Lecture 10 Compactness/rules for the missing connectives
Todays lecture is the last in propositional logic. What it will contain: Some final remarks on the completeness theorem and its proof A proof o
Homework 2 PHIL 151 Due Wed. Jan 19th in class at 10 am 1. (2 points) Problem 1b on page 20. 2. (8 points)Prove or nd a counter-example to (a) If |= then |= and |= (b) If |= then |= or |= where is a s
Homework 3 PHIL 151 Due Wed. Jan 26th in class at 10 am 1. (10 points) Do exercises 1 (d), 2c and 4 on page 39. In problem 1d), the expression abbreviates the conjunction of two implications. So to pr
Mid-term on propositional logic
You should be prepared to: Provide a recursive definition of a function on an inductively defined set.
Examples: problem 4, hw 1; problem 3, hw3.
Prove by induction tha
Midterm PHIL 151 Feb. 5, 2010 Apart from the natural deduction proofs you are asked to provide in problem 6, you may in your proofs use any lemma or theorem from the van Dalen text.
Problem 1. Suppose
Lecture 1: Introduction to PHIL 151
Phil 151 is an introduction to the concepts and techniques used in the mathematical analysis of deductive reasoning.
The main pre-mathematical notion being analyzed
Lecture 2: the sentences of propositional logic
Four general steps in analysis of the notion of logical consequence
Give a semantics for logic: specify how abstract sentences come to be true and false
Lecture 3 Inductively Defined Sets and Definition by Recursion
Review Inductively defined sets are generated from operations on base elements. Examples: Natural numbers-generated from 0 by operation o
Lecture 4 Semantics for Propositional Logic
Four general steps in analysis of the notion of logical consequence Specify logical form by formulating an abstract notion of sentence. Give a semantics for
Lecture 5 Algebra of propositional formulas/ Interdefinability of connectives
Definition (by recursion) of substitution function on PROP (def. 1.2.5) Given a propositional formula , the function repla
Lecture 6 Proof in Propositional Logic
Four general steps in analysis of the notion of logical consequence Specify logical form by formulating an abstract notion of sentence. Give a semantics for logi
Lecture 7 Completeness of Propositional LogicPart I
Four general steps in analysis of the notion of logical consequence Specify logical form by formulating an abstract notion of sentence. Give a seman
Lecture 8 Completeness of Propositional LogicPart II
The completeness theorem
|-
if and only if
|=
Last class we proved the direction: if |- then |= .
In other words, we proved that the formal sys
Lecture 9 Completeness of Propositional LogicPart III
We are half way through the proof of the hard direction of the completeness theorem. The hard direction, recall, is: if |= then |- The proof proce
Homework 1 PHIL 151 Due Wed. Jan 12th, in class at 10am
1. (5 points) Prove by induction that n=0 2i = 2n+1 1 i 2. (5 points) Write down explicit denitions of the functions f and g on the natural numb