Feature structures and unification

Attributes and values

The following object describes a class of persons: Attributes and values

The following object describes a class of persons: age 22 gender M nationality Norwegian Attributes and values

The following object describes a class of persons: age 22 gender M nationality Norwegian Attributes and values Attributes

The following object describes a class of persons: age 22 gender M nationality Norwegian Attributes and values Attributes Values

The following object describes a class of persons: age 22 gender M nationality Norwegian Attributes and values Let this be the class of persons described:

The following object describes a class of persons: age 22 gender M nationality Norwegian Attributes and values Let this be the class of persons described:

The following object describes a class of persons: age 22 gender M nationality Norwegian Attributes and values Let this be the class of persons described: Then remove a feature...

The following object describes a class of persons: age 22 nationality Norwegian Attributes and values Let this be the class of persons described: Then remove a feature...

The following object describes a class of persons: age 22 nationality Norwegian Attributes and values Let this be the class of persons described: Then remove a feature... and the class grows.

The following object describes a class of persons: age 22 nationality Norwegian Attributes and values Let this be the class of persons described: Then remove a feature... and the class grows. Add a feature instead...

The following object describes a class of persons: age 22 gender M nationality Norwegian eyecolour brown Attributes and values Let this be the class of persons described: Then remove a feature... and the class grows. Add a feature instead...

The following object describes a class of persons: age 22 gender M nationality Norwegian eyecolour brown Attributes and values Let this be the class of persons described: Then remove a feature... and the class grows. Add a feature instead... and the class shrinks.

The following object describes a class of persons: age 22 gender M nationality Norwegian A grammar example: Attributes and values

The following object describes a class of persons: age 22 gender M nationality Norwegian A grammar example: catNP numbersg person3 Attributes and values

The following object describes a class of persons: age 22 gender M nationality Norwegian A grammar example: catNP numbersg person3 This object describes a class of phrases: Attributes and values

The following object describes a class of persons: age 22 gender M nationality Norwegian A grammar example: catNP numbersg person3 This object describes a class of phrases: Attributes and values a man the horse some red car the King’s man water nice beer...

The following object describes a class of persons: age 22 gender M nationality Norwegian A grammar example: catNP numbersg person3 This object describes a class of phrases: Remove a feature... Attributes and values a man the horse some red car the King’s man water nice beer...

The following object describes a class of persons: age 22 gender M nationality Norwegian A grammar example: catNP person3 This object describes a class of phrases: Remove a feature... Attributes and values a man the horse some red car the King’s man water nice beer...

The following object describes a class of persons: age 22 gender M nationality Norwegian A grammar example: catNP person3 This object describes a class of phrases: Remove a feature... and the class grows. Attributes and values a man the horse some red car the King’s man water nice beer... men the horses some red cars the King’s men waters nice beers...

catNP numbersg person3 f1: Feature structures as functions

catNP numbersg person3 A set of ordered pairs (of attributes and values) f1: Feature structures as functions

catNP numbersg person3 A set of ordered pairs (of attributes and values) Never more than one occurrence of a given attribute f1: Feature structures as functions

catNP numbersg person3 A set of ordered pairs (of attributes and values) Never more than one occurrence of a given attribute Never more than one value of a given attribute (but different attributes can have the same value) f1: Feature structures as functions

catNP numbersg person3 A set of ordered pairs (of attributes and values) Never more than one occurrence of a given attribute Never more than one value of a given attribute (but different attributes can have the same value) Hence such a structure can be considered as a function from attributes to values f1: Feature structures as functions

catNP numbersg person3 A set of ordered pairs (of attributes and values) Never more than one occurrence of a given attribute Never more than one value of a given attribute (but different attributes can have the same value) Hence such a structure can be considered as a function from attributes to values Example: f1(cat)=NP f1(number)=sg f1(person)=3 f1: Feature structures as functions

catNP numbersg person3 A set of ordered pairs (of attributes and values) Never more than one occurrence of a given attribute Never more than one value of a given attribute (but different attributes can have the same value) Hence such a structure can be considered as a function from attributes to values Example: f1(cat)=NP f1(number)=sg f1(person)=3 Values can be atomic or complex: f1: Feature structures as functions

catNP numbersg person3 A set of ordered pairs (of attributes and values) Never more than one occurrence of a given attribute Never more than one value of a given attribute (but different attributes can have the same value) Hence such a structure can be considered as a function from attributes to values Example: f1(cat)=NP f1(number)=sg f1(person)=3 Values can be atomic or complex: f1: agreement cat NP numbersingular personthird Feature structures as functions

Subsumption

cat NP Subsumption

cat NP agreement cat NP numbersingular Subsumption

cat NP agreement cat NP numbersingular agreement cat NP numbersingular personthird Subsumption

cat NP agreement cat NP numbersingular agreement cat NP numbersingular personthird agreement cat NP numbersingular personthird subject numbersingular personthird Subsumption

cat NP agreement cat NP numbersingular agreement cat NP numbersingular personthird agreement cat NP numbersingular personthird subject numbersingular personthird agreement cat NP numbersingular personthird subject 1 1 Subsumption

Not subsumption

agreement cat NP numbersingular 1 Not subsumption

agreement cat NP numbersingular agreement cat NP personthird 1 2 Not subsumption

agreement cat NP numbersingular agreement cat NP personthird , 2 1 Not subsumption

agreement cat NP numbersingular agreement cat NP personthird agreement cat NP numberplural , 2 1 Not subsumption

agreement cat NP numbersingular agreement cat NP personthird agreement cat NP numberplural , , 3 1 Not subsumption

agreement cat NP numbersingular agreement cat NP personthird agreement cat NP numberplural agreement cat NP numbersingular personthird , , 3 1 Not subsumption

agreement cat NP numbersingular agreement cat NP personthird agreement cat NP numberplural agreement cat NP numbersingular personthird , , Not subsumption

agreement cat NP numbersingular agreement cat NP personthird agreement cat NP numberplural agreement cat NP numbersingular personthird , , Not subsumption

agreement cat NP numbersingular agreement cat NP personthird agreement cat NP numberplural agreement cat NP numbersingular personthird , , = 4 Not subsumption

agreement cat NP numbersingular agreement cat NP personthird agreement cat NP numberplural agreement cat NP numbersingular personthird , , = 4 13 = fail Not subsumption

agreement cat NP numbersingular agreement cat NP personthird agreement cat NP numberplural agreement cat NP numbersingular personthird , , = 4 13 = fail Unification: a b = c if and only if a c and b c and there is no d such that a d and b d and d c Not subsumption

