State-based Modal Logics for Free Choice
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We study the mathematical properties of bilateral state-based modal logic (BSML), a modal logic employing state-based semantics (also known as team semantics), which has been used to account for free choice inferences and related linguistic phenomena. This logic extends classical modal logic with a non-emptiness atom which is true in a state if and only if the state is empty. We introduce two extensions of BSML and show that the extensions are expressively complete, and we develop natural deduction axiomatizations for the three logics.
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