of the node %x
• (?[[%x]]) retrieves the first entry in the dictionary with the same UW of the node %x
• (?[%x],ATT=%x) retrieves the first entry in the dictionary with the same headword of the node %x and whose attribute ATT has the same value of the attribute ATT of the node %x

Example

Dictionary search is used mainly in natural language generation

• (N,NUM,GEN,@def,%noun):=(?[[]],?ART,?DEF,?NUM=%noun,?GEN=%noun)(%noun,-@def);

In case of node %noun with the features noun (N), number (NUM) and gender (GEN), and with the attribute @def (definite), search the first entry in the dictionary associated with the UW "" (empty UW) with the features ART and DEF, and whose attributes NUM and GEN have the same values of the ones of the node %noun, and insert it in front of the noun. Remove @def from the noun in order to avoid an infinite loop.

Triggering rules (!)

Inflectional rules are triggered in the grammar by the command "!"<ATTRIBUTE>.
Given the dictionary entry:

• [foot] "foot" (POS=NOU, NUM(PLR:="oo":"ee")) <eng,0,0>;

The rule NUM(PLR:="oo":"ee") is triggered by !NUM
For instance:

• (NUM=PLR,^inflected):=(!NUM,+inflected); or
• (PLR,^inflected):=(!NUM,+inflected); or
• (NUM,^inflected):=(!NUM,+inflected);

In the first case (NUM=PLR), the system verifies if the attribute "NUM" is set and if it has the value "PLR". In the second and in the third case, the system simply verifies if the word has any feature (attribute or value) equal to "PLR" or "NUM".
It's important to stress that, as the features of the dictionary are defined by the user, there is no way of pre-assigning attribute-value pairs. In that sense, it's not possible to infer that "PLR" will be a value of the attribute "NUM" except through an assignment of the form "NUM=PLR" (i.e., given only "PLR" or "NUM", is not possible to state "NUM=PLR").

Transformations over hyper-nodes

Changes

Hyper-nodes, as nodes, have elements, which may be altered by the use of the operators + (add) and - (delete). The operator + may be omitted. Changes affect only the scopes indicated.

Changes to the main scope

• (%a,"a",[a],[[a]],A,(%b,"b")):=(%a,"c");(the string of the hyper-node is set to "c"; the internal node %b is not affected)
• (%a,"a",[a],[[a]],A,(%b,"b")):=(%a,"");(the string of the hyper-node is set to ""; the internal node %b is not affected)
• (%a,"a",[a],[[a]],A,(%b,"b")):=(%a,-"a");(the same as above)
• (%a,"a",[a],[[a]],A,(%b,"b")):=(%a,[c]);(the headword of the hyper-node is set to [c]; the internal node %b is not affected)
• (%a,"a",[a],[[a]],A,(%b,"b")):=(%a,[[c]]);(the UW of the hyper-node is set to [[c]]; the internal node %b is not affected)
• (%a,"a",[a],[[a]],A,^B,(%b,"b")):=(%a,+B);(add the feature B to the hyper-node %a; the internal node %b is not affected)
• (%a,"a",[a],[[a]],A,^B,(%b,"b")):=(%a,B); (the same as above: add the feature B to %a)
• (%a,"a",[a],[[a]],A,(%b,"b")):=(%a,-A);(delete the feature A from the hyper-node %a; the internal node %b is not affected)

Changes to inner scopes

• (%a,(%b,"b",[b],[[b]],B)):=(%a,(%b,"c"));(the string of the inner node %b is set to "c"; the hyper-node %a is not affected)
• (%a,(%b,"b",[b],[[b]],B)):=(%a,(%b,""));(the string of the inner node %b is set to ""; the hyper-node %a is not affected)
• (%a,(%b,"b",[b],[[b]],B)):=(%a,(%b,-"b"));(the same as above)
• (%a,(%b,"b",[b],[[b]],B)):=(%a,(%b,[c]));(the headword of the inner node %bis set to [c]; the hyper-node %a is not affected)
• (%a,(%b,"b",[b],[[b]],B)):=(%a,(%b,[[c]]));(the UW of the inner node %b is set to [[c]]; the hyper-node %a is not affected)
• (%a,(%b,"b",[b],[[b]],B,^C)):=(%a,(%b,+C));(add the feature C to the inner node %b; the hyper-node %a is not affected)
• (%a,(%b,"b",[b],[[b]],B,^C)):=(%a,(%b,C)); (the same as above: add the feature C to %b)
• (%a,(%b,"b",[b],[[b]],B)):=(%a,(%b,-B));(delete the feature B from the inner node %b; the hyper-node %a is not affected)