Unification

cat NP Unification

cat NP agreementnumbersingular Unification

cat NP agreementnumbersingular = agreement cat NP numbersingular Unification

cat NP agreementnumbersingular = cat NP agreement cat NP numbersingular Unification

agreement cat NP numbersingular cat NP agreementnumbersingular = cat NP agreement cat NP numbersingular Unification

agreement cat NP numbersingular cat NP agreementnumbersingular = cat NP agreement cat NP numbersingular agreement cat NP numbersingular = Unification

agreement cat NP numbersingular Unification

agreement cat NP numbersingular = agreement cat NP numbersingular Unification

agreement cat NP numbersingular subject = agreementnumbersingular agreementnumbersingular agreement cat NP numbersingular Unification

agreement cat NP numbersingular subject = agreementnumbersingular agreementnumbersingular subjectagreementpersonthird agreement cat NP numbersingular Unification

agreement cat NP numbersingular subject = agreementnumbersingular agreementnumbersingular subjectagreementpersonthird agreement cat NP numbersingular subject agreementnumbersingular agreement numbersingular personthird = Unification

subject agreementnumbersingular agreementnumbersingular Unification

subject agreementnumbersingular agreement 1 1 subject agreementnumbersingular agreementnumbersingular Compare with: Unification

subject agreementnumbersingular agreement subjectagreement 1 personthird 1 subject agreementnumbersingular agreementnumbersingular Unification Compare with:

subject agreementnumbersingular agreement subjectagreement numbersingular personthird = 1 1 subjectagreement 1 1 subject agreementnumbersingular agreementnumbersingular Unification Compare with:

Unification

subject agreement 1 2 f1: Unification

subject agreement 1 2 f1: f1(agreement) = f1(subject)(agreement) Unification

subject agreement 1 2 f1: f1(agreement) = f1(subject)(agreement) 123 = Unification

subject agreement 1 2 f1: f1(agreement) = f1(subject)(agreement) 123 = subject agreement f1: 3 3 Unification

subject agreement 1 2 f1: f1(agreement) = f1(subject)(agreement) 123 = subject agreement f1: 3 3 agreement subject agreement f1: Unification

subject agreement 1 2 f1: f1(agreement) = f1(subject)(agreement) 123 = subject agreement f1: 3 3 agreement subject agreement f1: Unification

subject agreement 1 2 f1: f1(agreement) = f1(subject)(agreement) 123 = subject agreement f1: 3 3 agreement subject agreement f1: Unification

Unification through constraints:

subject agreement 1 2 f1: f1(agreement) = f1(subject)(agreement) Unification through constraints:

subject agreement 1 2 f1: f1(agreement) = f1(subject)(agreement) Unification through constraints: Alternative notation with paths:

subject agreement 1 2 f1: f1(agreement) = f1(subject)(agreement) Unification through constraints: Alternative notation with paths: ‹agreement› = ‹subject agreement› This means that the two paths have the same (unspecified) value.

subject agreement 1 2 f1: f1(agreement) = f1(subject)(agreement) Unification through constraints: Alternative notation with paths: ‹agreement› = ‹subject agreement› This means that the two paths have the same (unspecified) value. A constraint may also specify a value:

subject agreement 1 2 f1: f1(agreement) = f1(subject)(agreement) Unification through constraints: Alternative notation with paths: ‹agreement› = ‹subject agreement› This means that the two paths have the same (unspecified) value. A constraint may also specify a value: ‹agreement number› = sg

subject agreement 1 2 f1: f1(agreement) = f1(subject)(agreement) Unification through constraints: Alternative notation with paths: ‹agreement› = ‹subject agreement› This means that the two paths have the same (unspecified) value. A constraint may also specify a value: ‹agreement number› = sg We thus have two types of constraints:

subject agreement 1 2 f1: f1(agreement) = f1(subject)(agreement) Unification through constraints: Alternative notation with paths: ‹agreement› = ‹subject agreement› This means that the two paths have the same (unspecified) value. A constraint may also specify a value: ‹agreement number› = sg We thus have two types of constraints: ‹attribute path› = Atomic value (The path has the specified value) ‹attribute path› = ‹attribute path› (The two paths have the same value)

Incorporating unification in a phrase structure grammar

VP S NP sleepsJohn Phrase structure tree: Incorporating unification in a phrase structure grammar

VP S NP sleepsJohn Grammar: S → NP VP Lexicon: John NP sleeps VP sleep VP A one-rule grammar with lexicon:Phrase structure tree: Incorporating unification in a phrase structure grammar

VP S NP sleepsJohn Grammar: S → NP VP A one-rule grammar with lexicon:Phrase structure tree: We incorporate features and unification to handle agreement. Incorporating unification in a phrase structure grammar Lexicon: John NP sleeps VP sleep VP

VP S NP sleepsJohn Grammar: S → NP VP A one-rule grammar with lexicon:Phrase structure tree: We incorporate features and unification to handle agreement. Grammar: S -> NP VP ‹f:S› = ‹f:VP› ‹f:S subject› = ‹f:NP› Incorporating unification in a phrase structure grammar Lexicon: John NP sleeps VP sleep VP

VP S NP sleepsJohn Grammar: S → NP VP A one-rule grammar with lexicon:Phrase structure tree: We incorporate features and unification to handle agreement. Lexicon: John NP ‹f:NP agreement number› = singular ‹f:NP agreement person› = third sleeps VP ‹f:VP subject agreement number› = singular ‹f:VP subject agreement person› = third sleep VP ‹f:VP subject agreement number› = plural Grammar: S -> NP VP ‹f:S› = ‹f:VP› ‹f:S subject› = ‹f:NP› Incorporating unification in a phrase structure grammar Lexicon: John NP sleeps VP sleep VP

Incorporating unification in a phrase structure grammar The rule now describes this subtree:

Incorporating unification in a phrase structure grammar The rule now describes this subtree: 1 subject 2 2 NPVP 1 S

Incorporating unification in a phrase structure grammar The rule now describes this subtree: 1 subject 2 2 NPVP 1 The lexical entries: S

