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- W4387398410 abstract "We give a positive solution to the decidability problem for the fragment of set theory, dubbed BST ⊗, consisting of quantifier-free formulae involving the Boolean set operators of union, intersection, and set difference, along with the unordered Cartesian product operator ⊗ (where (s otimes := t big lbrace lbrace u,vrbrace ,texttt {|}: u in s wedge v in t big rbrace ) ), and the equality predicate, but no membership. Specifically, we provide nondeterministic exponential decision procedures for both the ordinary and the finite satisfiability problems for BST ⊗. We expect that these decision procedures can be adapted for the standard Cartesian product and, with added technicalities, to the cases involving membership, providing a solution to a longstanding problem in computable set theory." @default.
- W4387398410 created "2023-10-07" @default.
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- W4387398410 date "2023-10-06" @default.
- W4387398410 modified "2023-10-07" @default.
- W4387398410 title "Decidability of the satisfiability problem for Boolean set theory with the unordered Cartesian product operator" @default.
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- W4387398410 doi "https://doi.org/10.1145/3626823" @default.
- W4387398410 hasPublicationYear "2023" @default.
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