A Minimalist Grammar (MG) as Interpreted Regular Tree ......Nov 24, 2018 · Meaghan Fowlie and...
Transcript of A Minimalist Grammar (MG) as Interpreted Regular Tree ......Nov 24, 2018 · Meaghan Fowlie and...
A Minimalist Grammar (MG)as Interpreted Regular Tree Grammar (IRTG)
Martin van Harmelen
Language Science and TechnologyComputational Linguistics & Phonetics (CoLi)
Universitat des Saarlandes
22-11-2018
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Minimalist Tree vs. String Grammar
1. Minimalist Tree vs. String Grammar
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Minimalist Tree vs. String Grammar
Derived Tree vs. Derived String
〈make tortillas, =D V, ∅〉
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Minimalist Tree vs. String Grammar
move: Deleting vs. Storing
〈Maria will make tortillas, T, ∅〉
〈will make tortillas, +nom T, {nom 7→ 〈Maria, ε〉}〉
〈will make tortillas, =D +nom V, ∅〉 〈Maria, D -nom, ∅〉
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Minimalist String Grammar
2. Minimalist String Grammar
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Minimalist String Grammar
Objects
Derived string: 〈string , stack , storage〉storage: {feature 7→ 〈string , stack〉}
Example
〈Matt presented, T, ∅〉〈will make tortillas, +nom T, {nom 7→ 〈Maria, ε〉}〉
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Minimalist String Grammar
Derivation Tree
〈Matt presented, T, ∅〉move1
〈presented, +nom T, {nom 7→ 〈Matt, ε〉}〉merge1
〈ε, =V +nom T, ∅〉 〈presented, V, {nom 7→ 〈Matt, ε〉}〉merge2
〈presented, =D V, ∅〉 〈Matt, D -nom, ∅〉
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Minimalist String Grammar
Lexicon
〈ε, =V +nom T, ∅〉〈klingon, D, ∅〉〈Matt, D -nom, ∅〉〈Teresa, D -nom, ∅〉〈presented, =D V, ∅〉〈presented, =D =D V, ∅〉〈speaks, =D =D V, ∅〉
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Minimalist String Grammar
Grammar Rules: merge1
〈presented, +nom T, {nom 7→ 〈Matt, ε〉}〉merge1
〈ε, =V +nom T, ∅〉 〈presented, V, {nom 7→ 〈Matt, ε〉}〉
If the feature X matchesand the feature-stack is emptythen concatenate strings and combine storages
merge1 (〈s, =Xα,S〉 , 〈t, X,T〉) = 〈s · t, α,S⊕ T〉
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Minimalist String Grammar
Grammar Rules: merge2
〈presented, V, {nom 7→ 〈Matt, ε〉}〉merge2
〈presented, =D V, ∅〉 〈Matt, D -nom, ∅〉
If the feature X matchesand there are more features on the stack
(starting with -)then store string t and remaining features β under f
(for when you find +f)
merge2 (〈s, =Xα,S〉 , 〈t, X -fβ,T〉) = 〈s, α,S⊕ T⊕ {f 7→ 〈t, β〉}〉
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Minimalist String Grammar
Grammar Rules: move1
〈Matt presented, T, ∅〉move1
〈presented, +nom T, {nom 7→ 〈Matt, ε〉}〉
If the feature f exists in storageand the stored feature-stack is emptythen left-concatenate the stored string
move1 (〈s, +fα,S〉) = 〈t · s, α,S− f〉 if S(f) = 〈t, ε〉
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Minimalist String Grammar
Grammar Rules: move2
〈presented, T, {wh 7→ 〈Who, ε〉}〉move2
〈presented, +nom T, {nom 7→ 〈Who, -wh〉}〉
If the feature f exists in storageand there are more features on the stored stack
(starting with -)then re-store string t and remaining features γ under g
(for when you find +g)
move2 (〈s, +fα,S〉) = 〈s, α, (S− f)⊕ {g 7→ 〈t, γ〉}〉 if S(f) = 〈t, -gγ〉
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Minimalist String Grammar
Grammar Rules