Incorporating unification in a phrase structure grammar The rule now describes this subtree: 1 subject 2 2 NPVP 1 The lexical entries: agreement Johnsleeps number singular person third agreement number singular person third subject NP VP S

Incorporating unification in a phrase structure grammar 1 subject 2 2 NPVP 1 agreement Johnsleeps number singular person third agreement number singular person third subject NP VP What happens if we insert ‘John’ as the NP daughter? S

Incorporating unification in a phrase structure grammar 1 subject 2 2 NPVP 1 agreement Johnsleeps number singular person third agreement number singular person third subject NP VP S

Incorporating unification in a phrase structure grammar 1 subject 2 2 NPVP 1 agreement Johnsleeps number singular person third agreement number singular person third subject NP VP S

Incorporating unification in a phrase structure grammar 1 subject 2 S 2 NPVP 1 John sleeps agreement number singular person third subject VP agreement number singular person third

Incorporating unification in a phrase structure grammar 1 subject 2 S 2 NPVP 1 John sleeps agreement number singular person third subject VP agreement number singular person third 'sleeps' can now only be inserted if its agreement-features are compatible with 'John'.

Incorporating unification in a phrase structure grammar 1 subject 2 S 2 NPVP 1 John sleeps agreement number singular person third subject VP agreement number singular person third

Incorporating unification in a phrase structure grammar 1 subject 2 S 2 NPVP 1 John sleeps agreement number singular person third subject VP agreement number singular person third

Incorporating unification in a phrase structure grammar 1 subject 2 S 2 NPVP 1 Johnsleeps agreement number singular person third

Feature structures in Lexical-Functional Grammar

1.[ S I forced him [ S PRO to be kind]] Phrase structure analyses in traditional transformational grammar:

1.[ S I forced him [ S PRO to be kind]] 2.[ S I believed [ S him to be kind]] Phrase structure analyses in traditional transformational grammar:

1.[ S I forced him [ S PRO to be kind]] 2.[ S I believed [ S him to be kind]] 3.[ S NP seems [ S John to shout]] Phrase structure analyses in traditional transformational grammar:

1.[ S I forced him [ S PRO to be kind]] 2.[ S I believed [ S him to be kind]] 3.[ S NP seems [ S John to shout]] 4.[ S NP tends [ S John to shout]] Phrase structure analyses in traditional transformational grammar:

1.[ S I forced him [ S PRO to be kind]] 2.[ S I believed [ S him to be kind]] 3.[ S NP seems [ S John to shout]] 4.[ S NP tends [ S John to shout]] 5.[ S Bill [ VP killed John]] Phrase structure analyses in traditional transformational grammar:

1.[ S I forced him [ S PRO to be kind]] 2.[ S I believed [ S him to be kind]] 3.[ S NP seems [ S John to shout]] 4.[ S NP tends [ S John to shout]] 5.[ S Bill [ VP killed John]] 6. [ S NP [ VP was killed John]] Phrase structure analyses in traditional transformational grammar:

1.[ S I forced him [ S PRO to be kind]] 2.[ S I believed [ S him to be kind]] 3.[ S NP seems [ S John to shout]] 4.[ S NP tends [ S John to shout]] 5.[ S Bill [ VP killed John]] 6. [ S NP [ VP was killed John]] 1.[ S I forced him [ VP' to be kind]] Phrase structure analyses in Lexical Functional Grammar: Phrase structure analyses in traditional transformational grammar:

1.[ S I forced him [ S PRO to be kind]] 2.[ S I believed [ S him to be kind]] 3.[ S NP seems [ S John to shout]] 4.[ S NP tends [ S John to shout]] 5.[ S Bill [ VP killed John]] 6. [ S NP [ VP was killed John]] 1.[ S I forced him [ VP' to be kind]] 2.[ S I believed him [ VP' to be kind]] Phrase structure analyses in Lexical Functional Grammar: Phrase structure analyses in traditional transformational grammar:

1.[ S I forced him [ S PRO to be kind]] 2.[ S I believed [ S him to be kind]] 3.[ S NP seems [ S John to shout]] 4.[ S NP tends [ S John to shout]] 5.[ S Bill [ VP killed John]] 6. [ S NP [ VP was killed John]] 1.[ S I forced him [ VP' to be kind]] 2.[ S I believed him [ VP' to be kind]] 4.[ S John tends [ VP' to shout]] Phrase structure analyses in Lexical Functional Grammar: Phrase structure analyses in traditional transformational grammar:

1.[ S I forced him [ S PRO to be kind]] 2.[ S I believed [ S him to be kind]] 3.[ S NP seems [ S John to shout]] 4.[ S NP tends [ S John to shout]] 5.[ S Bill [ VP killed John]] 6. [ S NP [ VP was killed John]] 1.[ S I forced him [ VP' to be kind]] 2.[ S I believed him [ VP' to be kind]] 4.[ S John tends [ VP' to shout]] 6.[ S John [ VP' was killed]] Phrase structure analyses in Lexical Functional Grammar: Phrase structure analyses in traditional transformational grammar:

1.[ S I forced him [ S PRO to be kind]] 2.[ S I believed [ S him to be kind]] 3.[ S NP seems [ S John to shout]] 4.[ S NP tends [ S John to shout]] 5.[ S Bill [ VP killed John]] 6. [ S NP [ VP was killed John]] 1.[ S I forced him [ VP' to be kind]] 2.[ S I believed him [ VP' to be kind]] 4.[ S John tends [ VP' to shout]] 6.[ S John [ VP' was killed]] Phrase structure analyses in Lexical Functional Grammar: Phrase structure analyses in traditional transformational grammar: How does LFG capture

1.[ S I forced him [ S PRO to be kind]] 2.[ S I believed [ S him to be kind]] 3.[ S NP seems [ S John to shout]] 4.[ S NP tends [ S John to shout]] 5.[ S Bill [ VP killed John]] 6. [ S NP [ VP was killed John]] 1.[ S I forced him [ VP' to be kind]] 2.[ S I believed him [ VP' to be kind]] 4.[ S John tends [ VP' to shout]] 6.[ S John [ VP' was killed]] Phrase structure analyses in Lexical Functional Grammar: Phrase structure analyses in traditional transformational grammar: How does LFG capture the difference between 1 and 2,

