Lecture Notes 5 - SYNTAX AND SEMANTICS THE SYNTAX OF A...

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26 SYNTAX AND SEMANTICS THE SYNTAX OF A LANGUAGE IS ITS GRAMMAR. IN FORMAL LANGUAGES, SYNTACTICAL NOTIONS ARE THOSE COMPLETELY CHARACTERIZED BY THE PHYSICAL SHAPES OF THE SYMBOLS AND THE RULES OF HOW THEY CAN BE ARRANGED. THE SYNTAX OF THE SENTENTIAL LOGIC WE HAVE SET UP AT THIS POINT CONSISTS OF: (1) THE BASIC VOCABULARY: ENGLISH CAPITAL LETTERS, OPERATOR SYMBOLS, AND PARENTHESES. (2) THE WELL-FORMED FORMULA FORMULATION RULES THE SEMANTICS OF A LANGUAGE IS ITS MEANING. IN FORMAL LANGUAGES, SEMANTIC NOTIONS ARE THOSE CHARACTERIZED BY APPEAL TO TRUTH VALUES. FOR EXAMPLE, THE SEMANTICS OF OUR SENTENTIAL LOGIC IS GIVEN BY THE FIVE TRUTH TABLE SCHEMATA ABOUT TO BE INTRODUCED. TRUTH SEMANTIC DEFINITIONS AND TRUTH TABLES TRUTH FUNCTIONAL OPERATORS: AN OPERATOR IS TRUTH-FUNCTIONAL IF AND ONLY IF THE TRUTH VALUE OF THE COMPOUND SENTENCE IT FORMS IS COMPLETELY DETERMINED BY THE TRUTH-VALUES OF THE COMPONENT PARTS.
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27 CLAIM: 1) OUR FIVE AFOREMENTIONED OPERATORS ARE TRUTH FUNCTIONAL
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