Consider the following context-free grammar, partially augmented with semantic rules: {NP.sem(VP.sem)} + Det Nominal {Det.sem(Nominal.sem)} Nominal → Adj Nominal {Adj.sem(Nominal.sem)} { ...} { {.…..}...

Extracted text: Consider the following context-free grammar, partially augmented with semantic rules: {NP.sem(VP.sem)} + Det Nominal {Det.sem(Nominal.sem)} Nominal → Adj Nominal {Adj.sem(Nominal.sem)} { ...} { {.…..} ...} { …..} S → NP VP NP Det → every Det + a .. → small Nominal → dog → barks Adj VP Now consider the following two sentences, with their desired meaning represen- tations: A1 every dog barks A2 Vd Dog (d) = Je Barking(e) A Barker(e,d) B1 a small dog barks B2 3d Dog (d) A Small(d) A 3e Barking(e) A Barker(e, d) Complete the above augmented grammar, by giving the semantics of 'every', 'a', 'small', 'dog', and 'barks', so that the desired meaning representations are obtained for A1 and B1. Show that your solution is correct, by first giving the lambda expressions obtained from A1 and B1 before any beta reductions, and then showing step-by-step that the beta reductions lead to A2 and B2.