1.[ S I forced him [ S PRO to be kind]] 2.[ S I believed [ S him to be kind]] 3.[ S NP seems [ S John to shout]] 4.[ S NP tends [ S John to shout]] 5.[ S Bill [ VP killed John]] 6. [ S NP [ VP was killed John]] 1.[ S I forced him [ VP' to be kind]] 2.[ S I believed him [ VP' to be kind]] 4.[ S John tends [ VP' to shout]] 6.[ S John [ VP' was killed]] Phrase structure analyses in Lexical Functional Grammar: Phrase structure analyses in traditional transformational grammar: How does LFG capture the difference between 1 and 2, the non-argument status of the subject of 3 and 4,

1.[ S I forced him [ S PRO to be kind]] 2.[ S I believed [ S him to be kind]] 3.[ S NP seems [ S John to shout]] 4.[ S NP tends [ S John to shout]] 5.[ S Bill [ VP killed John]] 6. [ S NP [ VP was killed John]] 1.[ S I forced him [ VP' to be kind]] 2.[ S I believed him [ VP' to be kind]] 4.[ S John tends [ VP' to shout]] 6.[ S John [ VP' was killed]] Phrase structure analyses in Lexical Functional Grammar: Phrase structure analyses in traditional transformational grammar: How does LFG capture the difference between 1 and 2, the non-argument status of the subject of 3 and4, and the semantic role of the subject of 6?

1.[ S I forced him [ S PRO to be kind]] 2.[ S I believed [ S him to be kind]] 3.[ S NP seems [ S John to shout]] 4.[ S NP tends [ S John to shout]] 5.[ S Bill [ VP killed John]] 6. [ S NP [ VP was killed John]] 1.[ S I forced him [ VP' to be kind]] 2.[ S I believed him [ VP' to be kind]] 4.[ S John tends [ VP' to shout]] 6.[ S John [ VP' was killed]] Phrase structure analyses in Lexical Functional Grammar: Phrase structure analyses in traditional transformational grammar: How does LFG capture the difference between 1 and 2, the non-argument status of the subject of 3 and 4, and the semantic role of the subject of 6? Answer: Don’t operate on the trees, but annotate them with relevant information about syntactic functions and semantic arguments.

VP VNP S I forced kindbe him VP' TOVP AP to V

VP VNP S I forced kindbe him VP' TOVP AP to VP VNP S I believed kindbe him VP' TOVP VAP to V

VP VNP S I forced kindbe him VP' TOVP VAP to VP VNP S I believed kindbe him VP' TOVP VAP to VP V S NP John tends shout VP' TOVP V to

VP VNP S I forced kindbe him VP' TOVP VAP to VP VNP S I believed kindbe him VP' TOVP VAP to VP V S NP John tends shout VP' TOVP V to VP V S NP John was Bill VP VPP NP killed by P

VP VNP S I forced kindbe him VP' TOVP VAP to VP VNP S I believed kindbe him VP' TOVP VAP to VP V S NP John tends shout VP' TOVP V to VP V S NP John was Bill VP VPP NP killed by P INF ’FORCE ‹SUBJ OBJ XCOMP›’ PRET XCOMPOBJ SUBJ

VP VNP S I forced kindbe him VP' TOVP VAP to VP VNP S I believed kindbe him VP' TOVP VAP to VP V S NP John tends shout VP' TOVP V to VP V S NP John was Bill VP VPP NP killed by P INF XCOMPOBJ SUBJ ’FORCE ‹SUBJ OBJ XCOMP›’ PRET XCOMPOBJ SUBJ PRET BELIEVE ‹SUBJ XCOMP› OBJ’

VP VNP S I forced kindbe him VP' TOVP VAP to VP VNP S I believed kindbe him VP' TOVP VAP to VP V S NP John tends shout VP' TOVP V to VP V S NP John was Bill VP VPP NP killed by P PRES SUBJ INF XCOMP INF XCOMPOBJ SUBJ ’FORCE ‹SUBJ OBJ XCOMP›’ PRET XCOMPOBJ SUBJ TEND ‹XCOMP› SUBJ’ PRET BELIEVE ‹SUBJ XCOMP› OBJ’

VP VNP S I forced kindbe him VP' TOVP VAP to VP VNP S I believed kindbe him VP' TOVP VAP to VP V S NP John tends shout VP' TOVP V to VP V S NP John was Bill VP VPP NP killed by P PRES SUBJ INF OBLag XCOMP INF SUBJ XCOMPOBJ SUBJ ’FORCE ‹SUBJ OBJ XCOMP›’ PRET XCOMPOBJ SUBJ TEND ‹XCOMP› SUBJ’ PRET KILL ‹OBLag SUBJ›’ BELIEVE ‹SUBJ XCOMP› OBJ’

The functional information in the annotations is represented in a separate functional structure (f-structure), in the form of an attribute-value graph:

SUBJ PRED’I’ CASEnom TENSEpret OBJ PRED’HE’ CASEobl NUMsg XCOMP SUBJ PRED’LEAVE‹ SUBJ › ’ PRED’FORCE‹ SUBJ OBJ XCOMP ›’ F-structure for I forced him to leave f1 f2 f5 f6

SUBJ PRED’I’ CASEnom TENSEpret OBJ PRED’HE’ CASEobl NUMsg XCOMP SUBJ PRED’LEAVE‹ SUBJ › ’ F-structure for I forced him to leave f1 f2 f5 f6 PRED’FORCE‹ SUBJ OBJ XCOMP ›’

SUBJ PRED’I’ CASEnom TENSEpret OBJ PRED’HE’ CASEobl NUMsg XCOMP SUBJ PRED’LEAVE‹ SUBJ › ’ PRED’FORCE‹ SUBJ OBJ XCOMP ›’ F-structure for I forced him to leave f1 f2 f5 f6

SUBJ PRED’I’ CASEnom TENSEpret OBJ PRED’HE’ CASEobl NUMsg XCOMP SUBJ PRED’LEAVE‹ SUBJ › ’ PRED’FORCE‹ SUBJ OBJ XCOMP ›’ F-structure for I forced him to leave f1 f2 f5 f6

