Formal Logic and Formal Semantics #2
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This chapter provides a more detailed examination of the formal semantics for quantificational logic (QL) and particularly useful method for testing QL sequents for semantic validity. It then supplements the existing set of development rules with genuinely semantic rules. None the less, the new syntactical rules remain essential to the method even when supplemented so as to become a genuinely semantic method. Hence, we can again rest assured that every provable sequent of the monadic fragment of QL is also a semantically valid sequent of QL and that every semantically valid sequent of that fragment of QL is also a provable sequent of that fragment of QL. In logic and mathematics, an effective method for solving a problem is a method for computing the answer that, if followed correctly and as far as may be necessary, is logically bound to give the right answer (and no wrong answers) in a finite number of steps.