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A Decision Procedure for a Sublanguage of Set Theory Involving Monotone, Additive, and Multiplicative Functions, I: The Two-Level Case

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Abstract

2LS is a decidable many-sorted set-theoretic language involving one sort for elements and one sort for sets of elements. In this paper we extend 2LS with constructs for expressing monotonicity, additivity, and multiplicativity properties of set-to-set functions. We call the resulting language 2LSmf. We prove that 2LSmf is decidable by reducing the problem of determining the satisfiability of its sentences to the problem of determining the satisfiability of sentences of 2LS. Furthermore, we prove that the language 2LSmf is stably infinite with respect to the sort of elements. Therefore, by using a many-sorted version of the Nelson–Oppen combination method, 2LSmf can be combined with other languages modeling the sort of elements.

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Authors and Affiliations

  1. LORIA and INRIA, Lorraine, 615, rue du Jardin Botanique, BP 101, 54602, Villers-lès-Nancy Cedex, France

    Calogero G. Zarba

  2. Dipartimento di Matematica e Informatica, Università di Catania, Viale Andrea Doria 6, 95125, Catania, Italy

    Domenico Cantone

  3. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY, 10012, USA

    Jacob T. Schwartz

Authors
  1. Calogero G. Zarba
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  2. Domenico Cantone
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  3. Jacob T. Schwartz
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Correspondence to Calogero G. Zarba.

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Zarba, C.G., Cantone, D. & Schwartz, J.T. A Decision Procedure for a Sublanguage of Set Theory Involving Monotone, Additive, and Multiplicative Functions, I: The Two-Level Case. J Autom Reasoning 33, 251–269 (2004). https://doi.org/10.1007/s10817-004-6243-3

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  • DOI: https://doi.org/10.1007/s10817-004-6243-3

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