Decidable sublanguages of set theory

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In mathematical logic, various sublanguages of set theory are decidable.^[1][2] They are referred to as syllogistics. Together with the operations of set algebra, decidable languages include:

• Sets with monotone, additive, and multiplicative functions, but without quantifiers.^[3]
• Sets with restricted quantifiers.^[4]

References

1. ^ Cantone, D., E. G. Omodeo and A. Policriti, "Set Theory for Computing. From Decision Procedures to Logic Programming with Sets," Monographs in Computer Science, Springer, 2001.
2. ^ "Decision procedures for elementary sublanguages of set theory: XIII. Model graphs, reflection and decidability", by Franco Parlamento and Alberto Policriti Journal of Automated Reasoning, Volume 7, Issue 2 (June 1991), Pages: 271 - 284
3. ^ "A Decision Procedure for a Sublanguage of Set Theory Involving Monotone, Additive, and Multiplicative Functions", by Domenico Cantone and et al.
4. ^ "A tableau-based decision procedure for a fragment of set theory involving a restricted form of quantification", by Domenico Cantone, Calogero G. Zarba, Viale A. Doria, 1997^{[permanent dead link]}