Conflating syntactic closure properties with semantic decidability equivocates between computational and logical notions of symmetry, a distinction central to complexity-theoretic separations.

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Closure properties(analogous concept in complexity theory): In mathematics and logic, the quality of a system being 'closed' when operations performed on its elements always produce results that also belong to the system.
Complexity-theoretic separations(in theoretical computer science): Proof that two types of computational problems are fundamentally different in how hard they are to solve—like showing that some problems require much more time or resources than others.
Conflating: Conflating means mixing together or treating two different things as if they were the same thing, when they're actually distinct. It's a logical error where someone blurs important differences between concepts, ideas, or situations to make an argument seem stronger than it is. For example, conflating "being critical of a policy" with "being disloyal to your country" wrongly equates two separate things.
Decidability/Decidable(in logic and computation): Whether a question or problem can be solved with a definite yes or no answer through a step-by-step procedure, like a computer algorithm.

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