Logic & Proofs

Learning objectives by module

Part 1: Introduction

• Chapter 1: Statements and Arguments
  • Determine whether or not a sentence of English expresses a statement, and if so,
    to identify the statement expressed.
  • Explain what a statement is, and discuss how statements are related to
    sentences.
  • Explain what an argument is, and determine whether or not a givenpassage
    constitutes an argument.
  • Identify the premises and conclusion of an argument, andrepresent the argument
    in standard form.
  • List the criteria an argument must meet in order to be considereda good
    argument, and explain why each criterion is necessary.

Part 2: Introduction

• Chapter 2: Statements, Premises, and Conclusions
  • Create diagrams that graphically depict the premises-and-conclusion structure of
    arguments.
  • Determine whether or not a sentence of English expresses a statement, and if so,
    to identify the statement expressed.
  • Determine whether premises support the conclusion jointly or independently.
  • Explain what a statement is, and discuss how statements are related to
    sentences.
  • Explain what an argument is, and determine whether or not a givenpassage
    constitutes an argument.
  • Identify the premises and conclusion of an argument.
• Chapter 3: Arguments, Validity, and Structure
  • Analyze logically structured support that can link premises and conclusion of an
    argument.
  • Create diagrams that graphically depict the structure of arguments.
  • Determine whether a given argument is a bad or a good argument, and why this is
    the case.
  • Explain what a structured statement is and give examples of statement structures
    that are logically important.

Part 3: Sentential Logic

• Chapter 4: Syntax and Symbolization
  • Construct and identify formulae of sentential logic.
  • Construct and use parse trees.
  • Discern the logical structure of English sentences.
  • Explain the grammar of the logical language of sentential logic.
  • Symbolize English sentences as formulae of sentential logic.
• Chapter 5: Semantics
  • Construct a truth-table for a given formula or argument.
  • Determine the truth-value of a formula relative to a given truth-value
    assignment.
  • Explain what a truth-value assignment is.
  • Explain what tautological, contingent, and contradictory formulae are.
  • Find a counterexample to an invalid argument, using a truth-table or truth-tree.
  • Give the truth-conditions for the logical connectives.
  • Use truth-tables to analyze arguments and formulae.
• Chapter 6: Derivations
  • Apply and identify applications of rules of inference within a derivation.
  • Establish the validity of rules of inference.
  • Explain the structure of derivations.
• Chapter 7: Indirect Rules
  • Apply and identify applications of the inference rules for negation.
  • Explain the structure of indirect rules of inference.
  • Find contradictions to use in applications of indirect rules.
• Chapter 8: Strategies and Derived Rules
  • Apply and identify applications of derived rules.
  • Approach proof construction problems in a strategic fashion.
  • Provide explanations of and explain some significant properties of the logical
    connectives.
• Chapter 9: Elementary Metamathematics
  • Explain how a biconditional can be considered logically equivalent to a formula
    in disjunctive normal form.
  • Explain the connection between truth-tables and Boolean circuits.
  • Find a disjunctive normal form equivalent to any formula.
  • Show that two formulae are logically equivalent just in case their biconditional
    is a tautology.

Part 4: Predicate Logic

• Chapter 10: Syntax and Semantics I
  • Analyze the internal logical structure of English sentences.
  • Construct atomic formulae from predicates and singular terms according to
    syntactic rules.
  • Identify and distinguish between predicates and singular terms.
  • Semantically interpret and evaluate formulae constructed using predicates and
    singular terms.
• Chapter 11: Syntax and Semantics II
  • Analyze the internal logical structure of English sentences involving quantity
    terms.
  • Construct arbitrary predicate formulae according to the syntactic rules.
  • Semantically interpret and evaluate predicate formulae.
• Chapter 12: Derivations
  • Apply and identify applications of the inference rules for the quantifiers.
• Chapter 13: Strategies and Derived Rules
  • Convert an arbitrary formula into an equivalent formula in prenex normal form.
  • Develop, apply, and identify applications of derived rules.
  • Extend the strategic considerations for the construction of proofs to predicate
    logic.
• Chapter 14: Identity and Functions
  • Apply and identify applications of the inference rules for identity.
  • Give the Russellian analysis of sentences involving definite descriptions.
  • Translate English sentences involving identity into the extended language of
    predicate logic.
  • Use function symbols in translating both English sentences and mathematical
    statements.