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16 Cards in this Set
 Front
 Back
In FOL

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 stepbystep 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 nonspurious row assigns True to S

Logical true=every nonspurious 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
