The document proposes an order independent incremental evolving fuzzy grammar fragment learner. It discusses learning the underlying grammar patterns from text fragments in an order independent manner. The method learns grammar fragments from examples and combines them using minimal rules, ensuring the extracted grammars have equal parsing coverage regardless of the order of examples. A formal proof is provided to show the approach is order independent.

3. ** Source from World Incidents Tracking System Human is able to understand a class without following a strict pattern

5. TEXT FRAGMENT LEARNING learn the underlying grammar patterns of similar texts ; exploiting both syntactical and semantic properties Text Fragment Examples XML Tag: Event Type - Bomb exploded - Explosion occurred - detonated a bomb -detonated a timed improvised explosive device Bombing - Attacks to occur - Attackers threw a grenade - Assailants attacked a security vehicle - Gunmen killed a member Armed Attack

10. GRAMMAR SIMILARITY Table 1: Example of string edit distance operation (*I:Insert, D:Delete, S:Substitute) Table 2: Example of Grammar Edit Distance Operation (*I:Insert, D:Delete, S:Substitute) Cost(sg ,tg) = <I D S Rs Rt>=<1 1 1 null null> I:Insert D:Delete S:Substitute Rs: remaining in Source Rt: remaining in Target Source string W E D N E S D A Y Target string T U E S D A Y Edit distance* S=1 S=1 D=1 D=1 = = = = = Source grammar, sg Number Word Word Streetending Placename Target grammar, tg Number Placename Streetending Placename Countyname Edit distance* = S=1 D=1 = = I=1

11. GRAMMAR COMBINATION Start s=new string maxMem=membership(s,TG) maxMem<1? costST=costTS=1 Y gx=Combine(sg,tg) costST=1 && costTS=0 gx=sg N Y N costST=0 && costTS=1 gx=tg Y Update TG: GTj={GTj-1-gti} union {gx} gx=sg N sg=deriveGrammar(s) tg=target grammar with maxMem costST=grammarSimilarity(sg,tg) costTS=grammarSimilarity (tg,sg) End Y N

12. MINIMAL COMBINATION RULES Source Grammar Target Grammar Cost (Source, Target) Cost (Target, Source) Combination Operation Combined grammar a-b-c a-b 0 1 0 - - 1 0 0 - - Insert a-b-[c] a-b a-b-c 1 0 0 - - 0 1 0 - - Insert a-b-[c] a-b-c a-B-c 0 0 0 - - 0 0 1 - - Merge a-B-c, B>b a-B-c a-b-c 0 0 1 - - 0 0 0 - - Merge a-B-c, B>b a-F-c a-G-c 0 0 1 - - 0 0 1 - - Create a-X-c , X:=F||G,

15. Let: Ext(GS j ) = Ext(GS j-1 ) ∪ Ext(gs j ) g x =Combine(gs j ,gt i ) Ext(g x ) = Ext(gs j ) ∪ Ext (gt i ) Case1: Combine( gs j ,gt i ) if Cost(gs j ,gt i )=Cost(gt i , gs j )= 1 In this case, Ext(GT i ) = Ext(GT i-1 - {gt i }) ∪ Ext(g x ) Hence Ext(GT i ) = (Ext(GTi-1) - (Ext(gt i )) ∪ Ext(g x ) = Ext(GT x-1 ) ∪ Ext(gs j ) Case2: Combine( gs j ,gt i ) if gs j is more general than gt i i.e. Ext(gt i ) ⊆ Ext(gs j ) In this case, Ext(GT i ) = Ext(GT i-1 ) ∪ Ext(gs j ) Case3: Combine( gs j ,gt i ) if gt i is more general than gs j i.e. Ext(gs j ) ⊆ Ext (gt i ) In this case, Ext(GT i ) = Ext(GT i-1 ) Therefore Ext(GS j-1 ) = Ext(Gt j-1 ) implies Ext(GS j ) = Ext(Gt i ) Thus in all cases the inductive hypothesis is true and Ext(GSj)=Ext(Gti) ■