Elementary Logic Chapter 7 Propositional Logic

Biconditional

A compound statement consisting of two conditionals--one indicated by the word "if" and the other indicated by the phrase "only if." The triple bar symbol is used to translate a biconditional statement

inconsistent statements

Two (or more) statements that do not have even one line on their respective truth tables where the main operators are true (but they can be false) at the same time

substitution instance

occurs when a uniform substitution of statements for the variables results in a statement, or when a uniform substitution of statements for the variable results in the argument

simple statement

one that does not have any other statement or logical operator as a component

logical operators

special symbols that can be used as part of ordinary language statement translations

contingent statements

statements that are sometimes true or sometimes false

logically equivalent

statements that have the same truth values

consistent statements

Two (or more) statements that have at least one line on their respective truth tables where the main operators are true

necessary condition

Whenever one thing is essential, mandatory, or required in order for another thing to be realized. in other words, the falsity of the consequent ensures the falsity of the antecedent

Inclusive disjunction

a compound statement in which both disjuncts can be true at the same time

exclusive disjunction

a compound statement in which both disjuncts cannot be true at the same time

disjunction

a compound statement that has two distinct statements (called disjuncts) connected by the wedge symbol (V)

conjunction

a compound statement that has two distinct statements called conjuncts connected by the dot symbol (.)

Compound statement

a statement that has at least one simple statement and at least one logical operator components

tautology

a statement that is necessarily true

modus pones

a valid argument form, affirming the antecedent

Modus tollens

a valid argument form, denying the consequent

well formed formula (wwf)

an arrangement of operator symbols such that the resulting symbolic expressions are grammatically correct

Statement form

an arrangement of statement variables and operators such that the uniform substitution of statements in place of the variables results in a statement

truth table

an arrangement of truth values for a truth functional compound proposition that displays for every possible case how the truth value of the proposition is determined by the truth values of its simple components

Fallacy of Affirming the Consequent

an invalid argument form, it is a formal fallacy

fallacy of denying the antecedent

an invalid argument form, it is a formal fallacy

Statement variable

can stand for any statement, simple or compound

conditional statement

in ordinary language, the word "if" typically precedes the antecedent of a conditional and the statement that follows the word "then" is referred to as the consequent

Argument form

refers to the structure of an argument, not to its content.In propositional logic, argument form is an arrangement of logical operators and statement variables.

Propositional Logic

the basic components in propositional logic are statements

main operator

the operator that has the entire well-formed formula in its scope

order of operations

the order of handling the logical operators within a proposition, it is a step by step method of generating a complete truth table

scope

the statement or statements that a logical operator connects

Truth-functional proposition

the truth value of a compound proposition that uses one of the five logical operators can be determined solely on the basis of the truth value of its components

non-contingent statements

the truth values in the main operator column do not depend on the truth values of the components parts

negation

the word "not" and the phrase "it is not the case that" are used to deny the statement that follows them, and we refer to their use as negation (~)

contradictory statements

two statements that have opposite truth values on every line of their respective truth tables

sufficient condition

whenever one event ensures that the other event is realized. in other words, the truth of the antecedent guarantees the truth of the consequent