satisfiability
Quick Summary
In logic, satisfiability refers to whether a statement or formula can be true. The predicate calculus, a branch of formal logic, deals with statements containing variables. A key concept is that if a statement is consistent (meaning its negation is not a theorem), then it is satisfiable, meaning it has a valid interpretation or model.1
The problem of determining satisfiability for all sentences in the predicate calculus is undecidable. This means there is no general algorithm or mechanical procedure that can determine for every sentence whether it is satisfiable or not. This undecidability is closely linked to other unsolvable problems, such as the halting problem for Turing machines.21
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metalogicLogic and metalogic…all possible worlds) and of satisfiability (or having a model—i.e., being true in some particular interpretation). Hence, the completeness of a logical calculus has quite a different meaning from that of a formal system: a logical calculus permits many sentences such that neither the sentence nor its negation is a…
Read More…all possible worlds) and of satisfiability (or having a model—i.e., being true in some particular interpretation). Hence, the completeness of a logical calculus has quite a different meaning from that of a formal system: a logical calculus permits many sentences such that neither the sentence nor its negation is a…
Read More- metalogicThe first-order predicate calculus
…valid; and, therefore, A is satisfiable; i.e., it has an interpretation, or a model. But to say that A is consistent means nothing other than that ∼A is not a theorem. Hence, from the completeness, it follows that if A is consistent, then A is satisfiable. Therefore, the semantic concepts…
Read More…valid; and, therefore, A is satisfiable; i.e., it has an interpretation, or a model. But to say that A is consistent means nothing other than that ∼A is not a theorem. Hence, from the completeness, it follows that if A is consistent, then A is satisfiable. Therefore, the semantic concepts…
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