Topic 2: Logic Flashcards
Mathematical Logic
The use of formal languages and grammars to represent the syntax and semantics of computation.
Philosophical Logic
The study of thought and reasoning, including arguments and proof techniques. (Classical Logic)
Well-formed Formula (WFF)
A correctly-structured expression of a language.
Proposition (aka statement)
A claim that is either true or false with respect to an associated context.
Simple Proposition
A proposition containing no logical operators.
Compound Proposition
A statement that is a logical combination of multiple simple propositions.
Logically Equivalent
Two propositions are (logically) equivalent when both evaluate to the same result when presented with the same input.
Tautology
A proposition that always evaluates to true.
Contradiction
A proposition that always evaluates to false.
Contingency
A proposition that is neither a tautology nor a contradiction.
Conditional Proposition
A proposition expressible in the form: p->q.
p and q are propositions.
Inverse
The inverse of p->q is p’->q’.
Converse
The converse of p->q is q->p.
Contrapositive
The contrapositive of p->q is q’->p’.
Biconditional Proposition (aka biimplication)
The expression of pq and is represented by the symbol .
