Classical Copying versus Qantum Entanglement in Natural Language: - PowerPoint PPT Presentation

Classical Copying versus Qantum Entanglement in Natural Language: the Case of VP-ellipsis Gijs Jasper Wijnholds 1 Mehrnoosh Sadrzadeh 1 Qeen Mary University of London, United Kingdom g.j.wijnholds@qmul.ac.uk SYCO 2 December 17, 2018

DISTRIBUTIONAL SEMANTICS: MEANING IN CONTEXT G. J. Wijnholds SYCO 2 2 / 41

COMPOSING WORD EMBEDDINGS: A CHALLENGE − − − − − − − − − − − − − − − → Coordination dancing and running = ?? − − − − − − − − − − − − − − − − − − − − − − − − → Every student likes some teacher = ?? Qantification − − − − − − − − − − → Anaphora shaves himself = ?? − − − − − − − − − − − − − − − − − − − − − − − − − − − − → ⇒ Ellipsis Mat went to Croatia and Max did too = ?? G. J. Wijnholds SYCO 2 3 / 41

VERB PHRASE ELLIPSIS ◮ Ellipsis is a natural language phenomenon in which part of a phrase is missing and has to be recovered from context. ◮ In verb phrase ellipsis, the missing part is… a verb phrase. ◮ There is ofen a marker that indicates the type of the missing part. G. J. Wijnholds SYCO 2 4 / 41

VERB PHRASE ELLIPSIS ◮ Ellipsis is a natural language phenomenon in which part of a phrase is missing and has to be recovered from context. ◮ In verb phrase ellipsis, the missing part is… a verb phrase. ◮ There is ofen a marker that indicates the type of the missing part. Bob drinks a beer and Alice does too � �� � � �� � ant VP marker G. J. Wijnholds SYCO 2 4 / 41

ELLIPSIS NEEDS COPYING AND MOVEMENT drinks a beer drinks a beer Bob drinks a beer and Alice does too ant VP marker G. J. Wijnholds SYCO 2 5 / 41

ELLIPSIS NEEDS COPYING AND MOVEMENT drinks a beer drinks a beer Bob drinks a beer and Alice does too ant VP marker G. J. Wijnholds SYCO 2 6 / 41

ELLIPSIS NEEDS COPYING AND MOVEMENT drinks a beer drinks a beer ✘✘✘✘ ✘ Bob drinks a beer and Alice does too ant VP marker G. J. Wijnholds SYCO 2 7 / 41

THE CHALLENGE: COMPOSE WORD VECTORS TO GET A MEANING REPRESENTATION FOR VP ELLIPSIS G. J. Wijnholds SYCO 2 8 / 41

THE BIG PICTURE Qantum Entanglement Functor SOURCE TARGET L ♦ , F FVect Classical H der H lex SOURCE INTER TARGET λ NL λ FVec Frob L ♦ , F G. J. Wijnholds SYCO 2 9 / 41

QUANTUM ENTANGLEMENT G. J. Wijnholds SYCO 2 10 / 41

LAMBEK VS. LAMBEK The core of the Lambek calculus: application, co-application B ⊗ B \ A → A A → B \ ( B ⊗ A ) A / B ⊗ B → A A → ( A ⊗ B ) / B ( A ⊗ B ) ⊗ C ↔ A ⊗ ( B ⊗ C ) Interpretation: words have types, and type-respecting embeddings Word Type embedding − − → john ∈ N john np sleeps np \ s sleep ∈ N ⊗ S ( ← matrix) likes ( np \ s ) / np like ∈ N ⊗ S ⊗ N ( ← cube) − − → beer np beer ∈ N (Coecke et al., 2013) G. J. Wijnholds SYCO 2 11 / 41

IN PICTURES A ⊗ A \ B → B B → A \ ( A ⊗ B ) A A B B A A B / A ⊗ A → B B → ( B ⊗ A ) / A B A A B A A (Co ecke et al., 2013) G. J. Wijnholds SYCO 2 12 / 41

