Lecture Notes 8 - PRELIMINARIES FOR THE TRUTH TABLE TEST...

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40 PRELIMINARIES FOR THE TRUTH TABLE TEST FOR VALIDITY... FORM AND INSTANCE: A CONSTANT IS A AN EXPRESSION WITH A DEFINITE VALUE A VARIABLE IS AN EXPRESSION WITH A RANGE OF VALUES EXAMPLE: ALGEBRA… CONSTANTS MAY BE SUBSTITUTED FOR VARIABLES TO GET PARTICULAR SUBSTITUTION INSTANCES OF THE GENERAL CLAIM EX: GENERAL: x + y = y + x ; 2 + 99 = 99 + 2 IN LOGIC, WE WILL USE A SIMILAR DISTINCTION: A STATEMENT CONSTANT IS A CAPITAL LETTER THAT WE USE TO SYMBOLIZE A PARTICULAR SENTENCE IN THE LANGUAGE OF SL A STATEMENT VARIABLE IS A LOWER-CASE LETTER (MID-ALPHABET) THAT CAN TAKE AS SUBSTITUTION INSTANCES ANY STATEMENT, SIMPLE OR COMPLEX, OF SL A STATEMENT IS ANY WELL FORMED FORMULA OF SL A STATEMENT FORM IS A WELL FORMED FORMULA OF SL WITH ONE EXCEPTION- IT USES STATEMENT VARIABLES AS ELEMENTARY COMPONENTS. A SUBSTITUTION INSTANCE OF A FORM IS A STATEMENT THAT RESULTS FROM UNIFORMLY SUBSTITUTING SOME STATMENT (SIMPLE OR COMPLEX) FOR EACH VARIABLE IN THE FORM.
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