Consider the problem of deciding whether a propositional logic sentence is true in a given model.

a. Write a recursive algorithm PL-TRUE? (s m) that returns true if and only if the sentence s is true in the model in (where in assigns a truth value for every symbol in s). The algorithm should run in time linear in the size of the sentence. (Alternatively, use a version of this function from the online code repository.)

b. Give three examples of sentences that can be determined to be true or false in a partial model that does not specify a truth value for some of the symbols.

c. Show that the truth value (if any) of a sentence in a partial model cannot be determined efficiently in general.

d. Modify your PL-TRUE algorithm so that it can sometimes judge truth from partial models, while retaining its recursive structure and linear runtime. Give three examples of sentences whose truth in a partial model is not detected by your algorithm.

e. Investigate whether the modified algorithm makes TT-ENTAILS more efficient.