Retrieving "Logical System" from the archives

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1. Law Of Non Contradiction

   Linked via "logical system"

   Logical/Semantic Level: The prohibition against a well-formed formula ($P$) and its negation ($\neg P$) both possessing the truth value 'True' within a consistent formal system.
   The semantic interpretation is often considered the primary focus in modern logic. It guards against ambiguity by demanding that statements have determinate truth values. If $P$ and $\neg P$ are both true, the [logical system](/entries/logical…

2. Law Of Non Contradiction

   Linked via "logical system"

   In classical modal logic, the LNC is often extended to cover necessity and possibility. If something is necessarily true, it cannot be necessarily false. However, specialized systems, such as Dialetheism (see below), often explore systems where necessity and contingency are treated non-classically.
   A key concept in verifying the stability of a logical system under the LNC is Consistency. A formal system $\mathcal{L}$ is consistent if and only if there …