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- W4200633105 abstract "As a contribution to quantitative set-theoretic inferencing, a translation is proposed of conjunctions of literals of the forms $x=ysetminus z$, $x neq ysetminus z$, and $z ={x}$, where $x,y,z$ stand for variables ranging over the von Neumann universe of sets, into unquantified Boolean formulae of a rather simple conjunctive normal form. The formulae in the target language involve variables ranging over a Boolean ring of sets, along with a difference operator and relators designating equality, non-disjointness and inclusion. Moreover, the result of each translation is a conjunction of literals of the forms $x=ysetminus z$, $xneq ysetminus z$ and of implications whose antecedents are isolated literals and whose consequents are either inclusions (strict or non-strict) between variables, or equalities between variables. Besides reflecting a simple and natural semantics, which ensures satisfiability-preservation, the proposed translation has quadratic algorithmic time-complexity, and bridges two languages both of which are known to have an NP-complete satisfiability problem." @default.
- W4200633105 created "2021-12-31" @default.
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- W4200633105 date "2021-12-09" @default.
- W4200633105 modified "2023-10-14" @default.
- W4200633105 title "Complexity assessments for decidable fragments of Set Theory. IV: A quadratic reduction of constraints over nested sets to Boolean formulae" @default.
- W4200633105 doi "https://doi.org/10.48550/arxiv.2112.04797" @default.
- W4200633105 hasPublicationYear "2021" @default.
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