merge(1|2): eat a =X, X feature-pair
move(1|2): eat a +f and stored (-)f
(merge|move)1: stick together strings
(merge|move)2: store strings (using features as index)
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IRTG
3. IRTG
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IRTG
IRTG
Regular Tree Grammar (specifies allowed combinations)
Interpretation(s)
TreehomomorphismAlgebra
objects (things to be combined & result of evaluation)operations (different ways to combine)evaluation (specifies result of operations)
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IRTG Algebra
3.1. Algebra
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IRTG Algebra
Algebra Functionality
merge(1|2): eat a =X, X feature-pair
move(1|2): eat a +f and stored (-)f
(merge|move)1: stick together strings
(merge|move)2: store strings (using features as index)
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IRTG Algebra
Algebra Terminology
object 〈string , stack , {feature 7→ 〈string , stack〉 }〉operation ≈ (merge|move)(1|2)
term combinations of above (= tree)
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IRTG Algebra
Algebra Evaluation: merge
merge1 (〈s,S〉 , 〈t,T〉) = 〈s · t, α,S⊕ T〉
If the feature X matchesand the feature-stack is emptythen concatenate strings and combine storages
merge2f (〈s,S〉 , 〈t,T〉) = 〈s,S⊕ T⊕ {f 7→ t}〉
If the feature X matchesand there are more features on the stack
(starting with -)then store string t and remaining features β under f
(for when you find +f)
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IRTG Algebra
Algebra Evaluation: move
move1f (〈s,S〉) = 〈t · s, α,S− f〉 where S(f) = t
If the feature f exists in storageand the stored feature-stack is emptythen left-concatenate the stored string
move2f-g (〈s,S〉) = 〈s, (S− f)⊕ {g 7→ t}〉 where S(f) = t
If the feature f exists in storageand there are more features on the stored stack
(starting with -)then re-store string t and remaining features γ under g
(for when you find +g)
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IRTG Regular Tree Grammar
3.2. Regular Tree Grammar
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IRTG Regular Tree Grammar
Regular Tree Grammar Functionality
merge(1|2): eat a =X, X feature-pair
move(1|2): eat a +f and stored (-)f
(merge|move)1: stick together strings
(merge|move)2: store strings (using features as index)
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IRTG Regular Tree Grammar
RTG Terminology
non-terminal 〈string , stack , {feature 7→ 〈string , stack〉 }〉
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IRTG Regular Tree Grammar
How-To
1 MG lexicon 7→strip strings RTG lexical rules
2 applications of (merge|move)(1|2) 7→ RTG non-lexical rules
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IRTG Regular Tree Grammar
The Grammar
lexicon from minimalist grammar
〈ε, =V +nom T, ∅〉〈klingon, D, ∅〉〈Matt, D -nom, ∅〉〈Teresa, D -nom, ∅〉〈presented, =D V, ∅〉〈presented, =D =D V, ∅〉〈speaks, =D =D V, ∅〉
lexical rules of regular tree grammar
〈=V +nom T, ∅〉 → lexcase
〈D, ∅〉 → lexklingon
〈D -nom, ∅〉 → lexMatt
〈D -nom, ∅〉 → lexTeresa
〈=D V, ∅〉 → lexpresented
〈=D =D V, ∅〉 → lexpresented2
〈=D =D V, ∅〉 → lexspeaks
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IRTG Regular Tree Grammar
Lexical Rules (condensed)
1 〈=V +nom T, ∅〉 → lexcase2 〈D, ∅〉 → lexklingon3 〈D -nom, ∅〉 → lexMatt |lexTeresa4 〈=D V, ∅〉 → lexpresented5 〈=D =D V, ∅〉 → lexpresented2|lexspeaks