IN PICTURES A ⊗ A \ B → B B → A \ ( A ⊗ B ) A A B B A A B / A ⊗ A → B B → ( B ⊗ A ) / A B A A B A A LINEAR‼ (Co ecke et al., 2013) G. J. Wijnholds SYCO 2 13 / 41

LAMBEK WITH CONTROL OPERATORS: L ♦ , F The core of the Lambek calculus: application, co-application B ⊗ B \ A → A A → B \ ( B ⊗ A ) A / B ⊗ B → A A → ( A ⊗ B ) / B ( A ⊗ B ) ⊗ C ↔ A ⊗ ( B ⊗ C ) Modalities: application, co-application ♦� A → A A → �♦ A ◮ Linear logic: controlled duplication/deletion of resources via ! = ♦� . Here: controlled copying, reordering Controlled contraction, commutativity A → ♦ A ⊗ A ( ♦ A ⊗ B ) ⊗ C → B ⊗ ( ♦ A ⊗ C ) ♦ A ⊗ ( ♦ B ⊗ C ) → ♦ B ⊗ ( ♦ A ⊗ C ) G. J. Wijnholds SYCO 2 14 / 41

ILLUSTRATION ♦ ( np \ s ) np \ s np \ s ( s \ s ) / s ♦ ( np \ s ) \ ( np \ s ) np np Bob drinks a beer and Alice does too ant VP marker G. J. Wijnholds SYCO 2 15 / 41

IN PICTURES A → ♦ A ⊗ A A ⊗ A \ B → B B → A \ ( A ⊗ B ) A ◦ A A B B A A A A B / A ⊗ A → B B → ( B ⊗ A ) / A ( ♦ A ⊗ B ) ⊗ C → B ⊗ ( ♦ A ⊗ C ) A B C B A A B A A B A C G. J. Wijnholds SYCO 2 16 / 41

QUANTUM ENTANGLEMENT AND ELLIPSIS Bob drinks a beer and Alice does too N ⊗ S N ⊗ S ⊗ S ⊗ N N S ⊗ S ⊗ S N ◦ ◦ · · · · · · · · · · · · · G. J. Wijnholds SYCO 2 17 / 41

QUANTUM ENTANGLEMENT AND ELLIPSIS and does too · · ◦ Bob drinks a beer Alice N N ⊗ S S ⊗ S ⊗ S N N ⊗ S ⊗ S ⊗ N ◦ ◦ · · · · · · · · · · · · · G. J. Wijnholds SYCO 2 18 / 41

QUANTUM ENTANGLEMENT AND ELLIPSIS Bob drinks a beer Alice N ⊗ S N N ◦ · · · · ( − Bob ⊙ − → Alice ) ⊤ × − − → − − − − − − − → drinks a beer G. J. Wijnholds SYCO 2 19 / 41

A MORE COMPLICATED CASE: SLOPPY READING Bob lov es his beer and Alice does too � Bob loves Bob’s beer and Alice loves Bob’s beer ♦ ( np \ s ) np \ s ♦ np np np \ s np ( np \ s ) / np ♦ np \ ( np / n ) n ( s \ s ) / s np ♦ ( np \ s ) \ ( np \ s ) Bob loves his beer and Alice does too ant VP marker G. J. Wijnholds SYCO 2 20 / 41

A MORE COMPLICATED CASE: SLOPPY READING Bob lov es his beer and Alice does too � Bob loves Bob’s beer and Alice loves Bob’s beer ♦ ( np \ s ) np \ s ♦ np np np \ s np ( np \ s ) / np ♦ np \ ( np / n ) n ( s \ s ) / s np ♦ ( np \ s ) \ ( np \ s ) Bob loves his beer and Alice does too ant VP marker G. J. Wijnholds SYCO 2 21 / 41

