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16 Cards in this Set

  • Front
  • Back
Every name must name an object
No name can name more than one object
An object can have more than one name or no name at all
Every predicate symbol comes with a single, fixed 'arity' a number that tells you how many names it needs to form an atomic sentence
Every predicate is interpreted by a determinate property or relation of the same arity as the predicate
Atomic sentences are formed by putting a predicate of arity "n" in front of "n" names
Atomic sentences are built from the identity predicate = using infix notation: the arguments are placed on either side of the predicate
The order of the names is crucial to forming atomic sentences
Complex terms are typically formed by putting a function symbol of arity "n" in front of "n" terms
Complex terms are used just like names in forming atomic sentences
A proof of a statement S from premises P, Q is a step-by-step demonstration which shows that S must be true in any circumstances in which the premises P, Q are all true
~P is true if and only if P is not true
P^Q is true if and only if P is true and Q is true
P v Q is true P is true or Q is true or both are true.
parenthesis must be used whenever ambiguity would result from their omission. Conjunctions and disjunctions must be wrapped in parenthesis when combined by some other connective
DeMorgans Laws
Double negation ~~P=P
DeMorgan ~(P ^ Q) = (~P V ~Q)
DeMorgan ~(P V Q) = (~P ^ ~Q)
S=sentence built of atomic sentences connected by truth functional connectives
Truth depends on truth of atomic parts
Tautology=Every row assigns true to S
Satisfiable=@ least one non-spurious row assigns True to S
Logical true=every non-spurious row assigns true to S
Proof by contradiction
~S=Assume S and prove contradiction
Distribution of ^ over V
P ^ (Q V R) = (P^Q) V (P^R)
Distribution of V over ^
P V (Q ^ R) = (PVQ) ^ (PVR)
Disjunctive Normal Form
Disjunction of one or more conjunctions
Conjunctive Normal Form
Cconjunction of one or more disjunctions
Any sentence can be in CNF or DNF or both
P -> Q false only when P is true but Q is false