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IRTG Regular Tree Grammar
Non-Lexical Rules: merge1
〈V, ∅〉 → mg1.1 (〈=D V, ∅〉 , 〈D, ∅〉)〈=D V, ∅〉 → mg1.2 (〈=D =D V, ∅〉 , 〈D, ∅〉)〈V, {nom 7→ ε}〉 → mg1.3 (〈=D V, {nom 7→ ε}〉 , 〈D, ∅〉)〈+nom T, ∅〉 → mg1.4 (〈=V +nom T, ∅〉 , 〈V, ∅〉)〈+nom T, {nom 7→ ε}〉 → mg1.5 (〈=V +nom T, ∅〉 , 〈V, {nom 7→ ε}〉)
If the feature X matchesand the feature-stack is emptythen concatenate strings and combine storages
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IRTG Regular Tree Grammar
Non-Lexical Rules: merge2
〈V, {nom 7→ ε}〉 → mg2.1 (〈=D V, ∅〉 , 〈D -nom, ∅〉)〈=D V, {nom 7→ ε}〉 → mg2.2 (〈=D =D V, ∅〉 , 〈D -nom, ∅〉)
If the feature X matchesand there are more features on the stackthen store string t and remaining features β under f
(for when you find +f)
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IRTG Regular Tree Grammar
Non-Lexical Rules: move1
〈T, ∅〉!→ mv1.1 (〈+nom T, {nom 7→ ε}〉)
If the feature f exists in storageand the stored feature-stack is emptythen left-concatenate the stored string
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IRTG Regular Tree Grammar
Non-Lexical Rules: move2
Example
lexicon from minimalist grammar
〈〈Who, D -nom -wh〉, ∅〉 〈〈ε, =T +wh C〉, ∅〉
rules of regular tree grammar
〈V, {nom 7→ -wh}〉 → mg2.3 (〈=D V, ∅〉 , 〈D -nom -wh, ∅〉). . .
〈T, {wh 7→ ε}〉 → mv2.1 (〈+nom T, {nom 7→ -wh}〉)
If the feature f exists in storageand there are more features on the stored stack
(starting with -)then re-store string t and remaining features γ under g
(for when you find +g)
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IRTG Arrows
3.3. Arrows
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IRTG Arrows
Derivation Tree
mv1.1
mg1.5
lexcase mg2.1
lexpresented lexMatt
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IRTG Arrows
Treehomomorphism
mv1.1 7→ move1nom(x1)
mg1.5 7→ merge1(x1, x2)
mg2.1 7→ merge2nom(x1, x2)
lexcase 7→ 〈ε, ∅〉lexpresented 7→ 〈presented, ∅〉
lexMatt 7→ 〈Matt, ∅〉. . .
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IRTG Arrows
Term of Algebra
move1nom
merge1
〈ε, ∅〉 merge2nom
〈presented, ∅〉 〈Matt, ∅〉
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IRTG Arrows
Evaluation
outcome of operations
Example
merge2nom
〈presented, ∅〉 〈Matt, ∅〉〈presented, {nom 7→ Matt}〉
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IRTG Arrows
Object of Algebra
〈Matt presented, ∅〉
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IRTG Arrows
Conclusion
RTG decides allowed combinations
Algebra decides outcome of combinations
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IRTG Arrows
Exercise
Say we would add the following two items to our Minimalist Grammar:
〈〈Who, D -nom -wh〉, ∅〉〈〈ε, =T +wh C〉, ∅〉
Do the following:
Write down the extra RTG rules needed
Write down the full homomorphism
Show how the following sentence would be derived:
Who presented Klingon?
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IRTG Arrows
References
Meaghan Fowlie and Alexander Koller. Parsing minimalist languages withinterpreted regular tree grammars. In Proceedings of the 13thInternational Workshop on Tree Adjoining Grammars and RelatedFormalisms (TAG), pages 11–20. Association for ComputationalLinguistics, September 2017. URLhttps://aclanthology.info/papers/W17-6202/w17-6202.
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