A MORE COMPLICATED CASE: STRICT READING Bob lov es his beer and Alice does too � Bob loves Bob’s beer and Alice loves Alice’s beer ♦ ( np \ s ) np \ s ♦ np np np \ s np ( np \ s ) / np ♦ np \ ( np / n ) n ( s \ s ) / s np ♦ ( np \ s ) \ ( np \ s ) Bob loves his beer and Alice does too ant VP marker G. J. Wijnholds SYCO 2 22 / 41

A MORE COMPLICATED CASE: STRICT READING Bob lov es his beer and Alice does too � Bob loves Bob’s beer and Alice loves Alice’s beer � � ♦ ( np \ s ) / s ⊗ ( ♦ np \ n ⊗ n ) ♦ np np ( np \ s ) / np ♦ np \ ( np / n ) ( s \ s ) / s ♦ ( np \ s ) \ ( np \ s ) np n np Bob loves his beer and Alice does too ant VP marker G. J. Wijnholds SYCO 2 23 / 41

A More Complicated Case: Sloppy Reading Bob lov es his beer and Alice does too N N ⊗ S ⊗ N N ⊗ N ⊗ N N S ⊗ S ⊗ S N N ⊗ S ⊗ S ⊗ N ◦ ◦ ◦ · · · · · · · · · · · · · · · · · G. J. Wijnholds SYCO 2 24 / 41

A More Complicated Case: Sloppy Reading his and does too · · · · ◦ ◦ Bob lov es beer Alice N N ⊗ S ⊗ N N ⊗ N ⊗ N N S ⊗ S ⊗ S N N ⊗ S ⊗ S ⊗ N ◦ ◦ ◦ · · · · · · · · · · · · · · · · · G. J. Wijnholds SYCO 2 25 / 41

A More Complicated Case: Sloppy Reading Bob lov es Bob’s beer and Alice loves Bob’s beer Bob Alice beer loves N ⊗ S ⊗ N N N N ◦ · · · · ∆( Bob ⊙ Alice ⊙ Beer ) ik loves ijk G. J. Wijnholds SYCO 2 26 / 41

A More Complicated Case: Strict Reading Bob lov es Bob’s beer and Alice loves Alice’s beer G. J. Wijnholds SYCO 2 27 / 41

A More Complicated Case: Strict Reading Bob lov es Bob’s beer and Alice loves Alice’s beer Bob Alice beer loves N ⊗ S ⊗ N N N N ◦ · · · · ∆( Bob ⊙ Alice ⊙ Beer ) ik loves ijk G. J. Wijnholds SYCO 2 27 / 41

WHAT NOW? G. J. Wijnholds SYCO 2 28 / 41

WHAT NOW? Classical Semantics G. J. Wijnholds SYCO 2 28 / 41

General Interpretation The syntax-semantics homomorphism interprets types and proofs of L ♦ , F as objects types and maps terms in a compact closed category non-linear lambda calculus: Type Level ⌊ A ⊗ B ⌋ = ⌊ A ⌋ × ⌊ B ⌋ ⌊ A / B ⌋ = ⌊ A ⌋ → ⌊ B ⌋ ⌊ A \ B ⌋ = ⌊ A ⌋ → ⌊ B ⌋ ⌊ ♦ A ⌋ = ⌊ � A ⌋ = ⌊ A ⌋ Application, co-application → A λ x .λ y . � y , x � B × ( B → A ) λ xM . M x − − − − − − − − − − − − − − − − → B → ( B × A ) → A λ x .λ y . � x , y � ( B → A ) × B λ Mx . Mx − − − − − − − − − − − − − − − → B → ( A × B ) Modalities ♦ , � are semantically vacuous, so only the control rules get a non-trivial interpretation: A λ x . � x , x � λ � x , y , z � . � y , x , z � − − − − − − − → A × A ( A × B ) × C − − − − − − − − − − − − − → B × ( A × C ) G. J. Wijnholds SYCO 2 29 / 41