propositional and predicate logic

Question 1

logic

Answer 1

the study of reasoning; rational ways of drawing conclusions

Question 2

proposition

Answer 2

claim about how things are; either true or false but not both
represented by letters

Question 3

atomic propositions

Answer 3

where the truth or falsity of this proposition doesn’t depend on the truth or falsity of another proposition

Question 4

compound propositons

Answer 4

a proposition created by combining atomic propositions through fundamental connectives

Question 5

what are the 6 fundamental connectives

Answer 5

and
or
xor
not
conditional/implication
biconditional

Question 6

∧

Answer 6

and; forms a third proposition from two other propositions called a conjunction
conjunction is true when both initial propositions are true

Question 7

∨

Answer 7

or; forms a third proposition from two other propositions called a disjunction
disjunction is true when at least one of the other propositions are true

Question 8

⊕

Answer 8

xor; forms a third proposition called an exclusive disjunction which is true when only one of the propositions are true

Question 9

¬ ~

Answer 9

not; forms a second proposition called a negation which is the opposite of the propostion

Question 10

→
what are the 2 parts
what makes them true

Answer 10

conditional; if.. then
has an antecedent (if) and a consequent (then)
if a is true then c is true
if both are false then the implication is true
if only the consequent is false then the implication is true

Question 11

↔

Answer 11

biconditonal; if and only if
combines two propositions into a biconditional which is true if both propositions have the same truth value

Question 12

what are the 4 types of logical properties

Answer 12

tautologies
contradictions
contingencies
equivalents

Question 13

tautologies

Answer 13

propositions that are always true regardless of their atomic propostions

Question 14

contradictions

Answer 14

propositions that are always false

Question 15

contingencies

Answer 15

propositions that are neither tautologies or contradictions

Question 16

equivalents

Answer 16

two propositions are logically equivalent if they have the exact same truth values under all circumstances

Question 17

inference rules

Answer 17

templates/shortcuts for building valid arguments

Question 18

replacement rules

Answer 18

rules for replacing parts of propositions with logically equivalent expressions

Question 19

what is predicate logic

Answer 19

an extension of propositional logic that deals with parts of propostions

Question 20

what are the three main limitations of propositional logic

Answer 20

doesn’t describe or link between parts of propositions
doesn’t have quantifiers

Question 21

terms

Answer 21

objects that are expressed through nouns and pronouns

Question 22

predicates

Answer 22

relations amongst terms expressed through verbs

Question 23

operators

Answer 23

connectives and quantifiers

Question 24

atomic formulae

Answer 24

functions that take in one or more arguments and returns a boolean value
made of a predicate and one or more terms

Question 25

closed/ground formulae

Answer 25

predicate arguments have only constants and no variables
propositions that have truth tables

Question 26

open/unground formulae

Answer 26

arguments have at least one variable and can have constants
these are not propositions and therefore have no truth values

Question 27

compound formulae

Answer 27

formulae created by applying logical connectives to atomic formulae

Question 28

atomic formulae arity

Answer 28

the number of variables taken as an argument
unary; 1 variable, arity 0
binary; 2 variables, arity 1
n-ary; n variables, arity more than 1

Question 29

quantifiers

Answer 29

operators showing the quantity of values from the universe of discourse for which an open formulae is true
combines with terms and variables in open formulae to create quantified formulae

Question 30

∀

Answer 30

universal quantifier; every/for all

Question 31

~∀

Answer 31

not all
there is at least one

Question 32

∃

Answer 32

existential quantifier; at least one/ there exists

Question 33

~∃

Answer 33

it is not the case that

Question 34

restricted quantifiers

Answer 34

some elements in the universe of discourse

Question 35

unrestricted quantifiers

Answer 35

all elements in the universe of discourse

Question 36

interpretation

Answer 36

used to identify the truth value of each formulae
includes: identifying the universe of discourse; assigning each value from the universe of discourse to the variable

Question 37

satisfiable formulae

Answer 37

there is at least one value from the universe of discourse that makes the formulae true