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A statement is simple iff it does not contain any other statement as a component. |
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A statement is compund iff it contains at least one simple statement as a component. |
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Well-Formed Formula (WFF) |
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A well-formed formula is a syntactically correct arrangement of symbols, i.e.,
a. Upper case letters
b. Operators
c. Logical punctuation marks (parentheses, brackets, braces, etc.)
d. Logical variables (p,q,r,s,etc.) |
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The main operator is the operator that determines the overall structure of a WFF. |
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a subformula is any well-formed part of a WFF |
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Tautology (Logical Truth, Necessary Truth) |
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a. Statement Form: A statement form is a tautology iff it is true for every substitution instance (i.e., the final colum of its truth table has only T truth values).
b. Statement: A statement is a tautology iff it is a substitution instance of a tautologous form. |
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Self-Contradiction (Logical Falsity, Necessary Falsity) |
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Statement Form: A statement form is a self-contradiction iff it is false for every substitution instance (i.e., the final colum of its truth table has only F truth values).
b. Statement: A statement is a self-contradiction iff it is a substitution instance of a self-contradictory form. |
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a. Statement Form: A statment form is a contingency iff it is true for at lesat one substitution instance and false for at least one substitution instance (i.e., the final column of its truth table has at least one T truth value and at least one F truth value).
b. Statement: A statement is a contingency iff it is a substitution instance of a contingent form |
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a. Statement Forms: Two statement forms are logically equivalent iff the two final columns of their joint truth table are identical
b. Statements: Two statements are logically equivalent iff they are substitution instances of logically equivalent forms. |
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a. Statement Forms: Two statement forms are inconsistent iff there is no line in the final columns of their joint truth table on which both forms have the T truth value.
b. Statements: Two statements are inconsistent iff they are substitution instances of inconsistent forms. |
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a. Statement Forms: Two statement forms are consistent iff there is at least one line in the final columns of their joint truth table on which both forms have the T truth value.
b. Statements: Two statements are consistent iff they are substitution instances of consistent forms. |
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a. Statement Forms: One statement form logically implies another form iff there is no line in the final columns of their joint truth table on which the first has the T truth value, while the second has the F truth value.
b. Statements: One statement logically implies another statement iff they are substitution instances of implicative forms. |
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It is not ture that _____ |
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It is not the case that _____ |
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Not only ___ but also ___ |
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___ On the other hand ___ |
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Conditional: ____ ) ____
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Conditional: ____ ) ____
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Conditional: ____ ) ____
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Conditional: ____ ) ____
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____Is A Sufficient Condition For____ |
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Conditional: ____ ) ____
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Conditional: ____ ) ____
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Conditional: ____ ) ____
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Conditional: ____ ) ____
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Conditional: ____ ) ____
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____On The Condition That____ |
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Conditional: ____ ) ____
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____Is A Necessary Condition That____ |
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Conditional: ____ ) ____
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Conditional: ____ ) ____
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Conditional: ____ ) ____
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Biconditional: _____ = ____ |
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____ Is Equivalent To ____ |
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Biconditional: _____ = ____ |
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____ Is A sufficient and Necessary Condition For ____ |
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Biconditional: _____ = ____ |
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____ Just In Case That ____ |
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Biconditional: _____ = ____ |
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____ Just in the event That ____ |
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Biconditional: _____ = ____ |
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____ Just insofar As ____ |
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Biconditional: _____ = ____ |
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