Logic Chapter 7
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
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 statement (called disjuncts) connected by the wedge symbol
Conjunction
A compound statement that has two distinct statements (called conjuncts) connected by the dot symbol
Compound Statement
A statement that has at least on simple statement and at least one logical operator as components
Self- Contradiction
A statement that is necessarily false
Tautology
A statement that is necessarily true
Statement Variable
A statement variable can stand for any statement, simple or compound
Substitution Instance
A substitution instance of a statement occurs when a uniform substitution of statements for the variable results in a statement. A substitution instance of an argument occurs when a uniform substitution of statements for the variable results in an argument
Modus Ponens
A valid argument form (affirming the antecedent)
Modus Tollens
A valid argument form (denying the consequent)
Valid
An argument in which assuming the premises are true, it is impossible for the conclusion to be false. In other words, the conclusion follows necessarily from the premises
Well-Formed Formula
An arrangement of operator symbols such that the resulting symbolic expressions are grammatically correct
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 (formal fallacy)
Fallacy of denying the antecedent
An invalid argument form; it is a formal fallacy
Conditional Statements
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
Statement Form
In propositional logic, an arrangement of logical operators and statement variables such that a uniform substitution of statements for the variable results in a statement
Simple Statement
One that does not have any other statement or logical operator as a component
Argument Form
Refers to the structure of an argument, not to its content. In propositional logic, an argument form is an arrangement of logical operators and statement variables
Logical Operators
Special symbols that can be used as part of ordinary language statement translations
Non contingent Statements
Statements such that the truth values in the main operator column do not depend on the truth values of the component parts
Contingent Statements
Statements that are neither necessarily true nor necessarily false ( they are sometimes true, sometimes false)
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
Negation
The word "not" and the phrase "its not the case that" are used to deny the statement that follows them, and we refer to their use as negation
Inconsistent Statements
Two (or more) statements that do not have even on line on their respective truth tables where the main operators are true (but they can be false) at the same time
Consistent Statements
Two (or more) statements that have at least one line on their respective truth tables where the main operators are true
Contradictory Statement
Two statements that have opposite truth values under the main operator on every line of their respective truth tables
Logically Equivalent
Two truth functional statements that have identical truth tables under the main operator. When this occurs, they are logically equivalent
Sufficient Condition
Whenever one event ensures that another event is realized In other words, the truth of the antecedent guarantees the truth of the consequent
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