Rules must have as many parentheses as the depth of the inner scope to be altered

• (%a,(%b,(%c,(%d,(%e,"e",[e],[[e]],E))))):=(%a,(%b,(%c,(%d,(%e,"f"))))); (the string of inner node %e is set to "f"; the enclosing nodes %d, %c, %b and %a are not affected)

Hyper-nodes do not need to be represented if the changes apply to nodes instead of nodes inside hyper-nodes

• (%a,(%b,"b",[b],[[b]],B)):=(%a,(%b,"c")); (the string of the inner node %b is set to "c"; the hyper-node %a is not affected)

could be represented simply as

• (%b,"b",[b],[[b]],B)):=(%b,"c");

if the changes apply to all nodes ("b",[b],[[b]],B) and not only to those inside scopes.

Deletion

Hyper-nodes, as any node, are deleted if they are not repeated (co-indexed) in the right side. In this case, all the inner nodes are deleted as well:

• (REL(%x;%y),%z):=; (the hyper-node %z will be deleted, and all its internal nodes and relations as well)

As any feature, inner nodes are conservative, and are not deleted even if they are not repeated (co-indexed) in the right side:

• (%a,A,^B):=(%a,+B); (the feature A is not deleted from the node %a)
• (%a,^B,(%b,"b")):=(%a,+B); (the node %b is not deleted from the hyper-node %a)

In order to delete inner nodes, the operator "-" must be used

• (%a,A,(%b,B)):=(%a,-(%b)); (the node %b is deleted from the hyper-node %a)
• (%a,A,rel(%b;%c)):=(%a,-rel(%b;%c)); (the relation rel(%b;%c) is deleted from the hyper-node %a)

Extraction

Nodes may be extracted from hyper-nodes by removing the corresponding parentheses. In this case, the hyper-node is deleted (along with its features), but the internal nodes and relations are preserved, if repeated on the right side.

• ((%x),%y):=(%x); (the hyper-node %y is deleted, but its internal node %x is preserved; in case %y have nodes other than %x, these nodes will be deleted as well, because they are not repeated in the right side)
• (REL(%x;%y),%z):=REL(%x;%y); (the hyper-node %z is deleted, but its internal relation REL(%x;%y) is preserved; in case %z have relations other than REL(%x;%y), and nodes other than %x and %y, these will be deleted as well, because they are not repeated in the right side.

Create

Hyper-nodes are created through the encapsulation of existing nodes

• (%x):=((%x),%y); (the hyper-node %y is created, with the node %x there inside)
• REL(%x;%y):=(REL(%x;%y),%z); (the hyper-node %z is created, with the relation REL between the nodes %x and %y inside)
• (%x)(%y):=((%x)(%y),%z); (the hyper-node %z is created, with the linear relation between the nodes %x and %y there inside)

Attention

relations and nodes must be repeated in the right side or they will be deleted

• (%x):=(%y); (the node %x will be simply replaced by %y; no hyper-node will be created)
• REL(%x;%y):=(%z); (the relation REL between the nodes %x and %y will be replaced by the node %z; no hyper-node will be created)

Transformations over relations and hyper-relations

Relations and hyper-relations do not have features, and are replaced, created and deleted by NN, TT, NT, TN, TL and LT rules:

• REL1(%x;%y):=REL2(%x;%y); (replacement)
• REL(%x;%y):=; (deletion)
• REL1(%x;%y):=+REL2(%w;%z); (creation)

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.)

Special types of transformation rules

• A-rule is a specific type of T-rule used for affixation (prefixation, infixation, suffixation)
• C-rule is a specific type of T-rule used for composition (word formation in case of compounds and multiword expressions)
• L-rule is a specific type of T-rule used for handling word order
• N-rule is a specific type of T-rule used for segmenting sentences and normalizing the input text
• S-rule is a specific type of T-rule used for handling syntactic structures

General properties of transformation rules

PRIORITY

Rules are applied serially, according to the order defined in the grammar. The first rule will be the first to be applied, the second will be the second, and so on. In case of the same rule being applicable more than once, rules are applied from left to right (in case of lists) and top-down (in case of graphs).

