11-722: Grammar Formalisms: Homework 3Categorial GrammarDue after class 25th April to Alan W [email protected] Categorial Grammar:forward application A/B + B = Abackward application B + A\B = Acomposition A/B + B/C = A/Cconjunctions A CONJ A’ = A”type raising A = X/(X\A)(1) Show syntacic analysis of the following sentences using the above syntaxCCG rules and the following lexical entriesJohn NPMary NPJill NPBob NPflowers NPchocolates NPwalks S\NPand CONJ1like (S\NP)/NPlikes (S\NP)/NPdislikes (S\NP)/NPa NP/Nman Ngave (S\NP)/NP/NPJohn walksJohn likes MaryJohn and Mary like BobJohn likes and Mary dislikes Boba man walks John gave Mary flowers and Jill chocolates(2) Show syntactic and semantic analysis of the following sentencesA/B:S + B:T = A:S.TB:T + A\B:S = A:S.TX:A CONJ X’:A’ = X’’:lambda S (A . S & A’. S)X/Y:A Y/Z:B => X/Z: lambda Q ( A . (B . Q))NP:a -> T/(T\NP): lambda R (R . a)John NP:jMary NP:mBob NP:bwalks S\NP: lambda X walks(X)and CONJ:like (S\NP)/NP: lambda Y lambda X like(X,Y)likes (S\NP)/NP: lambda Y lambda X likes(X,Y)dislikes (S\NP)/NP: lambda Y lambda X dislikes(X,Y)John walksJohn likes MaryJohn and Mary like BobJohn likes and Mary dislikes Bob2(3) Adding approrpriate features to the basic S, NP categories show howthe following could be treated in a categorial framework. Show your lexicalentries and the syntactic analysis, no semantic analysis is require for theseexamples.I walkYou walkHe walksHe walkedthe boy walksthe boy likes the moviethe boys like the