SYMBOLIC LOGIC
Notices and Notes
April
April 13
Clarification About Falsum Introduction
I have posted a very small handout concerning the introduction of the falsum. PLEASE READ IT!
About the Final
Here are some suggestions as to what you should study for the final.
Syntax for Quantification Logic
- Definition (2.1): Recursive definitions of terms of QL.
- Definition (2.7): Atomic Formulas of QL
- Definition (2.10): Well-Formed Formulas of QL
- Study exercise 5.
You should be able to to state these definitions precisely.
Symbolization in Quantification Logic
- Study the symbolization techniques provided in sections 7.7 and 7.8. I have decided that I won't burden you with the symbolization techniques provided in 7.9. They can be quite difficult and it would be unfair for you to know this material since we did not spend any time on this.
Derivations in Quantification Logic
Study all the examples I have provided in the handouts. Clearly I will not ask you to do very difficult and long derivations. If you can do all the derivations except for the very long derivations, you will be fine.
Semantics
We did not have time to do formal semantics for Quantification Logic. Nonetheless, I would like you to study pages 10-13, of the handout called "Polyadic Quantification without Identity: Exercises and Solutions". You should be able to do the derivation no. 8, and you should be able to show that the converse of that theorem does not hold; that is, you should be able to show that the converse fails in a universe of discourse containing only two individuals.
An instance of the theorem, as discussed in the handout is:
"If somebody loves everybody, then everybody is loved by somebody".
But the converse does not hold:
"If everybody is loved by somebody, then somebody loves everybody".
General Comment
I have decided not to include questions concerning Sentential Logic. If you have any questions please send me an email.
Good Luck!
April 9
I have posted 3 additional handouts: 1. A Note on Numerical Quantification; 2. Solutions to the Second Midterm; 3. Polyadic Quantification With Identity: Exercises and Solutions.
April 2
I have posted another handout called: Polyadic Quantification Without Identity; Exercises & Solutions: PART 2
March
March 28
I have posted two new handouts. "Polyadic Quantification Without Identity Exercises & Solutions" and "Derivation Rules for Polyadic Quantification with Identity". Please bring both to class.
March 23
I have just posted additional solutions to the exercises 7.7E and 7.8E. I very strongly recommend that you do ALL the symbolization problems and that you carefully study the symbolization techniques provided in the text. Always attempt to do the translations yourself. The purpose of the solutions is to help you to determine whether or not you did the translations correctly. If your translation differs from the solutions provided, that does not mean you are necessarily wrong. You may have provided a translation that looks different but is logically equivalent to the solution provided.
March 19
I have posted a handout called "(1) Quantification Logic Derivations." Please note that the second midterm is March 27.
March 5
I have posted two handouts. Please print them and bring them to class.
February
February 13
Just a reminder that the first midterm is on February 28. Here is a list of things you should study:
- Chapter 1: Study the concepts and definitions of Argument, Deductive Validity, Deductive Soundness, Logical Consistency, Logical Truth, Logical Falsity, Logical Indeterminacy and Logical Equivalence. You should be able to state the definitions of these concepts precisely (see the glossary of ch. 1)
- Chapter 2: Chapter 2 deals with symbolization and syntax. Review some of the discussions of symbolization. Especially study the table on page 47.
- You should be able to formally describe the syntax of sentential logic. We did this in class; but you can also find a discussion of this starting at page 67.
- Chaper 3: You should be able to state the definitions of the glossary. In addition you should have a clear understanding of the definitions. For example, if you are asked: is this set of wffs truth functionally consistent? you should be able to answer this question.
- Chapter 5: Again you should be able to state the definitions of the glossary and understand the concepts involved so that you can apply them.
What might be on the exam:
- Providing a formal description of the syntax of sentential logic.
- Providing formal definitions of the various concepts.
- Stating some of the additional rules of SD+ and then providing a deductive proof using only the rules of SD.
- Doing proofs to establish Derivability, Validity, Theorem, Equivalence and Inconsistency in SD.
- Symbolization of natural language arguments, short truth table check of their semantic validity, and if valid, providing a derivation either in SD or in SD+
January
January 25
There is a new handout on the web: Exercises in propositional derivations.
Please bring this to class tomorrow.
January 16
There are two handouts. Please print them out and bring to class tomorrow.
January 13
On Thursday we discussed some key concepts of chapter 3. I strongly suggest that you attempt some of the following exercises over the weekend. Try to do them first before you look at the solutions.
- 3.1E no 2
- 3.2E no 1, 4
- 3.3E no 1
- 3.4E no 1
- 3.5E no 1
I will start on chapter 5 next week and I will provide you with some handouts over the weekend. So, check Notices for further information before the Tuesday class next week.
I hope you have a good weekend!
January 10
Today we developed the syntax for deductive sentential logic. We also stated the semantic rules for sentential logic. On thursday I will continue to discuss concepts and problems from chapter 3.
I did not have time today to assign readings and problems
- Study section 3.1 of chapter 3 and do some of the exercises of 3.1E no. 2
- Do some of the exercises of 3.2E no. 1, and 4.
