In this paper we will explore the similarities and differences between two feature logic-based approaches to the composition of semantic representations. The first approach is formulated for Lexicalized Tree Adjoining Grammar (LTAG, Joshi and Schabes 1997), the second is Lexical Ressource Semantics (LRS, Richter and Sailer 2004) and was first defined in Head-driven Phrase Structure Grammar. The two frameworks have several common characteristics that make them easy to compare: 1 They use languages of two sorted type theory for semantic representations. 2. They allow underspecification. LTAG uses scope constraints while LRS provides component-of contraints. 3 They use feature logics for computing semantic representations. 4. they are designed for computational applications. By comparing the two frameworks we will also point outsome characteristics and advantages of feature logic-based semantic computation in genereal

Kallmeyer, Laura

Richter, Frank

English

Hochschulschriftenserver - Universität Frankfurt am Main

∗†≥ ∗†1e  126,e  126,e   126, e,t  2application →⎡⎢⎢ ⎢⎣type 2functor type in 1out 2 arg type 1⎤⎥⎥ ⎥⎦equation →⎡⎣type trutharg1 type 1arg2 type 1⎤⎦ e,t   e  t 3⎡⎢⎢⎢⎢ ⎢⎢⎢⎢⎢ ⎢⎢⎢⎢⎢⎢ ⎢⎢⎢⎢⎢ ⎢⎣signphonology phonological structuresynsem⎡⎢⎢⎢⎢ ⎢⎢⎢⎣local⎡⎢⎢⎢⎢ ⎢⎢⎢⎣category (local) syntactic structurecontent⎡⎢ ⎢⎢⎢⎢⎣contentindex⎡⎣ext-indexvar mephi index⎤⎦main me⎤⎥ ⎥⎥⎥⎥⎦⎤⎥⎥⎥⎥ ⎥⎥⎥⎦⎤⎥⎥⎥⎥ ⎥⎥⎥⎦lf⎡⎢ ⎢⎢⎣lrsexcont meincont meparts list(me)⎤⎥ ⎥⎥⎦⎤⎥⎥⎥⎥ ⎥⎥⎥⎥⎥ ⎥⎥⎥⎥⎥⎥ ⎥⎥⎥⎥⎥ ⎥⎦45⎡⎢⎢⎢ ⎢⎢⎢⎢⎢ ⎢⎢⎢⎢⎢⎣phon john ss loc⎡⎢⎢⎢⎣cat head nounsubcat   cont index var 1 johnmain 1 john ⎤⎥⎥⎥⎦lf⎡⎢⎣excont meincont 1 johnparts 1 john ⎤⎥⎦⎤⎥⎥⎥ ⎥⎥⎥⎥⎥ ⎥⎥⎥⎥⎥⎦⎡⎢⎢⎢ ⎢⎢⎢⎢⎢ ⎢⎢⎢⎣phon laughs ss loc⎡⎢⎣cat head verbsubcat NP 1  cont main 2a laugh⎤⎥⎦lf⎡⎢⎣excont meincont 