SUBJ PRED’I’ CASEnom TENSEpret OBJ PRED’HE’ CASEobl NUMsg XCOMP SUBJ PRED’LEAVE‹ SUBJ › ’ PRED’FORCE‹ SUBJ OBJ XCOMP ›’ F-structure for I forced him to leave f1 f2 f5 f6

Linking A verb form contains information about the way in which semantic arguments are linked to syntactic functions:

Linking A verb form contains information about the way in which semantic arguments are linked to syntactic functions: "reparerer":reparere SUBJ OBJ

Linking A verb form contains information about the way in which semantic arguments are linked to syntactic functions: "reparerer":reparere SUBJ OBJ "repareres":reparere  SUBJ

Linking A verb form contains information about the way in which semantic arguments are linked to syntactic functions: "reparerer":reparere SUBJ OBJ "repareres":reparere  SUBJ ”like":like SUBJ OBJ

Linking A verb form contains information about the way in which semantic arguments are linked to syntactic functions: "reparerer":reparere SUBJ OBJ "repareres":reparere  SUBJ ”like":like SUBJ OBJ ”behage":behage OBJ  SUBJ

Linking If we assume a universal hierarchy of semantic roles and let the order of the arguments reflect the hierarchy, we don’t need to name the semantic roles: "reparerer":reparere SUBJ OBJ "repareres":reparere  SUBJ ”like":like SUBJ OBJ ”behage":behage OBJ  SUBJ

Linking If we assume a universal hierarchy of semantic roles and let the order of the arguments reflect the hierarchy, we don’t need to name the semantic roles: "reparerer":reparere "repareres":reparere ”like":like ”behage":behage

Wellformedness constraints on functional structures: SUBJ PRED OBJ ADJUNCT "the boy" ”the bike" {”in the garage"} repair " ”The boy repairs the bike in the garage":

Wellformedness constraints on functional structures: SUBJ PRED OBJ ADJUNCT "the boy" ”the bike" {”in the garage"} repair " 1.Completeness: An f-structure must contain all grammatical relations mentioned in PRED’s subcategorization frame. SUBJ PRED ”the boy" ”use " *”The boy uses": ”The boy repairs the bike in the garage":

Wellformedness constraints on functional structures: SUBJ PRED OBJ ADJUNCT "the boy" ”the bike" {”in the garage"} repair " 1.Completeness: An f-structure must contain all grammatical relations mentioned in PRED’s subcategorization frame. 2.Coherence: An f-structure cannot contain any subcategorizable grammatical relations not mentioned in PRED’s subcategorization frame. SUBJ PRED "gutten" "sove " *"Gutten sover sykkelen": OBJ "sykkelen" ”The boy repairs the bike in the garage":

Wellformedness constraints on functional structures: SUBJ PRED OBJ ADJUNCT "the boy" ”the bike" {”in the garage"} repair " 1.Completeness: An f-structure must contain all grammatical relations mentioned in PRED’s subcategorization frame. 2.Coherence: An f-structure cannot contain any subcategorizable grammatical relations not mentioned in PRED’s subcategorization frame. 3.Uniqueness: No grammatical relation (or other attribute) may occur more than once in a functional structure. SUBJ PRED ”the boy" ”use " *”The boy uses the bike the car ”: OBJ "the bike" OBJ”the car" ”The boy repairs the bike in the garage":

SUBJ PRED’I’ CASEnom TENSEpret OBJ PRED’HE’ CASEobl NUMsg XCOMP SUBJ PRED’LEAVE‹ SUBJ › ’ PRED’FORCE‹ SUBJ OBJ XCOMP ›’ F-structure for I forced him to leave f1 f2 f5 f6 Describing parts of the structure by means of equations

SUBJ PRED’I’ CASEnom TENSEpret OBJ PRED’HE’ CASEobl NUMsg XCOMP SUBJ PRED’LEAVE‹ SUBJ › ’ PRED’FORCE‹ SUBJ OBJ XCOMP ›’ F-structure for I forced him to leave f1 f2 f5 f6 Describing parts of the structure by means of equations f1 (TENSE) = pret

SUBJ PRED’I’ CASEnom TENSEpret OBJ PRED’HE’ CASEobl NUMsg XCOMP SUBJ PRED’LEAVE‹ SUBJ › ’ PRED’FORCE‹ SUBJ OBJ XCOMP ›’ F-structure for I forced him to leave f1 f2 f5 f6 Describing parts of the structure by means of equations f1 (TENSE) = pret f1 (SUBJ) = f2

SUBJ PRED’I’ CASEnom TENSEpret OBJ PRED’HE’ CASEobl NUMsg XCOMP SUBJ PRED’LEAVE‹ SUBJ › ’ PRED’FORCE‹ SUBJ OBJ XCOMP ›’ F-structure for I forced him to leave f1 f2 f5 f6 Describing parts of the structure by means of equations f1 (TENSE) = pret f1 (SUBJ) = f2 f2 (CASE) = nom

SUBJ PRED’I’ CASEnom TENSEpret OBJ PRED’HE’ CASEobl NUMsg XCOMP SUBJ PRED’LEAVE‹ SUBJ › ’ PRED’FORCE‹ SUBJ OBJ XCOMP ›’ F-structure for I forced him to leave f1 f2 f5 f6 Describing parts of the structure by means of equations f1 (TENSE) = pret f1 (SUBJ) = f2 f2 (CASE) = nom f1 (SUBJ)(CASE) = nom

SUBJ PRED’I’ CASEnom TENSEpret OBJ PRED’HE’ CASEobl NUMsg XCOMP SUBJ PRED’LEAVE‹ SUBJ › ’ PRED’FORCE‹ SUBJ OBJ XCOMP ›’ F-structure for I forced him to leave f1 f2 f5 f6 Describing parts of the structure by means of equations f1 (TENSE) = pret f1 (SUBJ) = f2 f2 (CASE) = nom f1 (SUBJ)(CASE) = nom f2

SUBJ PRED’I’ CASEnom TENSEpret OBJ PRED’HE’ CASEobl NUMsg XCOMP SUBJ PRED’LEAVE‹ SUBJ › ’ PRED’FORCE‹ SUBJ OBJ XCOMP ›’ F-structure for I forced him to leave f1 f2 f5 f6 Describing parts of the structure by means of equations f1 (TENSE) = pret f1 (SUBJ) = f2 f2 (CASE) = nom f1 (SUBJ)(CASE) = nom f2 Alternative notation: (f1 TENSE) = pret (f1 SUBJ) = f2 (f2 CASE) = nom (f1 SUBJ CASE) = nom

