On the Succinctness of Atoms of Dependency
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Propositional team logic is the propositional analog to first-order team logic. Non-classical atoms of dependence, independence, inclusion, exclusion and anonymity can be expressed in it, but for all atoms except dependence only exponential translation are known. In this paper, we systematically classify their succinctness in the positive fragment, where negation is only allowed at the level of literals, and in full propositional team logic with unrestricted negation. By introducing a variant of the Ehrenfeucht--Fraïssé game called formula size game into team logic, we obtain exponential lower bounds in the positive fragment for all atoms. In the full fragment, we present polynomial upper bounds again for all atoms.
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