2 laugh( 1)parts 2 laugh( 1), 2a laugh ⎤⎥⎦⎤⎥⎥⎥ ⎥⎥⎥⎥⎥ ⎥⎥⎥⎦⎡⎢⎢⎢⎢⎢ ⎢⎢⎢⎢⎢⎢ ⎢⎢⎣phon always ss loc⎡⎢⎢⎢⎣cat⎡⎢⎣head advmod V[loc cont main 2a ] subcat elist⎤⎥⎦cont main 5a always⎤⎥⎥⎥⎦lf⎡⎢⎣excont meincont 5 always( 3)parts 5 always( 3), 5a always ⎤⎥⎦⎤⎥⎥⎥⎥⎥ ⎥⎥⎥⎥⎥⎥ ⎥⎥⎦& 2a   3678 e,t lrs →⎛⎝⎡⎣excont 1incont 2parts 3⎤⎦∧ member( 2, 3) ∧ 2   1⎞⎠phrase →   nh-dtr lf excont 1parts 2  ∧ member( 1, 2) u-sign →∀ 1 ∀ 2 ∀ 3 ∀ 4⎛⎜⎜⎝  lf excont 1parts 2  ∧ 3   1 ∧ member( 4, 2) →(member( 3, 2) ∧ 4   1)⎞⎟⎟⎠phrase → lf excont 1h-dtr lf excont 1 phrase → lf incont 1h-dtr lf incont 1 phrase →⎛⎝⎡⎣lf parts 1h-dtr lf parts 2nh-dtr lf parts 3⎤⎦ ∧ append( 2, 3, 1)⎞⎠NP ⎡⎣exc 1inc 1pts   1 john ⎤⎦JohnA⎡⎢⎢⎣ss l c hd mod V:[main 2a ]lf⎡⎣exc 5inc 5 always( 3)parts   5, 5a always ⎤⎦⎤⎥⎥⎦& 2a   3alwaysV ⎡⎣exc 4inc 2 laugh( 1)pts   2, 2a laugh ⎤⎦laughsadj headVP ⎡⎣exc 4inc 2pts   2, 2a, 5, 5a ⎤⎦& 5   4comp headS ⎡⎣exc 4 always(laugh(john))inc 2pts   2, 2a, 5, 5a, 1 ⎤⎦↓↓∗μμ↓∗np vpx ≥ y x y1 e s s,t 9   l1l1l144l1 : ( 1)⎡⎢⎢⎣            l1  ⎤⎥⎥⎦semtbbindingsvare e var s,t vars s10⊥0, 1,...a(u)( ( ( 0))) = 1∧( ( ( 0))) = 4∧( ( ( 0))) = l1⎡⎢⎢⎣            l1  ⎤⎥⎥⎦γ1 ... p ...  pγ2 ... r ...  γ1 ... p ......  pγ2 ... r ... f ...  γ1 γ2 p• p γ1γ2 γ1 p γ2 r r• γ2γ2 p γ1 γ1 pγ2 f f γ2γ p γγ pγ p (x)l1 : ( 1)⎡⎢⎢⎢⎣            l1  ⎤⎥⎥⎥⎦l3 : (x) l2 : ( 6) 6 ≥ 7       x    ⎡⎢⎢ ⎢⎢⎣r     l2  f        ⎤⎥⎥ ⎥⎥⎦x116 7l21 = xf7 = l1r4 = l2δδ δc1,c 2 δ   c1 = c2 c1 c2 δgg• n c δ   n = cg( n)=c• n1 c δ   n1 = cn2 δ   n1 = n2g( n1 )= n2l1 : (x),l 2 : ( 6),l 3 : (x) 6 ≥ l16 → l1 6 l26 l2 6 l36 l16 ≥ l1 (x) ∧  ( (x))l1,l 2,l 3,...O(n6)x ≥ y∃1x( (x) ∧ ) ∀x( (y) → ) (x,y)∃ > ∀,∀ > ∃∀ > ∃ >t w oseem > ∀,∀ > seemthree > likely,likely > three12x yy xl1 : ( 1)2 ≥ 3l2 : (x, 4, 5)l3 : (x)4 ≥ l36 ≥ 5 5 ≥ 7⎡⎢⎣ l1       ⎤⎥⎦⎡⎢⎣ x       ⎤⎥⎦13= 2 = l1  l12 14 154 5  (x)4 ≥ l32q q(x,p1,p 2) q(λx.p1,λx.p 2)q   e, s,t  ,  e, s,t  ,  s,t   [ ] l4 : ( 3)⎡⎢⎢ ⎢⎢⎢⎢⎢⎣   ⎡⎢⎣    l4 ⎤⎥⎦⎤⎥⎥ ⎥⎥⎥⎥⎥⎦∗l3 : (x, 6, 7)6 ≥ 108 ≥ 7 7 ≥ 9⎡⎢⎢⎣⎡⎢⎣ x    ⎤⎥⎦⎤⎥⎥⎦5 6 7 6 ≥ 5 5 ≥ 72 ≥ 5, 5 ≥ l11 → x, 6 → 2, 7 → l1l1 : (x)l2 :  (x, 4, 5) l3 :  (x)2 ≥ l14 ≥ l3, 2 ≥ 5, 5 ≥ l12 → l2 4 → l3, 5 → l1 (x,  (x), (x))8 945l4∗1 2l1l2> > ∗ > >23 ≥ 2 l11 → x, 2 → l2, 6 → 3, 7 → l1, 9 → l1l1 : ( 1)3 ≥ 2⎡⎢⎢⎢⎢ ⎢⎢⎢⎢⎢⎣ l1                   l1  ⎤⎥⎥⎥⎥ ⎥⎥⎥⎥⎥⎦l3 : (x, 4, 5) l4 : (x)4 ≥ l4 6 ≥ 5 5 ≥ 7 l2 : ( 8) 8 ≥ 9⎡⎢⎣ x       ⎤⎥⎦⎡⎢⎣1   l2  2      ⎤⎥⎦l1 :  (x)l3 : (x, 4, 5) l4 : (x)l2 : ( 8)3 ≥ l24 ≥ l4 3 ≥ 5 5 ≥ l18 ≥ l13 → l3, 5 → l2, 8 → l1, 4 → l4l3 : (x,l4 : (x),l 2 : (l1 :  (x)))3 → l2, 8 → l3, 5 → l1, 4 → l4l2 : (l3 : (x,l4 : (x),l 1 :  (x)))⎡⎢⎢⎢ ⎢⎢⎢⎢⎢ ⎢⎢⎢⎢⎢⎣phon everybody ss loc⎡⎢⎢⎢⎣cat head nounsubcat   cont index var xmain every(x,α,β) ⎤⎥⎥⎥⎦lf⎡⎢⎣excont meincont 2 person(x)parts x, 2, 2aperson, 4 every(x,α,β) ⎤⎥⎦⎤⎥⎥⎥ ⎥⎥⎥⎥⎥ ⎥⎥⎥⎥⎥⎦& 2  α& x α& x β16(x,ρ,ν)ρ nh-dtr ss loc cat head detcont main gen-quantiﬁer  →⎛⎜⎜⎜ ⎜⎝⎡⎢⎢⎢⎣h-dtr lf excont 1incont 2 nh-dtr lf incont 1 gen-quantiﬁerrestr 3  ⎤⎥⎥⎥⎦∧ 2   3⎞⎟⎟⎟ ⎟⎠(x,ρ,ν)ν∀ 1⎛⎜⎜ ⎜⎜⎝⎡⎢⎢⎢ ⎢⎣nh-dtr⎡⎢⎢ ⎢⎣ss loc cat head nounsubcat   lf excont gen-quantiﬁerscope 1 ⎤⎥⎥ ⎥⎦⎤⎥⎥⎥ ⎥⎦→∃ 2   h-dtr lf incont 2 ∧ 2   1 ⎞⎟⎟ ⎟⎟⎠4  61  βNP ⎡⎣exc 4 every(x,α,β)inc 2 person(x)pts   2, 2a person, 2b x, 4 ⎤⎦& 2  αEverybodyVP ⎡⎣exc 6inc 1 laugh(x)pts   1, 1a laugh ⎤⎦laughscomp headS ⎡⎣exc 6 every(x,person(x),laugh(x))inc 1pts   1, 1a, 2, 2a, 2b, 4 ⎤⎦& 1  β& 4   62  α 1  β 4  6⎡⎢⎢⎢ ⎢⎢⎢⎢⎢ ⎢⎢⎢⎢⎢⎣phon three ss loc⎡⎢⎢⎢⎣cat head detsubcat   cont index var 4axmain 4 three(x,α,β) ⎤⎥⎥⎥⎦lf⎡⎢⎣excont meincont 4 three(x,α,β)parts 4, 4a ⎤⎥⎦⎤⎥⎥⎥ ⎥⎥⎥⎥⎥ ⎥⎥⎥⎥⎥⎦& x α& x β⎡⎢⎢⎢⎢ ⎢⎢⎢⎢⎢ ⎢⎢⎢⎢⎢⎢ ⎢⎣phon girls ss loc⎡⎢ ⎢⎢⎢⎣cat head nounsubcat DetP 4a  cont index var 4amain girl ⎤⎥ ⎥⎥⎥⎦lf⎡⎢⎢⎢⎣excont gen-quantiﬁervar 4a incont 2 girl( 4a)parts 2 girl( 4a), 2a girl ⎤⎥⎥⎥⎦⎤⎥⎥⎥⎥ ⎥⎥⎥⎥⎥ ⎥⎥⎥⎥⎥⎥ ⎥⎦xαDet ⎡⎣exc 4inc 4 three(x,γ,δ)ps   4, 4a x ⎤⎦threeN ⎡⎣exc 4inc 3 girl(x)ps   3, 3a girl ⎤⎦girlscomp headNP ⎡⎣exc 4 three(x,γ,δ)inc 3ps   4, 4a, 3, 3a ⎤⎦& 3  γ⎡⎢⎢⎢ ⎢⎢⎢⎢⎢⎢ ⎢⎢⎢⎢⎣phon likely ss loc⎡⎢⎢⎢⎢⎣cat⎡⎢⎣head adjsubcat  loc cat head verbcont main 1b   ⎤⎥⎦cont main 2a likely ⎤⎥⎥⎥⎥⎦lf⎡⎢⎣excont meincont 1parts 1, 2 likely(α), 2a ⎤⎥⎦⎤⎥⎥⎥ ⎥⎥⎥⎥⎥⎥ ⎥⎥⎥⎥⎦& 1  α& 1b   1= x   x     x=   x   x   xsNP ⎡⎣exc 4 three(x,γ,δ)inc 3 girl( 4ax)ps   4, 4a, 3, 3a ⎤⎦& 3  γThree girlsV⎡⎣exc 5inc 1ps 1 ⎤⎦areA ⎡⎣exc 2inc 1ps   1, 2 likely(α), 2a ⎤⎦& 1  αlikelyVP ⎡⎣exc 1inc 1 come(x)ps   1, 1a ⎤⎦to comehead compAP ⎡⎣exc 2inc 1ps   2, 2a, 1, 1a ⎤⎦head compVP  inc 1ps   2, 2a, 1, 1a  comp headS ⎡⎣exc 5inc 1 come(x)ps   4, 4a, 3, 3a, 2, 2a, 1, 1a ⎤⎦& 1  δs α δxx  γ1718=19∗ β⎡⎢ ⎢⎢⎢⎢⎢ ⎢⎢⎢⎢⎢⎢⎣wordphon  nikt ss loc cont index var 3b xmain 5 some(x,γ,δ) lf⎡⎢⎢⎢⎣lrsexcont 5 some(x,γ,δ)incont 3 person( 3bx)parts   3, 3aperson, 3b, 4¬β, 5 ⎤⎥⎥⎥⎦⎤⎥ ⎥⎥⎥⎥⎥ ⎥⎥⎥⎥⎥⎥⎦& 5  β& 3  γ& x  γ& x  δ⎡⎢ ⎢⎢⎢⎢⎢ ⎢⎢⎢⎢⎢⎢ ⎢⎣wordphon  nie przyszed  l ss loc cat subcat  loc cont index var 3b  cont main come lf⎡⎢⎢⎢⎣lrsexcont 0incont 1 come( 3b)parts   1, 1acome, 2¬α, ⎤⎥⎥⎥⎦⎤⎥ ⎥⎥⎥⎥⎥ ⎥⎥⎥⎥⎥⎥ ⎥⎦& 1  α& 2   0= (= ) β  δNP ⎡⎣excont 5 some(x,γ,δ)incont 3 person( 3bx)parts   3, 3aperson, 3b, 4¬β, 5 ⎤⎦& 5  β& 3  γNiktV ⎡⎣excont 0incont 1 come( 3bx)parts   1, 1acome, 2¬α ⎤⎦& 1  α& 2   0nie przyszed  lS ⎡⎣excont 0 ¬ some(x,person(x),come(x))incont 1parts   1, 1a, 2, 3, 3a, 3b, 4, 5 ⎤⎦& 1  δyesnono3yes = yes yes39 1 = 99 ≥ 10yes7 ≥ 61 = 7∗l2 : ( 2)4 ≥ l2⎡⎢⎢ ⎢⎢⎢⎢⎢ ⎢⎢⎢⎣⎡⎢⎣ l2⎤⎥⎦               ⎤⎥⎥ ⎥⎥⎥⎥⎥ ⎥⎥⎥⎦l3 : (x, 5, 6) l4 : (x)5 ≥ l4 7 ≥ 6 6 ≥ 8l1 : ¬ 99 ≥ 10⎡⎢⎢⎣         ⎤⎥⎥⎦⎡⎢⎣⎡⎢⎣      ⎤⎥⎦⎤⎥⎦l2 :  (x) l3 :  (x, 5, 6) l4 :  (x) l1 : ¬ 14 ≥ l2 5 ≥ l4 1 ≥ 6 6 ≥ l2 1 ≥ l2•••• N F• S ∈ N• P A → f(A1,...,A n)n ≥ 0,f ∈ F A,A1,...,A n ∈ N• A ⇒ f() A → f()• A∗ ⇒ f(t1,...,t n) A → f(A1,...,A n)Ai∗ ⇒ ti 1 ≤ i ≤ nγγ γγγγ → fγ:p1,...,pn(γ1,...,γ n) γ,γ1,...,γ np1,...,p n γ γ1,...,γ nγ p1,...,p n2021fαl:1,2,22(fαj(),f β: (fβ()),f αm())αj αmαlβ∗NAαj → fαj() αjαm → fαm() αmβ → fβ() ββ → fβ: (β) β βαl → fαl:1,22(αj,α m) αj αm αlαl → fαl:1,22(αj,α j)αl → fαl:1,22(αm,α j)αl → fαl:1,22(αm,α m)αl → fαl:1,2,22(αj,β,α m) αj β αm αlαl → fαl:1,2,22(αj,β,α j)αl → fαl:1,2,22(αm,β,α j)αl → fαl:1,2,22(αm,β,α m)αlαj βα m βfαl:1,2,22fαj fβ:  fαmfβG• G• γ22fγγ → fγ()  jp p · j• γ p1,...,p n γγ1,...,γ np1,...,p n n fγ:p1,...pnγ → fγ:p1,...pn(γ1,...,γ n)• γ → fγ() [[fγ()]]syn := γ• γ → fγ:p1,...pn(γ1,...,γ n)[[fγ:p1,...pn(t1,...,t n)]]syn := γ[p1,[[t1]] syn]...[pn,[[tn]] syn]23[[fαj()]]syn = αj [[fαm()]]syn = αm [[fβ()]]syn = β[[fβ: (X)]]syn = β[ ,[[X]] syn][[fαl:1,22(X,Y )]]syn = αl[1,[[X]] syn][22,[[Y ]] syn][[fαl:1,2,22(X,Y,Z)]]syn = αl[1,[[X]] syn][2,[[Y ]] syn][22,[[Z]] syn][[fαl:1,2,22(fαj(),f β: (fβ()),f αm())]]syn = αl[1,α j][2,β[ ,β]][22,α m]αl[1,α j][2,β[ ,β]][22,α m]αl 1t1 t2 222 t3 t1,t 2,t 3 t1 αjt3 αmt2 β[ ,β]β  βσσγσ σ(γ)γ[p,γ ] γ  p γγ[p,γ ] γ  γ pγ  p γγ[p,γ ] γ  γ p γ[p,γ ]σ(αj)= σαj,δ αj  :=     (x)     x   σ(αm)= σαm,δ αm  :=     (y)     y   σ(αl)= σαl,δ αl  :=    l1 : ( 2, 3)⎡⎢⎢⎢ ⎢⎢⎢⎣                  l1  ⎤⎥⎥⎥ ⎥⎥⎥⎦σ(β)= σβ,δ β  :=   l2 : ( 6)6 ≥ 7⎡⎢⎣    l2        ⎤⎥⎦σfγ...24δtop(δ)top(δαj)= 0,top(δαm)=1 ... σγ,δ γ,top(δγ)  σ,δ  σ σδ[[fαj()]]sem :=  σαj,δ αj,top(δαj) δ αj = δαj { (p(top(δαj))) = (p(top(δαj)))|p αj}αjδαj δαjδαj σαjfαm() fβ()[[fβ: (X)]]sem :=  σβ ∪ σX,δ ,top(δβ)  [[X]] sem =  σX,δ X,top X δ  = δβ ∧ δX∧ ( (top(δβ))) = ( (topX)) ∧ ( (top(δβ))) = (fX(topX))  { (p(top(δβ))) = (p(top(δβ)))|p  =  ,p β}fX γ Xfγ...