SUBJ PRED’I’ CASEnom TENSEpret OBJ PRED’HE’ CASEobl NUMsg XCOMP SUBJ PRED’LEAVE‹ SUBJ › ’ PRED’FORCE‹ SUBJ OBJ XCOMP ›’ F-structure for I forced him to leave f1 f2 f5 f6 Describing parts of the structure by means of equations f1 (TENSE) = pret f1 (SUBJ) = f2 f2 (CASE) = nom f1 (SUBJ)(CASE) = nom f2 Alternative notation: (f1 TENSE) = pret (f1 SUBJ) = f2 (f2 CASE) = nom (f1 SUBJ CASE) = nom (f1 OBJ) = (f1 XCOMP SUBJ)

SUBJ PRED’I’ CASEnom TENSEpret OBJ PRED’HE’ CASEobl NUMsg XCOMP SUBJ PRED’LEAVE‹ SUBJ › ’ PRED’FORCE‹ SUBJ OBJ XCOMP ›’ F-structure for I forced him to leave f1 f2 f5 f6 Describing parts of the structure by means of equations f1 (TENSE) = pret f1 (SUBJ) = f2 f2 (CASE) = nom f1 (SUBJ)(CASE) = nom f2 Alternative notation: (f1 TENSE) = pret (f1 SUBJ) = f2 (f2 CASE) = nom (f1 SUBJ CASE) = nom (f1 OBJ) = (f1 XCOMP SUBJ)

How to incorporate f-structure information into a grammar

S->NPVP VP->V(NP)(VP')

S->NPVP VP->V(NP)(VP')  ( SUBJ)   ( OBJ)   ( XCOMP)    

S->NPVP VP->V(NP)(VP') forced:( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)  ( SUBJ)   ( OBJ)   ( XCOMP)       

S->NPVP VP->V(NP)(VP') forced:( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)  ( SUBJ)   ( OBJ)   ( XCOMP)        VP VNP S I forced him VP' to leave

S->NPVP VP->V(NP)(VP') forced:( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)  ( SUBJ)   ( OBJ)   ( XCOMP)        VP VNP S I forced him VP' to leave  ( SUBJ)      ( OBJ)   ( XCOMP) 

S->NPVP VP->V(NP)(VP') forced:( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)  ( SUBJ)   ( OBJ)   ( XCOMP)        VP VNP S I forced him VP' to leave  ( SUBJ)      ( OBJ)   ( XCOMP)  ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)    

S->NPVP VP->V(NP)(VP') forced:( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)  ( SUBJ)   ( OBJ)   ( XCOMP)        VP:3 V:4NP:5 S:1 NP:2 I forced him VP':6 to leave  ( SUBJ)      ( OBJ)   ( XCOMP)  ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)     Index the c-structure nodes

S->NPVP VP->V(NP)(VP') forced:( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)  ( SUBJ)   ( OBJ)   ( XCOMP)        VP:3 V:4NP:5 S:1 NP:2 I forced him VP':6 to leave     ( OBJ)   ( XCOMP)  ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)     (f1 SUBJ)  Instantiate the metavariables: Replace them with f-structure variables based on the node indices.

S->NPVP VP->V(NP)(VP') forced:( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)  ( SUBJ)   ( OBJ)   ( XCOMP)        VP:3 V:4NP:5 S:1 NP:2 I forced him VP':6 to leave     ( OBJ)   ( XCOMP)  ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)     (f1 SUBJ)  f2 Instantiate the metavariables: Replace them with f-structure variables based on the node indices.

S->NPVP VP->V(NP)(VP') forced:( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)  ( SUBJ)   ( OBJ)   ( XCOMP)        VP:3 V:4NP:5 S:1 NP:2 I forced him VP':6 to leave    ( OBJ)   ( XCOMP)  ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)     (f1 SUBJ)  f2 f1  Instantiate the metavariables: Replace them with f-structure variables based on the node indices.

S->NPVP VP->V(NP)(VP') forced:( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)  ( SUBJ)   ( OBJ)   ( XCOMP)        VP:3 V:4NP:5 S:1 NP:2 I forced him VP':6 to leave    ( OBJ)   ( XCOMP)  ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)     (f1 SUBJ)  f2 f1  f3 Instantiate the metavariables: Replace them with f-structure variables based on the node indices.

S->NPVP VP->V(NP)(VP') forced:( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)  ( SUBJ)   ( OBJ)   ( XCOMP)        VP:3 V:4NP:5 S:1 NP:2 I forced him VP':6 to leave  ( OBJ)   ( XCOMP)  ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)     (f1 SUBJ)  f2 f1  f3 f3  Instantiate the metavariables: Replace them with f-structure variables based on the node indices.

S->NPVP VP->V(NP)(VP') forced:( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)  ( SUBJ)   ( OBJ)   ( XCOMP)        VP:3 V:4NP:5 S:1 NP:2 I forced him VP':6 to leave  ( OBJ)   ( XCOMP)  ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)     (f1 SUBJ)  f2 f1  f3 f3  f4 Instantiate the metavariables: Replace them with f-structure variables based on the node indices.

S->NPVP VP->V(NP)(VP') forced:( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)  ( SUBJ)   ( OBJ)   ( XCOMP)        VP:3 V:4NP:5 S:1 NP:2 I forced him VP':6 to leave  ( XCOMP)  ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)     (f1 SUBJ)  f2 f1  f3 f3  f4(f3 OBJ)  Instantiate the metavariables: Replace them with f-structure variables based on the node indices.

S->NPVP VP->V(NP)(VP') forced:( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)  ( SUBJ)   ( OBJ)   ( XCOMP)        VP:3 V:4NP:5 S:1 NP:2 I forced him VP':6 to leave  ( XCOMP)  ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)     (f1 SUBJ)  f2 f1  f3 f3  f4(f3 OBJ)  f5 Instantiate the metavariables: Replace them with f-structure variables based on the node indices.

