Modularizing Semantics Greg Kobele May 17, 2018 Universität Leipzig
Overview Modularity Semantic Parts This Talk 1
What it is understand a complex phenomenon by • factoring it into simple(r) parts • analysing these parts entire phenomenon = combination of parts 2
Linguistics Complex Phenomenon ability to use language Simple(r) Parts • Phonetics • Phonology • Morphology • Syntax • Semantics • Pragmatics 3
Semantics Complex Phenomenon Had a politician pushed the issue, he would have been arrested Simple(r) Parts? • argument structure • scope • intentionality • dynamics • context sensitivity • tense 4
What are semantic parts? A basic idea • so that it refmects the structure of the part 5 • semantic objects are λ -terms • a part specifjes how to ’update’ a λ -term
Modules An intentionality module • a non-intentional meaning • into an intentional one 6 a function INT which turns INT ( no ( student )( λ x . can ( laugh ( x )))) = λ w . no ( student ( w ))( λ x . ∃ w ′ . w R w ′ ∧ ( laugh ( w ′ )( x w ′ )))
The Ideal 1. identify a domain 2. specify non-predictable meanings • most things are predictable! 3. specify how to generate predictable meanings only works if compositional: • meanings of whole • determined by meanings of parts 7
Homomorphisms Strings replace a symbol • with a string Trees replace a symbol with k daughters • with a tree with k empty leaves replace a symbol of one type • with a term of similar type 8 λ -Terms
Term Homomorphisms we want to view simpler expressions as ’abbreviating’ more complex ones in a compositional way: 9 every ( kitten ) : ( e → t ) → t every ( kitten ) : ( e → t ) → t every ( kitten ) = every ( kitten ) ( e → t ) → t = ( e → t ) → t
Type homomorphism specify what each atomic type ’abbreviates’: extend this homomorphically to complex types: c Single type semantics 10 h ( c ) = α = h ( c ) α → β = α → β both e and t abbreviate q (with D q = D ( et ) t ) e → e → t = e → e → t = q → q → q
Lambda homomorphisms specify what each constant ’abbreviates’: extend this homomorphically to complex terms: k x M N You keep the structure of the term and just replace constants with their defjnitions 11 h ( k ) = M = h ( k ) = x = λ x . M λ x . M = M N
Type compatibility To make sense, we require that lambda homomorphisms and type homomorphisms come in pairs: This means that • of ’similar’ type 12 • you replace a symbol c : α • with a term c : α
I will show how this works • analyse context-sensitivity including dynamic binding • decompose this into two independent modules • discuss options • implementing instead dynamic dynamicity (à la DMG) • extensions to RST/SDRT 13 • CON implementing context-sensitivity • DYN implementing (static) dynamicity
Dynamics Discourse Modularizing Dynamics Example Discourse Structure 14
The dynamics of pronoun reference Sentences can set up discourse referents for other sentences model this as scope : • T can access discourse refs introduced by S • T cannot access discourse refs introduced by S the primitive notion here is sentence scope • motivated by context sensitivity • formally independent thereof 15 1. S ( . . . T ( . . . ) . . . ) 2. S ( . . . ) ∧ T ( . . . )
Interpreting sentences in discourse Basic observation context grows throughout the discourse Formal implementation sentences in a discourse scope over each other 16 [[ S . T . ]] = [[ S ]] ◦ [[ T ]] = λ x . [[ S ]]([[ T ]]( x ))
Dynamicization On types The intuition sentences scope over the rest of the discourse 17 e = e t = t → t
Inherent Dynamicity and some if… then DETs are internally dynamic 18 is internally and externally dynamic is internally and externally dynamic is internally dynamic
Break dynamicization into two steps 1. internal dynamicity 2. external dynamicity 19
Inherent Internal dynamicity Determiners and Conservativity strong weak Implication and Classical Equivalence Accounts for Internal Dynamicity! 20 int ( det S ) := λ P , Q . det P ( P → Q )) int ( det W ) := λ P , Q . det P ( P ∧ Q ) impl ( if…then ) := λφ, ψ. ¬ ( φ ∧ ¬ ψ )
Inherent external dynamicity and is externally dynamic some is externally dynamic 21 ext ( and ) := λ Φ , Ψ , ψ. Φ(Ψ ψ ) = B ext ( some ) := λ P , Q , ψ. some ( λ x . P x ⊤ )( λ x . Q x ψ )
Lambda homomorphisms impl k Dyn k ext k x Q x x P x some P Q ext some ext and ext k impl if…then dyn impl k int k Q P Q det P P int det S Q P Q det P P int det W int 22 ext ◦ impl ◦ int
