CIS 301. Captain's Log: Logical Foundations of Programming, Fall 2001.

• August 20: Syllabus, errata, course prerequisites and expected outcomes. Why are we studying this course? Examples of interesting properties from switching software, mechanical systems, aircraft software, mobile software; proof-carrying code. Examples of simple propositions. Please read the preface and pages 1-12 for next class.
• August 22: Assignment #1 out. Arguments, syntax of propositional logic, binding priorities of connectives. Natural deduction: rules for conjunction and double negation.
• August 24: Change in my office hours. Instead of Wednesdays 3:30 - 4:30 PM, I will hold it from 11:30 - 12:30 PM (as on Mondays). Please send e-mail to the TA (varsha@cis.ksu.edu) if you have not received e-mail from her yet or if you have added the class recently. Today's coverage: Rules for implication elimination and introduction, modus tollens and several examples. Please continue reading pp. 1- 18 of the book.
• August 27: Implication introduction (continued), provable equivalence, disjunction introduction and elimination.
• August 29: Assignment #1 in. Assignment #2 out.Those joining late, please e-mail the TA your e-mail address. Disjunction elimination (contd.), unary negation. Reading: upto pp. 27.
• August 31: Unary negation (contd.), Derived rules, more examples using Natural Deduction.
• September 3: University holiday.
• September 5: Assignment #2 in; Graded Assignment #1 out; Assignment #3 out. Provable equivalences: De Morgan's Laws; introduction to semantics of propositional logic; well-formed propositional formulae.
• September 7: Backus-Naur form; truth tables; semantics of propositional formulae. Reading: pp.33-34 (skip Section 1.2.5), pp. 38-51.
• September 10: Graded Assignment #2 out; Review solutions to Assignment #1 and Assignment #2.
• September 12: Assignment #3 in; Assignment #4 out; Semantic entailment; soundness and completeness theorems for propositional logic, satisfiability and validity; semantic equivalence.
• September 14: Checking validity; Intro. to Conjunctive normal form (CNF), Negation normal form (NNF).
• September 17: Algorithm to convert into CNF.
• September 19: Assignment #4 in; Assignment #5 out; CNF algorithm concluded; conversion to NNF; a worked out example. Reading: pp.56-83.
• September 21: Graded Assignment #3 out; Mathematical induction; course of values induction; worked examples; DATE OF FIRST EXAM: FRIDAY, OCTOBER 5.
• September 24: Course of values induction (contd.); structural induction and examples: tree induction, list induction. Reading: pp. 51-56.
• September 26: Assignment #5 in; Assignment #6 out; Graded Assignment #4 + Solutions out; Handout on list induction; Review solutions to Assignment #3; Show how to prove semantic equivalence; INDUCTION INCLUDED IN FIRST EXAM; Syllabus for first exam is Chapter 1, pp. 1-84; skip Section 1.5.3; also read class notes thoroughly.
• September 28: Handout: proving semantic equivalence; More examples of proofs by mathematical induction and structural induction.
• October 1: Handout: graded Assignment #5; Handout: solutions to Assignment #5; review solutions to Assignment #5; discussions on possible questions for Exam 1: function on well-formed propositional formulas (e.g., IMPL_FREE, NNF); proofs of semantic equivalences (MUST BE DONE SEMANTICALLY following September 28 handout); proofs of provable equivalences (MUST BE DONE SYNTACTICALLY, i.e., using proof rules); no proofs using structural induction but proofs using mathematical induction and course of values induction. Please bring your questions re: EXAM 1 to the next class.
• October 3: Assignment #6 in; review solutions to Assignment #6; Intro. to Predicate Logic; variables, predicates, "for all" and "there exists" quantifiers.
• October 5: EXAM 1; No lecture.
• October 8: Predicate logic continued: several examples of formulas in predicate logic; converting English sentences into predicate logic formulas; the equality predicate; function symbols and their use.
• October 10: No lecture: instructor ill. SORRY.
• October 12: Assignment #7 out; Graded Assignment #6 out (with solutions); predicate logic as a formal language; parse trees; free and bound variables; scope of a variable. Reading: chapter 2, pp. 90-109.
• October 15: No lecture.
• October 17: No lecture.
• October 19: Student holiday.
• October 22: Assignment #7 in; substitution; Graded Exam #1 out. Some discussions on Exam #1.
• October 24: Natural deduction proofs in predicate logic: rules for for all introduction and elimination, and existential introduction and elimination; examples. EXAM 2 WILL BE HELD THE WEEK OF NOVEMBER 12.
• October 26: More examples of natural deduction proofs for predicate logic; Reading: chapter 2, pp 112-128.
• October 29: More examples of natural deduction proofs for predicate logic; proofs using structural induction on formulas.
• October 31: Assignment #8 in; Assignment #9 out; Proofs using structural induction (concluded); semantics of predicate logic formulas (introduction).
• November 2: Handout: A proof by structural induction; Semantics of predicate logic formulas -- models. EXAM 2 WILL BE HELD ON FRIDAY, NOVEMBER 16.
• November 5: Graded assignment #8 out; Assignment #9 in; formal definition of models; environments; checking a formula against a model.
• November 7: Assignment #10 out (due MONDAY, November 12); more examples of checking formulas against a model; formal definition of satisfaction relation |=. SYLLABUS FOR EXAM 2: (a) Chapter 2 (Pages 90-140, EXCEPT Pgs. 110-111 and Section 2.4.3), (b) Induction (mathematical induction, course-of-values induction, structural induction).
• November 9: more examples of models and checking formulas; more explanations on why environments are needed.
• November 12: Assignment #10 in. Proving properties that are satisfied in all models. Generation of counter examples to show that a property is not satisfied.
• November 14: Handout: Solutions to Assignment #10. Introduction to program verification (Chapter 4 of the textbook). Semantics of a simple imperative language: the notion of state, semantics of expressions.
• November 16: Exam 2, no lecture.
• November 19: Assignment #10 out. Semantics of simple imperative language: semantics of commands (statements). Preconditions and postconditions -- Hoare triples. Definition of partial correctness. Simple examples. Proof calculus for partial correctness -- assignment, sequencing, if-then-else. READING: pages 216-245.
• November 21: No lecture; Assignment #11 out. Due Wednesday, November 28.
• November 23: No lecture; Thanksgiving break
• November 26: Examples of partial correctness for if-then-else (two different formulations).
• November 28: Handout: Graded EXAM 2 ; While loops and invariants; examples. Assignment #12 out.
• November 30: Handout: Solutions to Exam 2. Review of solutions to Assignment 11. LAST LECTURE
• December 3: No lecture. Office hours will be held 11:30--12:30.
• December 5: No lecture. Office hours will be held 11:30--12:30. Assignment #12 in by 11:00 AM to the front office. Please also pick up solutions to Assignment #12.
• December 7: EXAM 3: Syllabus: Same syllabus as EXAM 2 + Chapter 4 (till page 252).