{"id":28056,"date":"2021-03-08T13:00:12","date_gmt":"2021-03-08T13:00:12","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28056"},"modified":"2024-08-18T09:35:56","modified_gmt":"2024-08-18T09:35:56","slug":"semantic-consequence-and-equivalence","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/en\/semantic-consequence-and-equivalence\/","title":{"rendered":"Semantic Consequence and Equivalence"},"content":{"rendered":"
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Semantic Consequence and Equivalence<\/h1>\n

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SUMMARY<\/strong>
In this class, we will study Semantic Consequence and Equivalence in propositional logic, which is a natural continuation of what we have previously covered. We will learn how to derive the notion of semantic consequence from truth value assignments and how this idea relates to the deduction theorem. Additionally, we will see practical examples of using truth tables to obtain useful properties such as Conjunction Elimination and Disjunction Introduction. We will also explore the notion of Semantic Equivalence and see how it relates to properties we already know. Finally, we will show how using models and deduction techniques can simplify the study of problems of consequence and semantic equivalence.<\/em><\/p>\n

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LEARNING OBJECTIVES:<\/strong>
\nBy the end of this class, the student will be able to:\n<\/p>\n

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  1. Understand<\/strong> the notion of semantic consequence.<\/li>\n
  2. Understand<\/strong> the different interpretations of the symbol \u22a8.<\/li>\n
  3. Understand<\/strong> the proof of the deduction theorem in its semantic version and its use in the study of consequence and semantic equivalence.<\/li>\n
  4. Understand<\/strong> the definition of semantic equivalence and its relation to truth values.<\/li>\n
  5. Apply<\/strong> the deduction theorem in its semantic version to transform consequence problems into validity problems.<\/li>\n
  6. Apply<\/strong> useful properties in the use of truth tables to demonstrate semantic equivalences.<\/li>\n
  7. Apply<\/strong> the laws of absorption, distribution, and DeMorgan in the simplification of complex expressions.<\/li>\n
  8. Analyze<\/strong> the relationship between models and deductions in the study of propositional logic.<\/li>\n<\/ol>\n

    INDEX<\/strong>
    \nASSIGNMENTS AND MODELS<\/a>
    \n    THE DEDUCTION THEOREM (SEMANTIC VERSION)<\/a>
    \n    USING THE DEDUCTION THEOREM IN THE STUDY OF CONSEQUENCE AND SEMANTIC EQUIVALENCE<\/a>
    \n    SEMANTIC EQUIVALENCE AND PROPERTIES<\/a>
    \n    SYNTHESIS<\/a><\/p>\n