(...)  β  ββ• γ → fγ()  σγ,δ γ σ(γ)[[fγ()]]sem :=  σγ,δ γ,top(δγ) δ γ = δγ { (p(top(δγ))) = (p(top(δγ)))|p γ}• γ → fγ:p1,...pn(γ1,...,γ n)p1,...,p k 0 ≤ k ≤ np1,...p n σγ,δ γ  σ(γ)[[fγ:p1,...pn(X1,...,X n)]]sem :=  σγ ∪ σX1 ∪···∪σXn,δ ,top(δγ) δ  = δγ ∧ δX1 ∧ ...δ Xn  ni=1 (pi(top(δγ))) = ( (topXi))  ni=k+1 (pi(top(δγ))) = (fXi(topXi))  { (p(top(δγ))) = (p(top(δγ)))|p/ ∈{ p1,...,p n},p γ}fαl:1,2,22(fαj(),f β: (fβ()),f αm())GG[[fβ()]]sem =  σ1β,δ1β , 11 σ1β = l3 : ( 9) 9 ≥ 10δ1β  = ( ( ( 11))) = l3 ∧ ( ( ( 11))) = 10∧ ( ( 11)) = ( ( 11)) ∧ ( ( 11)) = ( ( 11))[[fβ: (fβ())]]sem =  σ2β,δ2β , 8 σ2β = l2 : ( 6) l3 : ( 9) 6 ≥ 7 9 ≥ l2δ2β  = ( ( ( 8))) = l2 ∧ ( ( ( 8))) = 7∧δ1β ∧ ( ( 8)) = ( ( 11)) ∧ ( ( 8)) = ( ( 11 ))∧ ( ( 8)) = ( ( 8))[[fαj()]]sem =  σαj,δ αj, 0 σαj = (x)δ αj = ( ( ( 0))) = x∧ ( ( 0)) = ( ( 0))[[fαm()]]sem =  σαm,δ αm, 1 σαm = (y)δ αm = ( ( ( 1))) = y∧ ( ( 1)) = ( ( 1))[[fαl:1,2,22(fαj(),f β: (fβ()),f αm())]]sem =  σαl,δ αl , 4 σαl = (x) (y) l1 : (x,y)l2 : ( 6) l3 : ( 9)6 ≥ l1 9 ≥ l2δ αl = ( ( ( 4))) = 2 ∧ ( ( ( 4))) = 3∧ ( ( ( 4))) = 5 ∧ ( ( ( 4))) = l1∧δ αj ∧ δ2β  ∧ δ αm∧ ( ( 0)) = ( ( 4))∧ ( ( 1)) = ( ( 4))∧ ( ( 4)) = ( ( 8)) ∧ ( ( 4)) = ( ( 8))∧ ( ( 4)) = ( ( 4)) ∧ ( ( 4)) = ( ( 4))b f()b(f()) := [[f()]]semrf f[[f(γ1,...,γ n)]]sem [[γ1]] sem,...[[γn]] semt tGμ25f(t1,...,t n)f t1,...,t n≥ 262728

Feature logic-based semantic composition : a comparison between LRS and LTAG

Abstract

Similar works

Full text

Available Versions

Hochschulschriftenserver - Universität Frankfurt am Main