Philosophy

Front 1

In FOL

Back 1

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

Front 2

Every predicate symbol comes with a single, fixed 'arity' a number that tells you how many names it needs to form an atomic sentence

Back 2

Every predicate is interpreted by a determinate property or relation of the same arity as the predicate

Front 3

Atomic sentences are formed by putting a predicate of arity "n" in front of "n" names

Back 3

Atomic sentences are built from the identity predicate = using infix notation: the arguments are placed on either side of the predicate

Front 4

The order of the names is crucial to forming atomic sentences

Back 4

Complex terms are typically formed by putting a function symbol of arity "n" in front of "n" terms

Front 5

Complex terms are used just like names in forming atomic sentences

Back 5

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

Front 6

~P is true if and only if P is not true

Back 6

P^Q is true if and only if P is true and Q is true

Front 7

P v Q is true P is true or Q is true or both are true.

Back 7

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

Front 8

DeMorgans Laws

Back 8

Double negation ~~P=P
DeMorgan ~(P ^ Q) = (~P V ~Q)
DeMorgan ~(P V Q) = (~P ^ ~Q)

Front 9

S=sentence built of atomic sentences connected by truth functional connectives
Truth depends on truth of atomic parts

Back 9

Tautology=Every row assigns true to S

Front 10

Satisfiable=@ least one non-spurious row assigns True to S

Back 10

Logical true=every non-spurious row assigns true to S

Front 11

Proof by contradiction

Back 11

~S=Assume S and prove contradiction

Front 12

Distribution of ^ over V

Back 12

P ^ (Q V R) = (P^Q) V (P^R)

Front 13

Distribution of V over ^

Back 13

P V (Q ^ R) = (PVQ) ^ (PVR)

Front 14

Disjunctive Normal Form

Back 14

Disjunction of one or more conjunctions

Front 15

Conjunctive Normal Form

Back 15

Cconjunction of one or more disjunctions

Front 16

Any sentence can be in CNF or DNF or both

Back 16

P -> Q false only when P is true but Q is false