For instance:

List structure

INPUT = [a][ ][beautiful][ ][book]

GRAMMAR =

RULE#1: ([ ]):=; (delete the blank space)

RULE#2: ([beautiful])([ ])([book]):=([book])([beautiful]); (replace "beautiful+blank+book" by "book+beautiful")

RESULT:

INITIAL STATE: [a][ ][beautiful][ ][book]

STATE#1: [a][beautiful][ ][book] (the RULE#1 is the first applicable rule to appear in the grammar and, therefore, is the first one to be applied, and it will apply to the leftmost blank)

STATE#2: [a][beautiful][book] (the RULE#1 applies a second time, because there is a second blank space in the input)

FINAL STATE: [a][beautiful][book] (the RULE#2 never applies, because its condition is no longer true after the second application of RULE#1)

Graph structure

INPUT = mod(book,beautiful)mod(book,new)

GRAMMAR =

RULE#1: mod(%x;%y):=NA(%x;%y); (replace the mod relation between the nodes %x and %y by a NA relation between the same nodes)

RESULT:

INITIAL STATE: mod(book,beautiful)mod(book,new)

STATE#1: NA(book,beautiful)mod(book,new) (the RULE#1 is the first applicable rule to appear in the grammar and, therefore, is the first one to be applied, and it will apply to the topmost relation, i.e., the first one to appear in the graph)

STATE#2: NA(book,beautiful)NA(book,new) (the RULE#1 applies a second time, because there is a second mod relation to be replaced)

FINAL STATE: NA(book,beautiful)NA(book,new)

RECURSIVENESS

Rules are applied recursively as long as their conditions are true. Because of that, special attention should be paid to ADD rules:

• (%x,A):=(%x,+B); (creates an infinite loop, because the feature B will be added infinitely to the node %x)
  

In order to avoid the endless repetition, the condition side must be changed to (%x,A,^B):=(%x,+B); (the rule applies only once)

• REL1(%x;%y):=+REL2(%x;%z); (creates an infinite loop, because the REL2 will be added infinitely to the graph)
  

In order to avoid the endless repetition, the condition side must be changed to REL1(%x;%y)^REL(%x;%z):=+REL2(%x;%z); OR REL1(%x,^BREAK;%y):=+REL2(%x,+BREAK;%z); (the rule applies only once)

COMPREHENSIVENESS

Grammars are applied comprehensively as long as there is at least one applicable rule.

CONSERVATION

Rules affect only the information clearly specified. No relation, node or feature is deleted unless explicitly informed.

For instance, in the examples below, the source node of the “agt” relation preserves, in all cases, the value “a”. The only change concerns the feature “c”, which is added to the source node of the “agt” in the first two cases; and the feature “b”, which is deleted from the target node in the third case.

agt(a;b):=agt(c;);

agt(a;b):=agt(+c;);

agt(a;b):=agt(;-b);

In any case, the ADD and DELETE rules (i.e., when the right side starts with “+” or “-“) preserve the items in the left side, except for the explicitly deleted ones:

INPUT: agt(%x;%y) obj(%x;%z) tim(%x;%w)

RULE: agt(%x;%y) ^mod(%x;%k):=+mod(%x;%k);

OUTPUT: agt(%x;%y) obj(%x;%z) tim(%x;%w) mod(%x;%k)

or

INPUT: agt(%x;%y) obj(%x;%z) tim(%x;%w)

RULE: agt(%x;%y):=-agt(%x;%y);

OUTPUT: obj(%x;%z) tim(%x;%w)

SCOPE

LL and LT rules apply over nodes, whereas NN, TT, NT, TN and TL rules apply over relations.

Nodes may be deleted only through LL and LT rules (i.e., when appearing in the left side of rules).

(A):=; (the node containing the feature "A" is deleted)

(%A,A):=-(%A); (the node containing the feature "A" is deleted - the same as above)

(%A,A)(%B,B):=(%A); (the node containing the feature "B" is deleted because not present in the right side - see indexes)

(%A,A)(%B,B)(%C,C):=REL(%A;%B); (the node containing the feature "C" is deleted, because not present in the right side - see indexes)

Nodes may not be deleted through NN, TT, NT, TN and TL rules (i.e., when not appearing in the left side of rules).

REL(%A,A;%B,B;%C,C):=(%A)(%B); (the relation between the nodes containing the features "A", "B" and "C" is replaced by a linear relation between the nodes containing the features "A" and "B". The node "C", however, is not deleted, even though absent from the right side - see indexes)

Relations may be deleted directly through NN, TT, NT, TN and TL rules, and indirectly through LL and LT rules (when their nodes are deleted).

