Propositional and Predicate Logic:

• Syntax: atoms, terms, predicate symbols, formulas, binding precedence of the connectives; free and bound variables
• translate natural language to formulas
• Natural deduction: rules, proving, variable conditions, rules for equality
• Semantics: valuations, truth-tables, models for predicate logic, when a formula is true/false in a model
• adequate sets of connectives for propositional logic
• satisfiability, validity, and how they are connected
• Soundness and Completeness: statement and how to use it to prove non-provability.
• Conjunctive normal form: definition and how to compute it from a formula or truth-table

Temporal Logic (LTL and CTL):

• Syntax: formulas, connectives, precedence of the connectives
• Semantics: transition systems, paths, definition when a CTL/LTL formula is satisfied at/on a state/path, equivalence of LTL/CTL formulas
• Given a transition system, in what states is a LTL/CTL formula satisfied?
• monotone functions, fixed points.

Other:

• induction and structural induction