CS470/570 Intro to Artificial Intelligence Chapter 8: First-Order Predicate Logics Written Homework

Instructions: Answers to the questions below must be presented in hardcopy, on the due date noted on the course website. All submissions must:

• have solutions presented in the order listed here, and clearly labeled.
• A stapled submission with a neatly printing cover sheet is required.

Typed answers are preferable, but clear handwritten work is acceptable.

The Problems:

8.6. The truth value of FOPL sentences. Being able to understand FOPL sentences and what they imply about the world is important. When you first look at this exercise, you might get confused: "So, they are asking which of these sentences is true? But that would depend on the facts that are known to be true in a given world!". Read it again: it is asking whether the statements are valid; which of course means "are true in all possible worlds". So ask yourself each question in two ways: is there any possible world (model) in which the given statement would be false? Or: can I explain how some assignment of variables would always make it true.

Naturally, you must not only state whether it is valid or not, but briefly and clearly explain your reasoning.

8.10. Representing real-world facts in FOPL. The infamous computer science saying of "garbage in, garbage out" was never more true than for AI systems! We can create the best automated reasoning systems in the world, but they will not be completely unreliable if we don't fill the KB with facts that accurately (in terms of syntax, of course, but more importantly in terms of semantics!) represent what we know about the world. This simple exercise asks you to translate plain English sentences into appropriate FOPL. The concept to translate are easy here...the focus is on correct use of existential and universal quantifiers as much as anything else. I'll give you the first one to get you started:
(a) Emily is either a surgeon or a lawyer. === Occupation(Emily, Surgeon) V Occupation(Emily, Lawyer). Explanation: no variables (and thus no quantifiers) were even needed here, since we weren't making a general statement about "things", but just naming completely specific facts about Emily.

Just as I've done here, briefly explain your reasoning in constructing each expression.

8.18. Wumpus World rides again! Remember how hard it was to express what we knew about Wumpus World in Propositional Logic? (e.g., to express that "Detect a breeze means there is a pit in an adjecent square", you had to explicitly write that out for every square in the game!). Let's see how much easier this is in FOPL! To keep everyone on the same page, assume that you have the predicate AT given in the book's problem statement, but also the predicates Adjacent(x,y), Smelly(s), Breezy(s) used in the chapter).

(a) As a warm-up, express what is known about pits in the wumpus world as FOPL sentence(s).

(b) Now do as the problem asks and express what's known about Wumpi, i.e., the knowledge of their location in relation to smelliness, as well as the fact that there is only one Wumpus (can't have one in more than one square!).

Naturally, you'll want to not only give your FOPL expression, but explain carefully your reasoning in constructing it.

8.23. Parts a,b,c only. Interpreting FOPL sentences. Being able to "debug" FOPL sentences to make sure that they really do express the real-world facts that they are supposed to is a valuable skill. For each of these given sentences, explain carefully what's wrong...and then propose a corrected version, explaining why it corrects the error(s).