REL(A;B):=; (The relation between the nodes containing the features "A" and "B" is deleted, but the nodes are preserved)

REL(A;B)REL(%C,C;%D,D):=REL(%C;%D); (The relation between the nodes containing the features "A" and "B" is deleted; its nodes and the relation between the nodes containing the features "C" and "D" are preserved)

(A):=; (The node containing the feature "A" is deleted, as well as all relations in which it figures as an argument)

INDEXATION

All instances of the same node must be co-indexed (or they will be considered different nodes). See Index.

ACTION

Rules may add or delete values to the source and the target nodes, but only in the right side items:

agt(a;b):=agt(+c;);

agt(a;b):=agt(;-b);

CONJUNCTION

Both the left and the right side of the rule may have as many items as necessary, as exemplified below:

SEM(A;B)SEM(C;D)SEM(E;F):=SEM(G;H)SEM(I;J)SEM(K;L);

DISJUNCTION

The left side of the rules may bring disjuncts, but not the right side. Disjuncts must be represented between {braces} and must be separated by |.

{SEM(A;B)|SEM(C;D)}^SEM(E;F):=+SEM(E;F);

SEM(A;B){SEM(C;D)|SEM(E;F)}:=-SEM(A;B);

agt(VER,{V01|V02};NOU,^SNG}:=;

REGULAR EXPRESSIONS

The left side of the rules may bring [Perl Compatible Regular Expressions] between "/", as indicated below:

/(agt|obj|aoj)/(A,%a;B,%b):=VS(%a;%b);

The rule above applies in case of agt(A;B), obj(A;B) and aoj(A;B)

/[a-z]{2,3}/(A,%a;B,%b):=VS(%a;%b);

The rule above applies in case of any sequence of two or three alphabetic characters in the position of relation of A and B

agt(/(VER|NOU)/,%a;%b):=VS(%a;%b);

The rule above applies in case of VER and NOU as features of the first node of the relation "agt"

agt(POS=/(VER|NOU)/,%a;%b):=VS(%a;%b);

The rule above applies in case of VER and NOU as values of the attribute POS of the first node of the relation "agt"

CONCISION

In order for rules to be as small as possible, the source and the target nodes may be simple place-holders or indexes:

cob(;):=obj(;);

tim(%01;[[in]]),obj([[in]];%02):=tim(%01;%02);

tim(VER,%01;[[in]]),obj([[in]];NOU,%02):=tim(%01;%02);

tim(VER;in),obj(in;NOU):=tim(;%04);

In the DELETE rules, the right side may be omitted in case of deletion of the entire left side:

obj(PRE;):=;

READABILITY

There can be blank spaces between variables and symbols. Comments can be added after the “;”.

obj ( ; ) := ; this rule deletes every “obj” relation.

COMMUTATIVITY

Inside the same side of NN, NT, TT and TN rules, the order of the factors does not affect the result

SEM(A;B):=SEM(C;D)SEM(E;F); IS EQUIVALENT TO SEM(A;B):= SEM(E;F)SEM(C;D);

SYN(A;B):=SYN(C;D)SYN(E;F); IS EQUIVALENT TO SYN(A;B):= SYN(E;F)SYN(C;D);

The order of the factors affect the result in case list-processing rules (LL, LT and TL):

(A):=(B)(C); IS DIFFERENT FROM (A):=(C)(B);

SYN(A;B):=(C)(D); IS DIFFERENT FROM SYN(A;B):=(D)(C);

(C)(D):=SYN(A;B); IS DIFFERENT FROM (D)(C):=SYN(A;B);

Additionally, the order of the features inside a relation does not affect the end result, but the order of the nodes is non-commutative.

SEM( VER,TRA ; NOU,MCL ) IS THE SAME AS SEM( TRA,VER ; MCL,NOU )

But:

SEM( VER,TRA ; NOU,MCL) IS DIFFERENT FROM SEM( NOU,MCL ; VER,TRA )

DICTIONARY ATTRIBUTES

Dictionary attributes can be used as variables (see indexes).

SYN(%x,^NUM;%y,NUM):=SYN(NUM=%y;%x);

DICTIONARY RULES (see also Inflection rules inside dictionary entries)

Dictionary rules are triggered by "!"<ATTRIBUTE>:

Dictionary

[foot] "foot" (NOU, NUM(PLR:=”oo”:”ee”)) <eng,0,0>;

[city] "city" (NOU, NUM(PLR:=”y”>”ies”)) <eng,0,0>;

Grammar

(@pl, NUM):=(!NUM,-@pl);

Output

foot>feet

city>cities

NLW SPLITTING

Sub-NLWs in complex entries are referred by # (see indexes).

