Reading and Homework Assignments

Readings for the course will mainly be from Formal Logic: Its Scope and Limits, by Richard Jeffery [henceforth "Jeffery"], with supplementary on-line readings from A Modern Formal Logic Primer, by Paul Teller [henceforth "Teller"]. Assignments will be listed by author and chapter (or page numbers), or by author with a link to an on-line source. Homework assignments will be posted here via hyperlinks.

• For Jan. 14: Teller, Vol. 2, Ch. 10. Try Ex. 10-1 and 10-2 (for practice).
• For Jan. 19: MLK Day--No Class.
• For Jan. 21: Read Jeffery, Ch. 1. Do Problem Set 1: Jeffery Ex. 1, 3, 5, 8, 18, 19.
• For Jan. 26: Read Jeffery, Ch. 2, pp. 21-29 and Teller, Vol. 1, Ch. 8. Do Problem Set 2: Jeffery Ex. 1 and 3 in Ch. 2.6 and Teller Ex. 8-1 and 8-3 in Teller.
• For Feb. 2: Read Teller, Vol. 1, Ch. 9. Get started on Problem Set 3: Teller Ex. 9-1 and 9-2 (which will be due Wed. 2/4). For 9-1, find the main connectives of sentences a)-d) by building up to each sentence via application of the Formation Rules defining sentences of FOL. For 9-2, think of the object in each case as using the Tree Rules to determine whether the conclusion of each argument is a Syntactic Consequence of the premises. For both problems be sure to use our notation for the connectives (rather than Teller's).
• For Feb. 4: Finish Problem Set 3 to hand in today. Read Jeffery Ch. 2, pp. 31-34.
• For Feb. 9: Do Problem Set 4: Teller Ex. 9-3 f)-j), 9-4 f)-j), and 9-6. Hand these in at the beginning of class on Monday. For 9-3, use the Tree Rules to determine which sentences are theorems, for 9-4 determine which sentences are anti-theorems (ruled out), and for 9-6 determine which pairs of sentences are mutually consequential. Then read Teller, Vol. 2, Ch. 11 and Teller, Vol. 2, Ch. 12.
• For Feb. 11: Re-read the Teller for 2/9 and Jeffery Ch. 2, pp. 31-34.
• For Feb. 18: Read the handout on Mathematical Induction and then do the MI Exercises to hand in at the beginning of class on 2/18. Also hand in a written out explanation/proof that the Soundness of our formal system (involving our formal language and the tree rules) can be understood as a matter of the Downward Adequacy of the tree method. Start with the general idea of Soundness as the claim that if we have a case of syntactic entailment, then we have a case of semantic entailment, where the former is expressed with the single turnstile and the latter with the double turnstile. Teller gives a statement of the Downward Adequacy of the tree method as D12 on p. 182.
• For Feb. 23: Re-read the Teller for 2/9 and Jeffery Ch. 2, pp. 31-34, and the handout on Mathematical Induction. Then get started on the MI Exercises 2 to hand in at the beginning of class on Wed. 2/25 [Hint: for some of these problems it might make the math easier to have the induction hypothesis include all cases at all levels up to and including level k, in order to prove that on that assumption the claim in question also holds for all cases at level k+1].
• For Mar. 2: Do MI Exercises 3 to hand in at the beginning of class. For some more practice (at least with mathematical problems involving MI), take a look at the problems posted here and here. Try them on your own, then check out the posted solutions linked on the problem pages.
• For Mar. 4: First Test! Bring an exam book to take your test in, and for good test-karma bring a spare for someone who forgets.
• For Mar. 11: Do MI Exercises 4 to hand in at the beginning of class. Also, re-read Teller, Vol. 2, Ch. 12, pp. 184-189.
• For Mar. 16: Do Problem Set 5: By appealing to the standard truth-tables for the relevant "input" sentences, prove the downward and upward correctness of the tree rules for conditional, negation conditional, biconditional and negation biconditional. Remember that this property of each rule is different from the Downward and Upward Adequacy of the whole system of tree rules. Be sure to give explanations in your proof of exactly what shows each rule to be downwardly and upwardly correct.
• For Mar. 23: On the basis of the proof of the Downward Adequacy of the tree method that I did in class, write out as much of a proof of the Upward Adequacy of the tree method as you can. The proof will appeal to the upward correctness of the tree rules and will reason from the openness of a path through a tree structure to there being an interpretation that makes every sentence written down on the path true.
• For Mar. 25: Complete the Truth-Functional Expressive Completeness Exercises to hand in at the beginning of class. Take another look at the end of Teller, Vol. 2, Ch. 12 on proving the Upward Adequacy of the tree method.
• For Mar. 30: Write out the proof for the Upward Adequacy of the tree method, being sure to include the explanation of how proving the Basis and proving the Induction Step combines to prove the claim desired in its full generality. Then extend the explanation to include an account of how establishing the Upward Adequacy of the tree method amounts to proving the Completeness of the Formal System that includes the tree rules. Then read Teller, Vol. 2, Ch. 14.
• For Apr. 1: Second Test! Bring an exam book to take your test in, and for good test-karma bring a spare for someone who forgets.
• For Apr. 13: Re-read Teller, Vol. 2, Ch. 14. Then read Teller, Vol. 2, Ch. 7 and Teller, Vol. 2, Ch. 8. Try Teller Ex. 7-1 b, d, e, g and Ex. 7-2. Remember that we use trees to test for the syntactic property of compatibility in order to determine syntactic consequence.
• For Apr. 15: Re-read Teller, Vol. 2, Ch. 14. Then read Jeffery Ch. 3 (pp. 35-54). Also, be ready to hand in the homework assigned for 4/13.
• For Apr. 20: To review the basics of Predicate Logic, read Teller, Vol. 2, Ch. 1, Ch. 2, and Ch. 3. Review the full range of Formation Rules of our formal language. To practice with the tree rules for Predicate Logic, do Teller Ex. 7-3. Remember that we use trees not to test validity of arguments, but rather to test for the syntactic property of sentence compatibility in order to determine syntactic consequence.
• For Apr. 22: Third Test! Bring an exam book to take your test in, and for good test-karma bring a spare for someone who forgets.
• For Apr. 27: Do Teller Ex. 7-4: l)-m); 8-5: a)-c); 8-6: a)-c). Then read Teller, Vol. 2, Ch. 15 (Sec. 1-2 and 5-6, so just pp. 220-234, 242-247). Do Teller Ex. 15-1, 15-2, 15-9, 15-10, 15-11.
• For Apr. 29: Do Teller Ex. 15-13 through 15-17. For fun, read "Formal Systems and Machines: An Isomorphism" by Peter Suber.
• For May 4: Review Session! 5:30pm-7pm, CBC C120. Also, if you want to do the Extra Credit Assignment, get started on that (due at the Final).
• For May 5: Review Session! 12pm-1:30pm in the conference room across from my office (CDC 426).
• For May 6: Final Exam! In our classroom at 3:10pm. Bring an exambook, and bring an extra for someone who forgets. Extra Credit Assignment due.

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Last updated April 26, 2009

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This document was created on January 9, 2009.