Course introduction and administration. Introduction to Logic.

• Syllabus
• Introduction slides [pdf] (revised)
• Chapter 1 of the textbook

• Moshe Vardi. From Aristotle to the iPhone [talk]

Introduction to propositional logic. Syntax and semantics. Parsing and precedence. Interpretations. Formula satisfiability, validity, and equivalence. Formula simplification via rewriting. Evaluation of formulas in an interpretation.

• Propositional Logic slides [pdf] (revised)
• Chapter 2, Sections 1-3, 5 of the textbook

• Textbook appendix on set theory (as needed)

From English to propositional logic. Motivation and issues. Translation heuristics. The Principle of Maximal Logical Revelation. Examples.

• From English to PL slides [pdf]

Propositional satisfiability. Truth tables method. Splitting algorithm. Examples.
Improving the performance of the splitting algorithm. Subformula polarity and pure literals. Conjunctive Normal Form and conversion to CNF. Motivation and conversion examples.

• Propositional satisfiability slides [pdf]
• CNF and DPLL slides [pdf]
• Chapter 2, Sections 1-4 of the textbook

Conversion to clause form: a space efficient CNF transformation. Unit propagation. The DPLL procedure, basic version. DPLL improvements: tautology and pure literal elimination, Horn case.

Required Readings:

• CNF and DPLL slides [pdf] (revised)
• Chapter 6, Sections 1-4 of the textbook

Encoding cardinality constraints in PL. Reducing puzzle solving to SAT solving. Examples: Sudoko, Loop the Loop.

Semantic Tableaux. Solving procedure and examples.

Required Readings:

• Semantic Tableaux slides [pdf]
• Chapter 2, Section 6 of the textbook

More on semantic tableaux. Properties of tableaux.

Introduction to Binary Decision Diagrams. Binary decision trees.

Required Readings:

• Semantic Tableaux slides [pdf] (revised)
• Binary Decision diagrams slides [pdf]
• Chapter 2, Section 7 of the textbook
• Chapter 5, Sections 1-2 of the textbook

From binary decision trees to binary decision diagrams (BDDs). Reduced BDDs. Ordered BDDs. Applying logical operators to OBDDs. Examples and exercises.

Required Readings:

• Binary Decision diagrams slides [pdf] (revised)
• Chapter 5, Sections 1-5 of the textbook

More on combining OBDDs. Examples.

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.

Required Readings:

• Satisfiability and Randomization slides [pdf]
• Chapter on Satisfiability and Randomization in KT&V. [pdf] (UI access only)

Semantic consequence/entailment. Examples. Inference Systems for Propositional Logic. Derivability. Relationship between derivability and entailment. Soundness and completeness.

Required Readings:

• Inference systems slides [pdf]

Midterm exam I

Natural deduction. Inferences rules. Examples of derivations.

Required Readings:

• Inference systems slides [pdf]
• Chapter 1 of Huth and Ryan (UI access only)

More natural deduction rules. Derived rules. Examples of derivations.
In-class exercises on natural deduction proofs.
Proofs of soundness and completeness of natural deduction.

Required Readings:

• Inference systems slides [pdf] (revised Mar 14) &
• Exercises [pdf]

More on the proof of completeness for natural deduction.

Introduction to quantified Boolean formulas. Game-theoretic view. Syntax and semantics. Free and bound variables. Prenex form. The splitting algorithm for satisfiability checking.

Required Readings:

• Inference systems slides [pdf] (revised Mar 15)
• Chapter 1 of Huth & Ryan (UI access only)
• QBF slides [pdf] (revised Mar 17)
• Chapter on Quantified Boolean Formulas in KT&V (UI access only)

More on QBFs. The splitting algorithm CNF for QBEs. DPLL for QBF. DPLL improvements (pure literal rule, universal literal deletion).

QBEs and BDDs. Quantification for OBDDs.

Required Readings:

• QBF slides [pdf] (revised Mar 22)
• Chapter on Quantified Boolean Formulas in KT&V (UI access only) (revised Mar 21)

Logic and modeling. State-changing systems. Propositional logic of finite domains (PLFD). PLFD and propositional logic. A tableau system for PLFD. Example tableau proof.

Encoding PLFD problems in SMT-LIB and solving them with the CVC4 solver.

Required Readings:

• PLFD slides [pdf]
• Chapter on PLFD in KT&V (UI access only) (revised Mar 30)

State-changing systems. Labelled Transition Systems. Representing states symbolically. Examples.

Required Readings:

• Transition systems slides [pdf]
• Chapter on transition systems in KT&V (UI access only) (rev. April 3)

No class

Midterm exam II

More on State-changing systems. Symbolic representation of transitions. Examples.

Required Readings:

• Transition systems slides [pdf] (revised Apr 10)
• Chapter on transition systems in KT&V (UI access only) (rev. April 3)

Introduction to Linear Temporal Logic. Computation trees. Expressing temporal properties of transition systems with LTL formulas.

Required Readings:

• LTL slides [pdf] (revised Apr 16)
• Chapter on Linear Temporal Logic in KT&V (UI access only) (rev. April 14)

No class. Instructional break

More on Linear Temporal Logic. Expressing temporal properties of paths with LTL formulas. Examples.

Required Readings:

• LTL slides [pdf] (revised Apr 16)
• Chapter on Linear Temporal Logic in KT&V (UI access only) (rev. April 14)

Formula equivalence in LTL. Noteworthy equivalences. Modeling systems as transition systems and expressing their properties with LTL formulas. Motivation and examples.

Required Readings:

• LTL slides [pdf] (revised Apr 23)
• Chapter on Linear Temporal Logic in KT&V (UI access only) (rev. April 23)

Model Checking Problem. Safety Properties and Reachability. Symbolic Reachability Checking. Forward and backward reachability. Examples.

Introduction to First-order Logic. Motivation. Syntax and semantics.

Required Readings:

• Model Checking slides [pdf] (revised Apr 28)
• First-order Logic slides [pdf]
• Sections 2.1,2.2,2.4 of Huth & Ryan on Predicate Logic (UI access only)

More on First-order Logic. Quantifiers and qualified quantifiers. Properties of quantifier. From English to FOL and from FOL to English. Examples.

The natural deduction calculus for FOL. Rules and example proofs. Soundness and completeness. Undecidability of validity in FOL.

Required Readings:

• First-order Logic slides [pdf] (revised May 7)
• Sections 2.1-2.5 of Huth & Ryan (UI access only)

Recommended Readings:

• Section 2.6 of Huth & Ryan (UI access only)

Final exam