Unit 2 Basic Concepts

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Author:
ceilingmoth
ID:
309139
Filename:
Unit 2 Basic Concepts
Updated:
2015-10-06 18:07:18
Tags:
logic
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logic
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  1. Simple statement
    A statement is simple if and only if it does not contain any other statement as a component
  2. Compound statement
    A statement is compound if and only if it contains at least one simple statement as a component
  3. Well formed formula (WFF)
    and 4 components
    A well-formed formula is a syntactically correct arrangement of symbols

    • a. upper case letters
    • b. operators
    • c. logical punctuation marks
    • d. logical variables
  4. Main operator
    the main operator is the operator that determines the overall structure of a well-formed formula
  5. Subformula
    a subformula is any well-formed part of a well-formed formula
  6. tautology statement form
    a statement form is a tautology if an only if it is true for every substitution instance
  7. tautology statement
    a statement is a tautology if and only if it is a substitution instance of a tautologous form
  8. self-contradiction
    logical falsity, necessary falsity
  9. self-contradiction statement form
    a statement form is a self-contradiction if and only if it is false for every substitution instance
  10. self contradiction statement
    a statement is a self-contradiction if and only if it is a substitution instance of a self-contradictory form
  11. tautology
    logical truth, necessary truth
  12. contingency statement form
    a statement form is a contingency if and only if it is true for at least one substitution instance and false for at least one substitution instance
  13. contingency statement
    a statement is a contingency if and only if it is a substitution instance of a contingent form
  14. logical equivalence statement forms
    two statement forms are logically equivalent if and only if the two final columns of their joint truth table are identical (true/true or false/false)
  15. logical equivalence statements
    two statements are logically equivalent if and only if they are substitution instances of logically equivalent forms
  16. inconsistency statement forms
    two statement forms are inconsistent if and only if there is no line in the final columns of their joint truth table on which both forms have the T truth value
  17. inconsistency statements
    two statements are inconsistent if and only if they are substitution instances of inconsistent forms
  18. consistency statement forms
    two statement forms are consistent if and only if there is at least one line in the final columns of their joint truth table on which both forms have the T truth value
  19. consistency statements
    two statements are consistent if and only if they are substitution instances of consistent forms
  20. logical implication statement forms
    one statement form logically implies another form if and only if there is no line in the final columns of their joint truth table on which the firm form has the T truth value, while the second had the F truth value
  21. logical implication statements
    one statement logically implied another statement if and only if they are substitution instances  of implicative forms

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