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On the Succinctness of Atoms of Dependency

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Yksityiskohdat

AlkuperäiskieliEnglanti
Sivut17:1-17:28
Sivumäärä28
JulkaisuLogical Methods in Computer Science
Vuosikerta15
Numero3
TilaJulkaistu - 20 elokuuta 2019
OKM-julkaisutyyppiA1 Alkuperäisartikkeli

Tiivistelmä

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 translations are known. In this paper, we systematically compare their succinctness in the existential fragment, where the splitting disjunction only occurs positively, and in full propositional team logic with unrestricted negation. By introducing a variant of the Ehrenfeucht-Fra\"{i}ssé game called formula size game into team logic, we obtain exponential lower bounds in the existential fragment for all atoms. In the full fragment, we present polynomial upper bounds also for all atoms.

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