Dictionary

[[bring] [back]] "bring back" (VER,MTW,VA(01>02), #01(HEAD,VER), #02(ADJT,PP)) <eng,0,0>;

Grammar

VC(VER,MTW,VA(01>02),%head;NOU,%obj):=VB(VC(%head#01;%obj);%head#02);

Formal Syntax of Transformation Rules

<TRANSFORMATION RULE> ::= <NN RULE> | <NT RULE> | <TT RULE> | <TL RULE> | <LL RULE> | <LT RULE> | <TN RULE>
<NN RULE>             ::= (<SEM>)+ ":=" ( ("-"|"+")? <SEM> )* ";"
<TT RULE>             ::= (<SYN>)+ ":=" ( ("-"|"+")? <SYN> )* ";"
<LL RULE>             ::= ( "(" <NODE> ")" )+ ":=" ( ("-"|"+")? "(" <NODE> ")" )* ";"
<NT RULE>             ::= (<SEM>)+ ":=" ( <SYN> )+ ";"
<TN RULE>             ::= (<SYN>)+ ":=" ( <SEM> )+ ";"
<TL RULE>             ::= (<SYN>)+ ":=" ( "(" <NODE> ")" )+ ";"
<LT RULE>             ::= ( "(" <NODE> ")" )+ ":=" ( <SYN> )+ ";"
<SEM>                 ::= <TEXT> "(" <NODE> ";" <NODE> ")"
<SYN>                 ::= <TEXT> "(" <NODE> ";" <NODE> ")"
<NODE>                ::= ( (<DESCRIPTION>)( "," <DESCRIPTION> )* )?
<DESCRIPTION>         ::= <STRING> | <ENTRY> | <SUB-ENTRY> | <FEATURE> | <INDEX> | <RELATION>
<STRING>              ::= """<text>"""
<ENTRY>               ::= "["<entry>"]"
<SUB-ENTRY>           ::= <INDEX>"#"[01-99]
<FEATURE>             ::= <VALUE> | <ATTRIBUTE> | <ATTRIBUTE>"="<VALUE>
<INDEX>               ::= ( "%"([01-99]|[a-zA-Z_]+) )+
<RELATION>            ::= <SEM>|<SYN>
<VALUE>               ::= <TEXT>
<ATTRIBUTE>           ::= <TEXT>
<TEXT>                ::= any sequence of characters except whitespace | <REGULAR EXPRESSION>
<REGULAR EXPRESSION>  ::= "/"<PERL COMPATIBLE REGULAR EXPRESSIONS>"/"

Where:
"" = constant
+ = to be repeated one or more times
* = to be repeated zero or more times
? = to be repeated zero or one time
| = or
[x-y] = from x to y

Examples of Rules

In the examples below:

• L(A;B) is a linear (list) relation between A and B (i.e., L(A;B) = (A)(B))
  
• REL(A;B) is a non-linear (tree or network) relation between A and B
  
• %X is the index for a node
  
• :X indicates that the following relation or node is inside the hyper-node X
  
• A,B,C,D,B1,B2,B3 and B4 are features of the nodes %A,%B,%C,%D,%B1,%B2,%B3 and %B4, respectively.
  

LL RULES

INITIAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) L:B(%B1;%B2) L:B(%B2;%B3) REL:B(%B1;%B4)

LL#1: (B):=;

(Delete all nodes having the feature B, wherever they are)

FINAL STATE: L(%A;%C) L(%C;%D)

The whole hyper-node %B will be deleted, including all its nodes, no matter in which level.

LL#2: (B1):=;

(Delete all nodes having the feature B1, wherever they are)

FINAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) L:B(%B2;%B3) :B(%B4)

Only the node (%B1) is deleted. The relation REL is also deleted, but the node %B4 is preserved as an isolated node inside the hyper-node %B.

LL#3: ((B1)):=;

(Delete any hyper-node that contains the node having the feature B1, wherever they are);

FINAL STATE: L(%A;%C) L(%C;%D)

The whole hyper-node %B will be deleted, including all its nodes, no matter in which level.