S->NPVP VP->V(NP)(VP') forced:( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)  ( SUBJ)   ( OBJ)   ( XCOMP)        VP:3 V:4NP:5 S:1 NP:2 I forced him VP':6 to leave ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)     (f1 SUBJ)  f2 f1  f3 f3  f4(f3 OBJ)  f5 (f3 XCOMP)  Instantiate the metavariables: Replace them with f-structure variables based on the node indices.

S->NPVP VP->V(NP)(VP') forced:( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)  ( SUBJ)   ( OBJ)   ( XCOMP)        VP:3 V:4NP:5 S:1 NP:2 I forced him VP':6 to leave ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)     (f1 SUBJ)  f2 f1  f3 f3  f4(f3 OBJ)  f5 (f3 XCOMP)  f6 Instantiate the metavariables: Replace them with f-structure variables based on the node indices.

S->NPVP VP->V(NP)(VP') forced:( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)  ( SUBJ)   ( OBJ)   ( XCOMP)        VP:3 V:4NP:5 S:1 NP:2 I forced him VP':6 to leave (f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4(f3 OBJ)  f5 (f3 XCOMP)  f6 Instantiate the metavariables: Replace them with f-structure variables based on the node indices.

S->NPVP VP->V(NP)(VP') forced:( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)  ( SUBJ)   ( OBJ)   ( XCOMP)        (f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4(f3 OBJ)  f5 (f3 XCOMP)  f6 The tree has done its job: Forget it.

S->NPVP VP->V(NP)(VP') forced:( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)  ( SUBJ)   ( OBJ)   ( XCOMP)        (f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4 (f3 OBJ)  f5 (f3 XCOMP)  f6 Collect the instantiated equations into an f-description

(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4 (f3 OBJ)  f5 (f3 XCOMP)  f6 Solve the equations in any order to constuct an f-structure

(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4 (f3 OBJ)  f5 (f3 XCOMP)  f6 F-structure for I forced him to leave Solve the equations in any order to constuct an f-structure

(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4 (f3 OBJ)  f5 (f3 XCOMP)  f6 F-structure for I forced him to leave

(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4 (f3 OBJ)  f5 (f3 XCOMP)  f6 SUBJ F-structure for I forced him to leave f1 f2

(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4 (f3 OBJ)  f5 (f3 XCOMP)  f6 SUBJ F-structure for I forced him to leave f1 f2

(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4 (f3 OBJ)  f5 (f3 XCOMP)  f6 SUBJ F-structure for I forced him to leave f1 f2 f3

(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4 (f3 OBJ)  f5 (f3 XCOMP)  f6 SUBJ F-structure for I forced him to leave f1 f2 f3

(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4 (f3 OBJ)  f5 (f3 XCOMP)  f6 SUBJ F-structure for I forced him to leave f1 f2 f3 f4

(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4 (f3 OBJ)  f5 (f3 XCOMP)  f6 SUBJ F-structure for I forced him to leave f1 f2 f3 f4

(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4 (f3 OBJ)  f5 (f3 XCOMP)  f6 SUBJ OBJ F-structure for I forced him to leave f1 f2 f5 f3 f4

(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4 (f3 OBJ)  f5 (f3 XCOMP)  f6 SUBJ OBJ F-structure for I forced him to leave f1 f2 f3 f4 f5

(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4 (f3 OBJ)  f5 (f3 XCOMP)  f6 SUBJ OBJ XCOMP F-structure for I forced him to leave f1 f2 f6 f3 f4 f5

(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4 (f3 OBJ)  f5 (f3 XCOMP)  f6 SUBJ OBJ XCOMP F-structure for I forced him to leave f1 f2 f6 f3 f4 f5

(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4 (f3 OBJ)  f5 (f3 XCOMP)  f6 SUBJ OBJ XCOMP PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' F-structure for I forced him to leave f1 f2 f6 f3 f4 f5

(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4 (f3 OBJ)  f5 (f3 XCOMP)  f6 SUBJ OBJ XCOMP PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' F-structure for I forced him to leave f1 f2 f6 f3 f4 f5

(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4 (f3 OBJ)  f5 (f3 XCOMP)  f6 SUBJ OBJ XCOMP PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' F-structure for I forced him to leave f1 f2 f6 f3 f4 f5

(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4 (f3 OBJ)  f5 (f3 XCOMP)  f6 SUBJ OBJ XCOMP PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' F-structure for I forced him to leave f1 f2 f6 f3 f4 f5

(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4 (f3 OBJ)  f5 (f3 XCOMP)  f6 SUBJ OBJ XCOMP PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' F-structure for I forced him to leave f1 f2 f6 f3 f4 f5

(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4 (f3 OBJ)  f5 (f3 XCOMP)  f6 SUBJ TENSEpret OBJ XCOMP PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' F-structure for I forced him to leave f1 f2 f6 f3 f4 f5

(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4 (f3 OBJ)  f5 (f3 XCOMP)  f6 SUBJ TENSEpret OBJ XCOMP PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' F-structure for I forced him to leave f1 f2 f6 f3 f4 f5

(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4 (f3 OBJ)  f5 (f3 XCOMP)  f6 SUBJ TENSEpret OBJ XCOMP SUBJ PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' F-structure for I forced him to leave f1 f2 f6 f3 f4 f5

(f4 PRED) = 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' (f4 TENSE) = pret (f4 OBJ) = (f4 XCOMP SUBJ) (f1 SUBJ)  f2 f1  f3 f3  f4 (f3 OBJ)  f5 (f3 XCOMP)  f6 SUBJ TENSEpret OBJ XCOMP SUBJ PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' F-structure for I forced him to leave f1 f2 f6 f3 f4 f5 Notice: The f-structure has fewer levels than the c-structure because of the nodes annotated with

SUBJ TENSEpret OBJ XCOMP SUBJ PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' The nodes in the tree and the elements of the f-structure now stand in a many-to-one relation: f1 f2 f6 f3 f4 f5 VP VNP S I forced him VP' to leave  ( SUBJ)      ( OBJ)   ( XCOMP) 

SUBJ TENSEpret OBJ XCOMP SUBJ PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' The nodes in the tree and the elements of the f-structure now stand in a many-to-one relation: f1 f2 f6 f3 f4 f5 VP VNP S I forced him VP' to leave  ( SUBJ)      ( OBJ)   ( XCOMP) 

