\title {Logic I \\ Fast Lecture 07}

\maketitle

\section{Every Time I Go to the Dentist Someone Dies}

\emph{Reading:} §11.2

\section{Every Time I Go to the Dentist Someone Dies}

\section{Truth-functional completeness}

\emph{Reading:} §7.4

\section{Truth-functional completeness}

7.25, 7.26, *7.28, 7.29

7.25, 7.26, *7.28, 7.29

\section{Proofs about Proofs}

\section{Proofs about Proofs}

\section{The Soundness Property and the Fubar Rules (fast)}

\emph{Reading:} §8.3

\section{The Soundness Property and the Fubar Rules (fast)}

7.32

7.32

\section{Proof of the Soundness Theorem}

\emph{Reading:} §8.3

\section{Proof of the Soundness Theorem}

\section{The Essence of the Completeness Theorem}

\emph{Reading:} §8.3

\section{The Essence of the Completeness Theorem}

\section{Lemma for the Completeness Theorem}

\emph{Reading:} §8.3

\section{Lemma for the Completeness Theorem}

\section{Proof of the Completeness Theorem}

\emph{Reading:} §8.3, §17.1, §17.2

\section{Proof of the Completeness Theorem}

\section{Proof of Proposition 4 for the Completeness Theorem}

\emph{Reading:} §15.1, §15.6

\section{Proof of Proposition 4 for the Completeness Theorem}

15.33--15.40 (second edition)

15.33, 15.37--15.39 (second edition)

\section{More Records Than the KGB}

\emph{Reading:} §14.1, §14.3

\section{More Records Than the KGB}

\section{The End Is Near}

\emph{Reading:} §14.3

\section{The End Is Near}

14.26, 14.28

14.2

14.4, 14.5

14.10, 14.11

14.26, 14.28

13.51–2, 14.13 %proofs

For each of the following sentences of FOL, give a logically equivalent sentence of idiomatic English using the specified interpretation. Your English sentences should be as concise as possible.

Domain : people and actions

D(x) : x is desirable

V(x) : x is virtuous

A(x) : x is an action

H(x) : x is a person

P(x,y) : x performed y

i. ∀x (( D(x) → V(x) )

ii. ∀x ( (A(x)∧ D(x) ) → V(x) ) )

iii. ∃x ( A(x) ∧ ¬( D(x) → V(x) ) )

*iv. ∃x(H(x)∧∀y((A(y)∧P(x,y))→V(y)))

**v. ¬∃x (∃y (H(x) ∧ P(x,y) ∧ A(y) ∧ ¬V(y)) ∧ ¬∃z[P(x,z) ∧ A(z) ∧ V(z)))