Lambda homomorphisms k Dyn k ext k x Q x x P x some P Q ext some ext and ext impl k dyn impl if…then impl int 22 ext ◦ impl ◦ int int ( det W ) = λ P , Q . det P ( P ∧ Q ) int ( det S ) = λ P , Q . det P ( P → Q ) int ( k ) = k
Lambda homomorphisms dyn Dyn k ext k x Q x x P x some P Q ext some ext and ext 22 int impl ext ◦ impl ◦ int int ( det W ) = λ P , Q . det P ( P ∧ Q ) int ( det S ) = λ P , Q . det P ( P → Q ) int ( k ) = k impl ( if…then ) = λφ, ψ. ¬ ( φ ∧ ¬ ψ ) impl ( k ) = k
Lambda homomorphisms impl ext dyn 22 int ext ◦ impl ◦ int int ( det W ) = λ P , Q . det P ( P ∧ Q ) int ( det S ) = λ P , Q . det P ( P → Q ) int ( k ) = k impl ( if…then ) = λφ, ψ. ¬ ( φ ∧ ¬ ψ ) impl ( k ) = k ext ( and ) = B ext ( some ) = λ P , Q , φ. some ( λ x . P ( x )( ⊤ ))( λ x . Q ( x )( φ )) ext ( k ) = Dyn ( k )
Sta e A A F Dyn a a Sta Dyn F Sta F Sta Sta t Dynamic Lifting Intrinsically static expressions are predictable Sta 23 Dyn α : α → α Dyn e ( a ) := a Dyn t ( φ ) := λψ.φ ∧ ψ Dyn αβ ( f ) := Dyn β ◦ f ◦ Sta α = λ A . Dyn β ( f ( Sta α A ))
Dyn e a Dynamic Lifting Dyn f Sta A Intrinsically static expressions are predictable Sta f A Dyn f Dyn Dyn t a Dyn 23 Sta α : α → α Sta e ( A ) := A Sta t (Φ) := Φ ⊤ Sta αβ ( F ) := Sta β ◦ F ◦ Dyn α = λ a . Sta β ( F ( Dyn α a ))
Examples 24 • Dyn tt ( not ) := λ Φ , ψ. not (Φ ⊤ ) ∧ ψ • Dyn eet ( praise ) := λ x , y , ψ. praise x y ∧ ψ • Dyn ( et )( et ) t ( every ) := λ P , Q , ψ. every ( λ x . P x ⊤ )( λ x . Q x ⊤ ) ∧ ψ
An example Start with: Let Then Where 25 a : ( et )( et ) t boy : et jump : et laugh : et and : ttt he : e φ = and ( a ( boy )( jump ))( laugh ( he )) : t dyn ( φ ) : t → t dyn ( φ ) ≡ λψ. a ( boy )( λ x . boy ( x ) ∧ laugh ( he ) ∧ ψ )
Discourse Relations 1. John had a lovely evening 2. He had a great meal 3. He ate salmon 4. He devoured cheese 5. He won a dancing competition Elaborating vs Narrating • 2 and 5 elaborate on 1 • 2 and 5 are a narrative • 3 and 4 elaborate on 2 • 3 and 4 are a narrative 26
Discorse Structure ELAB had lovely ELAB had great meal NARR ate salmon devoured cheese won dance- -ing comp 27 evening NARR
Right Frontier Constraint Pronouns can only refer to certain referents introduced in the previous discourse tree 1. start at rightmost leaf relation 28 2. walk anywhere except down a left branch of NARR
Example 1. John had a lovely -ing comp won dance- cheese devoured salmon ate NARR meal had great ELAB had lovely ELAB pink competition 5. He won a dancing cheese 4. He devoured 3. He ate salmon meal 2. He had a great evening 29 evening NARR 6. # It was nice and
2. walk anywhere except down a left branch of NARR Interpreting Relations Subordinating Coordinating Right Frontier Constraint Pronouns can only refer to certain referents introduced in the previous discourse tree 1. start at rightmost leaf relation 30 [[ ELAB ]] = λ Φ , Ψ , φ. Φ(Ψ φ ) [[ NARR ]] = λ Φ , Ψ , φ. (Φ ⊤ ) ∧ (Ψ φ )
Interpreting Relations Subordinating Coordinating Right Frontier Constraint Pronouns can only refer to certain referents introduced in the previous discourse tree 1. start at rightmost leaf 2. walk anywhere except down a left branch of NARR relation 30 [[ ELAB ]] = λ Φ , Ψ , φ. Φ(Ψ φ ) [[ NARR ]] = λ Φ , Ψ , φ. (Φ ⊤ ) ∧ (Ψ φ )
Summary • can study logic of discourse 31 • independently of context-sensitivity
Context Sensitivity Overview Pronouns as variables Pronouns as identity functions Identity functions vs variables Pronouns as defjnites Synthesis Modularizing Context Sensitivity Example Rethinking contexts 32
Modularity we now want to study context-sensitivity 33 • independently of discourse dynamics
Multiplicity of theories variable x 7 34 What is [[ he ]] ? id func λ x . x defjnite the ( λ x . boy ( x ) ∧ near ( x )( kim ))
De Groote (2006) All theories agree in main respects: The fjrst thought that a completely semantically naive person might have is that a pronoun just picks out in a discourse context some contextu- ally salient individual. (Jacobson 2015) just disagree in 1. what contexts are 2. how you pick out individuals 35
Next • why this is the case: • pronouns as variables • pronouns as identity functions • pronouns as defjnites • a synthesis 36
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