LL#4: (B1):=(NEW);

(Add the feature “NEW” to all nodes having the feature B1)

FINAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) L:B(%B1;%B2) L:B(%B2;%B3) REL:B(%B1;%B4) (NO CHANGE IN THE NODE STRUCTURE)

There is no indexes in the left and the right side, which have the same number of nodes. This means that they are automatically co-indexed. No node is deleted or replaced. The feature “NEW” is added to the the node %B1, because it contains the feature B1. This rule provokes a look, because the feature NEW will be added indefinitely to the node %B1. In order to avoid this, the condition should be set (B1,^NEW):=(NEW);

LL#5: (%x,B1):=(%y,NEW);

(Replace any node having the feature B1 by a new node having the feature NEW)

FINAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) L:B(%NEW;%B2) L:B(%B2;%B3) REL:B(%NEW;%B4)

The node %B1 is deleted and replaced by a new node %NEW. Notice that all instances of the node are replaced.

LL#6: ({(B1)|(B3)}):=;

(Delete any hyper-node that contains nodes having the features B1 or B3);

FINAL STATE: L(%A;%C) L(%C;%D)

The whole hyper-node %B will be deleted, including all its nodes, no matter in which level.

LL#7: ((B1)(B2)):=;

(Delete any hyper-node that contains the relation L(B1;B2));

FINAL STATE: L(%A;%C) L(%C;%D)

The whole hyper-node %B will be deleted, including all its nodes, no matter in which level.

LL#8: ((B1)(B3)):=;

(Delete any hyper-node that contains the relation L(B1;B3))

Nothing happens. The condition is not true in the case of the initial state indicated above.

LL#9: ((B1)):=(-feature);

(Remove the feature “feature” from any hyper-node containing a node with the feature B1)

As the left and the right side do not have indexes, they are automatically co-indexed. The co-indexation, however, is valid only to the hyper-node level, because the right side does not contain any inner node. In that sense, the feature “feature” is not removed from the inner node, but from the hyper-node.

LL#10: ((B1)):=((-feature));

(Remove the feature “feature” from anynode having the feature B1 which is inside a hyper-node)

The automatic indexation affects both levels: the hyper-node and the node, because they are equivalent. The rule is the same as (%x,(%y,B1)):=(%x,(%y,-feature));. The feature “feature” is now removed from the inner node and not from the hyper-node.

LL#11: ((%x,B1)):=((%y,NEW));

(Replace any node containing the feature B1 inside a hyper-node by a new node containing the feature 'NEW')

FINAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) L:B(%NEW;%B2) L:B(%B2;%B3) REL:B(%NEW;%B4)

The same as (%x,B1):=(%y,NEW); but inside a hyper-node (i.e., the rule applies only to the nodes having the feature B1 which are inside some other node).

LL#12: ((B1)):=((E)(F));

(Replace any node containing the feature B1 by a linear relation between two new nodes containing the features E and F, respectively)

FINAL STATE: : L(%A;%B) L(%B;%C) L(%C;%D) L:B(%B2;%B3) REL:B(%HB;%B4) L:HB(%E;%F)

The same as (%x,B1):=(%y,E)(%z,F); but inside a hyper-node (i.e., the rule applies only to the nodes having the feature B1 which are inside some other node). The linear relation between the nodes (%B1) and (%B2) disappear, because (%B1) is an argument of a non-linear relation REL(%B1;%B4) and should be replaced, therefore, by a hyper-node instead of a simple sequence of nodes (%E)(%F), since REL((%E)(%F);(%B4)) is not possible. As a consequence, the nodes (%E) and (%F) are created inside the hyper-node %HB and may not hold any linear relation with %B2, because they are now in different scopes.

LL#13: ((B1)):=(((E)(F),-B1));

(Replace any node containing the feature B1 by a new node containing a linear relation between two new nodes containing the features E and F, respectively)

FINAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) L:B(%HB;%B2) L:B(%B2;%B3) REL:B(%HB;%B4) L:HB(%E;%F)

The same as (%x,(%a,B1)):=(%x,(%b,E)(%c,F)); but inside a hyper-node (i.e., the rule applies only to the nodes having the feature B1 which are inside some other node). Differently from the previous example, the node containg the feature B1 is replaced by a hyper-node and not by two other nodes of the same level. As the system is conservative, the feature B1 has to deleted in order to prevent the rule from applying eternally.

