Abstract
This paper presents a sound and complete logical system whose atomic sentences are the equalities of recursive terms involving sets. There are two interpretations of this language: one makes use of non-wellfounded sets with finite transitive closure, and the other uses pointed finite graphs modulo bisimulation. Our logical system is a sequent-style deduction system. The main axioms and inference rules come from the \(\mbox{{\it FLR}$_0$}\)-proof system from [6], including the Recursion Inference Rule (but an additional axiom is needed), and also axioms corresponding to the extensionality axiom of set theory.
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Moss, L.S., Wennstrom, E., Whitney, G.T. (2012). A Complete Logical System for the Equality of Recursive Terms for Sets. In: Constable, R.L., Silva, A. (eds) Logic and Program Semantics. Lecture Notes in Computer Science, vol 7230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29485-3_12
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DOI: https://doi.org/10.1007/978-3-642-29485-3_12
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