Self Consistent
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In logic, a consistent theory (mathematical logic)|theory is one that does not contain a contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent if and only if it has a Model theory#First-order logic|model, i.e. there exists an interpretation (logic)|interpretation under which all Well-formed formula|formulas in the theory are true. This is the sense used in traditional Term logic|Aristotelian logic, although in contemporary mathematical logic the term satisfiable is used instead. The syntactic definition states that a theory is consistent if and only if there is no Formula (mathematical logic)|formula P such that both P and its negation are provable from the axioms of the theory under its associated deductive system. If these semantic and syntactic definitions are equivalent for a particular logic, the logic is Completeness#Logical completeness|complete. The completeness of sentential...
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