This page gives highlights of past lectures and provides lecture notes, reading assignments, and exercises.
| Dates | Topics and Readings | Exercises |
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Jan 19 Jan 21 |
Course introduction and administration. Introduction to Logic. Introduction to propositional logic. Syntax and semantics. Parsing and precedence. Interpretations. Required Readings:
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2.3-2.5, 2.9, 2.13, 2.16 of LRCS (Chap. 2) |
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Jan 24 Jan 26 Jan 28 |
More on propositional logic. Formula satisfiability, validity, and equivalence. Formula simplification via rewriting. Evaluation of formulas in an interpretation. From English to propositional logic. Motivation and issues. Translation heuristics. The Principle of Maximal Logical Revelation. Examples. Semantic consequence/entailment. Examples. Inference Systems for Propositional Logic. Derivability. Relationship between derivability and entailment. Soundness and completeness. Required Readings:
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Exercise in slides 3.1, 3.3-3.5, 3.9 of LRCS |
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Jan 31
Feb 2 Feb 4 |
Natural deduction.
Derivation rules.
Examples of derivations.
Required Readings: |
Exercise in slides |
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Feb 7 Feb 9 Feb 11 |
Proofs of completeness of natural deduction.
Propositional satisfiability.
Truth tables method.
Splitting algorithm.
Examples.
Required Readings: |
Exercises in slides |
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Feb 14 Feb 16 Feb 18 |
Semantic Tableaux. Solving procedure and examples. Soundness and completeness. In-class exercises. Tableaux as derivation systems. Tableaux derivation rules. Conjunctive Normal Form and conversion to CNF. Motivation and conversion examples. Conversion to clause form: a space efficient CNF-like transformation. Required Readings: |
6.2-6.4,6.6 of LRCS (Chap. 6) |
| Feb 21 |
Midterm exam I |
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Feb 23 Feb 25 |
Unit propagation. The DPLL procedure, basic version. DPLL improvements: tautology and pure literal elimination, Horn case. In-class exercises. Encoding cardinality constraints in PL. Reducing puzzle solving to SAT solving. Examples: Sudoko, Loop the Loop. Required Readings: |
7.3-7.5, 7.7, 7.8, 7.14, 7.15 of LRCS (Chap. 7) |
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Feb 28 Mar 2 Mar 4 |
Satisfiability and randomization. k-SAT problem vs SAT-problem. Random clause generation. Probability of generating an unsatisfiable clause set. The sharp phase transition of k-SAT problems. Local search algorithms. Random walk algorithms. Introduction to quantified Boolean formulas. Game-theoretic view. Syntax and semantics. Free and bound variables. Required Readings: |
11.8, 11.10 of LRCS (Chap. 11) |
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Mar 7 Mar 9 Mar 11 |
More on QBFs. Rectification. Prenex form. The splitting algorithm for satisfiability checking. CNF for QBEs. DPLL for QBF. DPLL improvements (pure literal rule, universal literal deletion). In-class exercise. Required Readings:
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Mar 14 Mar 16 Mar 18 |
Spring break |
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Mar 21 Mar 23 Mar 25 |
Logic and modeling. State-changing systems. Propositional logic of finite domains (PLFD). PLFD and propositional logic. A tableau system for PLFD. Example tableau proof. State-changing systems. Labelled Transition Systems. Representing states symbolically. Examples. Modeling a vending machine. Required Readings: |
Complete proofs in Examples 2,3 of PLFD notes 13.2, 13.3, 13.7-9, 13.12, 13.14, 14.1, 14.2, 14.4-12 of LRCS |
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Mar 28 Mar 30 |
Introduction to Linear Temporal Logic. Computation trees. Expressing temporal properties of transition systems with LTL formulas. Examples. Required Readings:
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15.3-5, 15.8-9 of LRCS |
| Apr 1 |
Midterm exam II |
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Apr 4 Apr 6 Apr 8 |
More on Linear Temporal Logic. Expressing temporal properties of paths with LTL formulas. Examples. Formula equivalence in LTL. Noteworthy equivalences and non-equivalences. Modeling systems as transition systems and expressing their properties with LTL formulas. Motivation and examples. In-class modeling exercise. Required Readings:
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Apr 11 Apr 13 Apr 15 |
The model checking problem. Safety properties and reachability. Symbolic reachability checking. Forward and backward reachability. Examples. Symbolic invariant checking. Inductive strengthening and k-induction. Examples. Required Readings:
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Apr 18 Apr 20 Apr 22 |
More on k-induction. Examples. Introduction to First-order Logic. Motivation. Syntax and semantics. Quantifiers and qualified quantifiers. Properties of quantifier. From FOL to English. Examples. Required Readings:
Recommended Readings:
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Apr 25
Apr 27 Apr 29 |
From English to Formula. In-class exercises. The natural deduction calculus for FOL. Rules and example proofs. Soundness and completeness. Undecidability of validity in FOL. Examples of system modeling and checking in Alloy Required Readings:
Recommended Readings:
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May 2 May 4 May 6 |
Introduction to Satisfiability Modulo Theories (SMT). Motivation and general idea. Eager and lazy SMT approaches. Modeling SAT and SMT solvers abstractly as transition systems. DPLL and CDCL transition systems. Transition rules and executions. Examples. Soundness, completeness and termination results. From propositional CDCL to CDCL modulo theories. Transition rules and executions. Examples. Soundness, completeness and termination results. Required Readings:
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| May 9 |
Final exam |
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