A statement is simple if and only if it does not contain any other statement as a component
Compound statement
A statement is compound if and only if it contains at least one simple statement as a component
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
Main operator
the main operator is the operator that determines the overall structure of a well-formed formula
Subformula
a subformula is any well-formed part of a well-formed formula
tautology statement form
a statement form is a tautology if an only if it is true for every substitution instance
tautology statement
a statement is a tautology if and only if it is a substitution instance of a tautologous form
self-contradiction
logical falsity, necessary falsity
self-contradiction statement form
a statement form is a self-contradiction if and only if it is false for every substitution instance
self contradiction statement
a statement is a self-contradiction if and only if it is a substitution instance of a self-contradictory form
tautology
logical truth, necessary truth
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
contingency statement
a statement is a contingency if and only if it is a substitution instance of a contingent form
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)
logical equivalence statements
two statements are logically equivalent if and only if they are substitution instances of logically equivalent forms
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
inconsistency statements
two statements are inconsistent if and only if they are substitution instances of inconsistent forms
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
consistency statements
two statements are consistent if and only if they are substitution instances of consistent forms
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
logical implication statements
one statement logically implied another statement if and only if they are substitution instances of implicative forms