LL#14:((B1)):=((E),(F));

(Replace the node containing the feature B1 by two new nodes containing the features E and F, respectively)

FINAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) L:B(%HB;%B2) L:B(%B2;%B3) REL:B(%HB;%B4) :HB(%E) :HB(%F)

The nodes (E) and (F) no longer constitute a linear relation, and are added as isolated notes to the hyper-node. Because of that, (B1) has to be replaced, necessarily, by a hyper-node. This means that this rule will have exactly the same effect of the rule below.

LL#15:((B1)):=(((E),(F),-B1));

(Replace the node containing the feature B1 by two new nodes containing the features E and F, respectively)

FINAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) L:B(%HB;%B2) L:B(%B2;%B3) REL:B(%HB;%B4) :HB(%E) :HB(%F)

The nodes (E) and (F) no longer constitute a linear relation, and are added as isolated notes to the hyper-node. As the system is conservative, the feature B1 has to deleted in order to prevent the rule from applying eternally.

LL#16: (REL(%B1;%B4)):=(NEWREL(%B1;%B5));

(Replace the relation REL between the nodes %B1 and %B4 by a new relation NEWREL between the existing node %B1 and a new node %B5)

FINAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) L:B(%B1;%B2) L:B(%B2;%B3) NEWREL:B(%B1;%B5) :B(%B4)

Nodes on both sides are automatically co-indexed, because their number is the same. Therefore, the relation on the left side is replaced by the relation on the right side in the same hyper-node. No node is deleted: notice that %B4 is still there. This is the same as REL(A;B):=REL(C;D);.

LL#17:(B1)(B2):=;

(The same as L(%B1;%B2):=; i.e., delete the linear relation between %B1 and %B2)

FINAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) :B(%B3) REL:B(%B1;%B4)

The linear relation between (%B1) and (%B2) is deleted, but the nodes (%B1) and (%B2) are preserved if part of other non-linear relations.

LL#18:(B1)(B2):=(B5);

(The same as L(%B1;%B2):=(%B5); i.e., replace the linear relation between %B1 and %B2 by %B5)

FINAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) L:B(%B5;%B3) REL:B(%B1;%B4)

The linear relation between (%B1) and (%B2) is replaced by %B5, but the nodes (%B1) and (%B2) are preserved if part of other non-linear relations.

LL#19:(%B1,B1)(B2):=(%B1);

(The same as L(%B1;%B2):=(%B1); i.e., replace the linear relation between %B1 and %B2 by %B1)

FINAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) L:B(%B1;%B3) REL:B(%B1;%B4)

The linear relation between (%B1) and (%B2) is replaced by %B1, but the nodes (%B1) and (%B2) are preserved if part of other non-linear relations.

LL#20:(B1)(%B2,B2):=(%B2);

(The same as L(%B1;%B2):=(%B2); i.e., replace the linear relation between %B1 and %B2 by %B2)

FINAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) L:B(%B2;%B3) REL:B(%B1;%B4)

The linear relation between (%B1) and (%B2) is replaced by %B2, but the nodes (%B1) and (%B2) are preserved if part of other non-linear relations.

LL#21:(%B1,B1)(%B2,B2):=(%B1,(%B2));

(replace the linear relation between %B1 and %B2 by the node %B1 with %B2 inside as an isolated node)

FINAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) L:B(%B1;%B3) REL:B(%B1;%B4) :B1(%B2)

The linear relation between (%B1) and (%B2) is replaced by %B1, but the nodes (%B1) and (%B2) are preserved if part of other non-linear relations.

LL#22: (%D,D):=(%D,-D,+D1)(%D,-D,+D2);

(Duplicate the node having the feature D, wherever they are)

FINAL STATE: L(%A;%B) L(%B;%C) L(%C;%D1) L(%D1;%D2) L:B(%B1;%B2) L:B(%B2;%B3) REL:B(%B1;%B4)

The whole hyper-node %D will be duplicated, including all its nodes, no matter in which level. Node duplication occurs only in LL rules. As the system is conservative, the feature D has to deleted in order to prevent the rule from applying eternally.

LT RULES

INITIAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) L:B(%B1;%B2) L:B(%B2;%B3) REL:B(%B1;%B4)

LT#1: (%B1,B1)(%B2,B2):=REL(%B1;%B2);

(Replace the relation L(%B1;%B2) by the relation REL(%B1;%B2))

FINAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) REL:B(%B1;%B2) L:B(%B2;%B3) REL:B(%B1;%B4)

No node is deleted, but there’s no longer a linear relation between %B1 and %B2. There’s still, however, a linear relation between %B2 and %B3 inside the hyper-node %B.

