The fundamental semantic notion: 1. Truth (tautology) (write |= S to indicate tautology) 2. Logical consequence Tautological consequence Write |= S (S is a logical consequence of ) = {AvB, A} S = {B} |= S S1 . . . Sn _ S Fact: The argument with pr
Midterm Coverage: Chapters 6 8 (Fitch), 15.1 15.6, 16.1 16.4, 17.1 17.2 Topics: Proofs in propositional logic (2) Set theory: definitions (for example, define subset), followed by proofs using those definitions, induction (similar to homework) So
- Midterm 3/27 - Problem set 5 due 3/25 - Review problems on the web by Sunday CT0: CT1: Def. A set of sentences is formally consistent just in case /- (just in case you can't derive falsum from gamma.) Otherwise, we call formally inconsistent. L
HW set due Tue after break Midterm Exam March 27 Chapters 15, 16, 17 & notes about first order language and semantics Boolos Jeffries chapter from website Soundness: S, then S. Recall: S means there exists a derivation such that S 1 through Si are
PvQ P . R Q . R R v Elim
P . ~P
~ Intro
. P
Elim
P . Q PQ . P Q . P . Q (A^B) C A B A^B C
Intro
Elim
GOAL: C
Elim 1, 4
BC A^B B C (A^B) C AB ~B A B ~A
GOAL: (A^B) C
Intro
GOAL: ~A
Elim 1, 3 ~ Intro
TO PROVE: ~(AvB) (~A ^~B)