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Consider an arbitrary system of logic that handles deontic notions such as "it is obligatory that..." or "it is permissible that...". My question is how -- in these systems -- are we supposed to interpret standalone formulas that don't have any deontic components to them? For example, consider the formula (p & q). If we see (p & q) as a premise in an inference, are we supposed to interpret that as "p is true or q is true" like we normally would in propositional logic, or do all formulas assume some deontic component in their interpretations? I'm assuming the former but just wanted to make absolutely sure.

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Your assumption is indeed correct.

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