LT#2: (%B1,B1)(%B2,B2):=+REL(%B1;%B2);

(Add the relation REL(%B1;%B2) to the graph )

FINAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) L:B(%B1;%B2) L:B(%B2;%B3) REL:B(%B1;%B4) REL(%B1;%B2)

No node or relation is deleted. A new relation is created in the graph.

LT#3: (%B1,B1)(%B2,B2)(%B3,B3):=REL(%B1;%B2);

(Replace the relations L(%B1;%B2)L(%B2;%B3) by the relation REL(%B1;%B2))

FINAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) REL:B(%B1;%B2) REL:B(%B1;%B4)

The node (%B3) is deleted because it is not present in the right side.

LT#4: (%B1,B1)(%B3,B3)(%B2,B2):=REL(%B1;%B2);

(Replace the relations L(%B1;%B3)L(%B3;%B2) by the relation REL(%B1;%B2))

Nothing happens. The condition is not true in this case.

LT#5: (%B1,B1):=REL(%B1;%B5); (Replace the node having the feature B1 by the relation REL(%B1;%B5))

FINAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) L:B(%B2;%B3) REL:B(%HB;%B4) REL:HB(%B1;%B5)

There is no longer a linear relation between %B1 and %B2, because the node was replaced by a relation and, therefore, removed from the list structure.

LT#6: (%B1,B1):=+REL(%B1;%B5); (Add the relation REL(%B1;%B5) to the graph)

FINAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) L:B(%B1;%B2) L:B(%B2;%B3) REL:B(%B1;%B4) REL(%B1;%B5)

No node is replaced or deleted. A new relation is added to the graph.

LT#7: (REL(%B1,B1;%B4,B4)):=NEWREL(%B1;%B4); (Replace the hyper-node containing the relation REL by the relation NEWREL(%B1;%B5)

FINAL STATE: L(%A;%C) L(%C;%D) NEWREL(%B1;%B4)

The whole hyper-node %B will be replaced by the new relation. All its inner nodes not referred to in the right side will be deleted as well.

LT#8: (REL(%B1,B1;%B4,B4)):=+NEWREL(%B1;%B4); (Add the relation NEWREL(%B1;%B4) to the graph)</nowiki>

FINAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) L:B(%B1;%B2) L:B(%B2;%B3) REL:B(%B1;%B4) NEWREL(%B1;%B4)

The hyper-node remains the same. The relation NEWREL(%B1;%B4) is added to its outer scope.

TL Rules

INITIAL STATE: L(%A;%B) L(%B;%C) REL:B(%B1;%B2) REL:B(%B1;%B3)

TL#1: REL(%B1;%B2)REL(%B1;%B3):=(%B1)(%B2);

(Replace the relation REL between the nodes %B1 and %B2 and the relation REL between the nodes %B1 and %B3 by a linear relation between %B1 and %B2)

FINAL STATE: L(%A;%B) L(%B;%C) L:B(%B1;%B2)

The node %B3 is deleted, because it does not have any other relation with any other node inside the hyper-node.

TL#2: REL(%B1;%B2):=(%B2);

(Replace the relation REL between the nodes %B1 and %B2 by the node %B1)

FINAL STATE: L(%A;%B) L(%B;%C) REL:B(%B1;%B3) :B(%B2)

The node %B1 is not deleted, because it still has a relation with the node %B3. The relation between %B1 and %B2 is replaced by a single node %B2.

TT or NN Rules

INITIAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) L:B(%B1;%B2) L:B(%B2;%B3) REL:B(%B1;%B4)

TT#1:REL(%x;%y):=NEWREL(%x;%y)

FINAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) L:B(%B1;%B2) L:B(%B2;%B3) NEWREL:B(%B1;%B4)

The relation is changed, but the arguments %x and %y are preserved.

TT#2: REL(%x;%y):=REL(%w;%z)

FINAL STATE: L(%A;%B) L(%B;%C) L(%C;%D) L:B(%B1;%B2) L:B(%B2;%B3) :B(%B4) REL(%w;%z)

The relation between %x and %y is deleted, but the nodes are preserved. Noticed that %B4 became an isolated node, but it’s still there, because no node may be deleted by a NN rule.

INITIAL STATE : REL(%x;%y;%z)

TT#3:REL(%x;%y;%z):=REL(%x;%y);

FINAL STATE: REL(%x;%y) (%z)

The node %z is not deleted.