First Order Languages: Further Syntax and Semantics1
نویسنده
چکیده
Third of a series of articles laying down the bases for classical first order model theory. Interpretation of a language in a universe set. Evaluation of a term in a universe. Truth evaluation of an atomic formula. Reassigning the value of a symbol in a given interpretation. Syntax and semantics of a non atomic formula are then defined concurrently (this point is explained in [16], 4.2.1). As a consequence, the evaluation of any w.f.f. string and the relation of logical implication are introduced. Depth of a formula. Definition of satisfaction and entailment (aka entailment or logical implication) relations, see [18] III.3.2 and III.4.1 respectively.
منابع مشابه
Notes on Logic
1. Syntax 1 2. Semantics 4 3. Boolean algebra 7 4. Classification 12 5. Quantum logic 15 6. Formal proofs 17 7. First-order languages and syntax 22 8. First-order semantics 25 9. Examples of first-order languages 28 10. Completeness and compactness 29 11. Consequences of compactness 31 12. Downwards Löwenheim-Skolem 34 13. Filters and ultrafilters 37 14. Voting 41 15. Ultraproducts 45 16. Forma...
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