20809261Elementary Logic
Course Information
Description
This course covers contemporary formal logic, including propositional and predicate logic with identity. Students will translate English sentences into symbolic form and evaluate arguments using truth tables, derivations, truth trees, and counterexamples. It fulfills the Quantitative Reasoning B requirement at UW-Madison and the logic requirement at Edgewood College. Assumes a strong background in algebra.
Total Credits
4
Course Competencies
  1. Translate complex English sentences into propositional and predicate logic
    Assessment Strategies
    Oral or Written product, problem set assignments, quiz, and/or exam
    Criteria
    Translate complex English sentences into symbolic notation accurately
    Identify scope and ambiguity in compound statements through linguistic analysis.
    Represent nested quantifiers and logical structure correctly
    Distinguish grammatical form from logical form

  2. Identify well-formed formulas in propositional and predicate logic
    Assessment Strategies
    Oral or Written product, problem set assignments, quiz, and/or exam
    Criteria
    Recognize well-formed formulas by applying formation rules
    Construct well-formed formulas accurately
    Explain what makes a formula syntactically correct
    Evaluate and correct symbolic strings for well-formedness

  3. Construct and interpret complete truth tables
    Assessment Strategies
    Oral or Written product, problem set assignments, quiz, and/or exam
    Criteria
    Build complete truth tables for compound formulas
    Classify formulas as tautologies, contradictions, or contingencies
    Interpret table results to assess consistency
    Complete multi-step truth table problems

  4. Use truth tables to determine validity of propositional arguments
    Assessment Strategies
    Oral or Written product, problem set assignments, quiz, and/or exam
    Criteria
    Apply truth tables to test for argument validity
    Identify valid and invalid forms using truth table techniques
    Discuss the structure of valid arguments
    Determine argument validity from complete truth tables

  5. Apply inference and replacement rules in propositional logic
    Assessment Strategies
    Oral or Written product, problem set assignments, quiz, and/or exam
    Criteria
    Complete derivations using rules of inference and replacement
    Identify correct rule applications
    Evaluate derivations for accuracy
    Construct formal proofs from given premises

  6. Use formal rules in predicate logic, including identity and quantifiers
    Assessment Strategies
    Oral or Written product, problem set assignments, quiz, and/or exam
    Criteria
    Construct derivations involving quantifiers and identity
    Apply rules for quantifier introduction and elimination
    Explain derivation steps involving quantifiers
    Solve formal proofs using predicate logic rules

  7. Construct and analyze truth trees
    Assessment Strategies
    Oral or Written product, problem set assignments, quiz, and/or exam
    Criteria
    Build truth trees to test validity and consistency
    Apply decomposition rules accurately
    Interpret open and closed branches
    Evaluate argument structure using truth trees

  8. Generate counterexamples to demonstrate invalidity
    Assessment Strategies
    Oral or Written product, problem set assignments, quiz, and/or exam
    Criteria
    Identify invalid argument forms through counterexamples
    Construct models that refute argument validity
    Justify counterexamples
    Analyze arguments and provide counterexamples

  9. Manipulate quantifiers and distinguish universal and existential claims
    Assessment Strategies
    Oral or Written product, problem set assignments, quiz, and/or exam
    Criteria
    Rewrite statements to clarify quantifier scope
    Identify differences between universal and existential claims
    Discuss the implications of quantifier order
    Apply quantifier manipulation to proofs and translations

  10. Apply the logic of identity in formal proofs and evaluations
    Assessment Strategies
    Oral or Written product, problem set assignments, quiz, and/or exam
    Criteria
    Use identity introduction and elimination in derivations
    Identify errors in identity reasoning
    Evaluate the role of identity in logical arguments
    Apply identity rules in formal proofs

  11. Recognize and prove logical equivalence using symbolic techniques
    Assessment Strategies
    Oral or Written product, problem set assignments, quiz, and/or exam
    Criteria
    Derive equivalence through formal rules
    Identify equivalent formulas using symbolic criteria
    Compare proof strategies for establishing equivalence
    Demonstrate logical equivalence through formal proofs

  12. Distinguish between formal symbolic validity and informal reasoning
    Assessment Strategies
    Oral or Written product, problem set assignments, quiz, and/or exam
    Criteria
    Identify formally valid arguments that fail informally
    Translate informal arguments and assess symbolic validity
    Classify arguments as formally valid or invalid
    Evaluate the strengths and limits of symbolic logic