SUBJ TENSEpret OBJ XCOMP SUBJ PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' The nodes in the tree and the elements of the f-structure now stand in a many-to-one relation: f1 f2 f6 f3 f4 f5 VP VNP S I forced him VP' to leave  ( SUBJ)      ( OBJ)   ( XCOMP) 

SUBJ TENSEpret OBJ XCOMP SUBJ PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' The nodes in the tree and the elements of the f-structure now stand in a many-to-one relation: f1 f2 f6 f3 f4 f5 VP VNP S I forced him VP' to leave  ( SUBJ)      ( OBJ)   ( XCOMP) 

SUBJ TENSEpret OBJ XCOMP SUBJ PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' The nodes in the tree and the elements of the f-structure now stand in a many-to-one relation: f1 f2 f6 f3 f4 f5 VP VNP S I forced him VP' to leave  ( SUBJ)      ( OBJ)   ( XCOMP) 

SUBJ TENSEpret OBJ XCOMP SUBJ PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' The nodes in the tree and the elements of the f-structure now stand in a many-to-one relation: f1 f2 f6 f3 f4 f5 VP VNP S I forced him VP' to leave  ( SUBJ)      ( OBJ)   ( XCOMP) 

SUBJ TENSEpret OBJ XCOMP SUBJ PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' The nodes in the tree and the elements of the f-structure now stand in a many-to-one relation: f1 f2 f6 f3 f4 f5 VP VNP S I forced him VP' to leave  ( SUBJ)      ( OBJ)   ( XCOMP) 

SUBJ TENSEpret OBJ XCOMP SUBJ PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' The nodes in the tree and the elements of the f-structure now stand in a many-to-one relation: f1 f2 f6 f3 f4 f5 VP VNP S I forced him VP' to leave  ( SUBJ)      ( OBJ)   ( XCOMP) 

SUBJ TENSEpret OBJ XCOMP SUBJ PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' The nodes in the tree and the elements of the f-structure now stand in a many-to-one relation: f1 f2 f6 f3 f4 f5 VP VNP S I forced him VP' to leave  ( SUBJ)      ( OBJ)   ( XCOMP) 

SUBJ TENSEpret OBJ XCOMP SUBJ PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' The nodes in the tree and the elements of the f-structure now stand in a many-to-one relation: f1 f2 f6 f3 f4 f5 VP VNP S I forced him VP' to leave  ( SUBJ)      ( OBJ)   ( XCOMP)  The relation is called a projection relation.

SUBJ TENSEpret OBJ XCOMP SUBJ PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' The nodes in the tree and the elements of the f-structure now stand in a many-to-one relation: f1 f2 f6 f3 f4 f5 VP VNP S I forced him VP' to leave  ( SUBJ)      ( OBJ)   ( XCOMP)  The relation is called a projection relation. A set of nodes which project the same f-structure are said to constitute a functional domain. A functional domain

Let us now move from I forced him to leave to I believed him to leave SUBJ TENSEpret OBJ XCOMP SUBJ PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' f1 f2 f6 f3 f4 f5

S->NPVP VP->V(NP)(VP') forced:( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)  ( SUBJ)   ( OBJ)   ( XCOMP)        VP VNP S I forced him VP' to leave  ( SUBJ)      ( OBJ)   ( XCOMP)  ( PRED) = 'FORCE‹( SUBJ)( OBJ)( XCOMP)›' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)     All we need to change is the lexical entry:

S->NPVP VP->V(NP)(VP') believed:( PRED) = ’BELIEVE‹( SUBJ) ( XCOMP)›( OBJ)' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)  ( SUBJ)   ( OBJ)   ( XCOMP)        VP VNP S I believedhim VP' to leave  ( SUBJ)      ( OBJ)   ( XCOMP)  ( PRED) = ’BELIEVE‹( SUBJ) ( XCOMP)›( OBJ)' ( TENSE) = pret ( OBJ) = ( XCOMP SUBJ)    All we need to change is the lexical entry: 

SUBJ TENSEpret OBJ XCOMP SUBJ PRED 'FORCE‹(f4 SUBJ)(f4 OBJ)(f4 XCOMP)›' f1 f2 f6 f3 f4 f5 This leads to the following change in the f-structure:

SUBJ TENSEpret OBJ XCOMP SUBJ PRED ’BELIEVE‹(f4 SUBJ)(f4 XCOMP)›(f4 OBJ)' f1 f2 f6 f3 f4 f5 This leads to the following change in the f-structure:

SUBJ TENSEpret OBJ XCOMP SUBJ PRED ’BELIEVE‹(f4 SUBJ)(f4 XCOMP)›(f4 OBJ)' f1 f2 f6 f3 f4 f5 This leads to the following change in the f-structure: The only change is in the mapping between syntactic functions and argument positions, as expressed in the value of PRED. The syntax as such is unchanged.

Constraint Equations Consider these lexical entries: ha V (↑PRED)='ha ' (↑ XCOMP PTC)=perf måtte V (↑PRED)='måtte ' (↑ XCOMP VFORM)=inf løpe V (↑PRED)='løpe ' (↑ VFORM)=inf løpt V (↑PRED)='løpe ' (↑ PTC)=perf

Constraint Equations Consider these lexical entries: ha V (↑PRED)='ha ' (↑ XCOMP PTC)=perf måtte V (↑PRED)='måtte ' (↑ XCOMP VFORM)=inf løpe V (↑PRED)='løpe ' (↑ VFORM)=inf løpt V (↑PRED)='løpe ' (↑ PTC)=perf This enables us to derive: gutten har løpt gutten måtte løpe

Constraint Equations Consider these lexical entries: ha V (↑PRED)='ha ' (↑ XCOMP PTC)=perf måtte V (↑PRED)='måtte ' (↑ XCOMP VFORM)=inf løpe V (↑PRED)='løpe ' (↑ VFORM)=inf løpt V (↑PRED)='løpe ' (↑ PTC)=perf This enables us to derive: gutten har løpt gutten måtte løpe But does it exclude the following? *gutten har løpe *gutten måtte løpt

Constraint Equations We need to change some equations into constraint equations: ha V (↑PRED)='ha ' (↑ XCOMP PTC)=c perf måtte V (↑PRED)='måtte ' (↑ XCOMP VFORM)=c inf løpe V (↑PRED)='løpe ' (↑ VFORM)=inf løpt V (↑PRED)='løpe ' (↑ PTC)=perf