Combining Combination Properties: Minimal Models

TL;DR

This paper investigates the property of computing minimal model cardinalities in theories related to SMT, exploring its connections to other theory combination properties to enhance understanding of their interplay.

Contribution

It introduces the analysis of the shiny property concerning minimal model cardinalities and explores its relationship with existing theory combination properties.

Findings

Established connections between minimal model cardinality computation and other properties.

Extended the understanding of shiny theories in the context of SMT.

Provided insights into the interplay of various theory combination properties.

Abstract

This is a part of an ongoing research project, with the aim of finding the connections between properties related to theory combination in Satisfiability Modulo Theories. In previous work, 7 properties were analyzed: convexity, stable infiniteness, smoothness, finite witnessability, strong finite witnessability, the finite model property, and stable finiteness. The first two properties are related to Nelson-Oppen combination, the third and fourth to polite combination, the fifth to strong politeness, and the last two to shininess. However, the remaining key property of shiny theories, namely, the ability to compute the cardinalities of minimal models, was not yet analyzed. In this paper we study this property and its connection to the others.