# hw2 - \documentclasscfw_article \newcountercfw_kbc...

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\documentclass{article} \newcounter{kbc} \newenvironment{kblist} {\begin{list}{(\arabic{kbc})}{\usecounter{kbc}}}{\end{list}} \title{CS 440: Introduction to AI} \author{Homework 2 - Part A (Part B will be available soon.)} \date{Due: September 23 11:59PM, 2010} \begin{document} \maketitle \emph{Your answers must be concise and clear. Explain sufficiently that we can easily determine what you understand. We will give more points for a brief interesting discussion with no answer than for a bluffing answer.} \section{Validity and Satisfiability} Determine whether each formula is valid, satisfiable (but not valid), or unsatisfiable. \begin{enumerate} \item $P(x)$ \item $\forall x\ P(x)$ \item $\exists x \forall y \ P(x,y)$ \item $\forall x\ P(x) \vee \neg P(x)$ \item $\exists x \forall y \ P(x,y) \Rightarrow \forall x \exists y \ P(x,y)$ \item $\exists x \ P(x) \Rightarrow \neg P(x)$ \item $\exists x \ \neg ( \neg P(x) \vee P(x))$ \item $\forall x \forall y \ (\neg P(x) \vee P(y)) \Rightarrow (P(x) \Rightarrow P(y))$ \end{enumerate} \section{Sentence Translation} This problem has two parts. In the first part, you are asked to translate some first order predicate calculus (FOPC) sentences into English sentences. The meanings of the predicates and functions in the FOPC sentences are given. You should give as natural the English translations as possible. Few points will be given for an English sentence like For all $x$ there exists a $y$ such that either $P$ of $x$ and $y$ or $Q$ of $y$.'' In the second part, you are asked to translate English sentences into

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## This note was uploaded on 04/30/2011 for the course ECE 448 taught by Professor Levinson during the Spring '08 term at University of Illinois, Urbana Champaign.

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hw2 - \documentclasscfw_article \newcountercfw_kbc...

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