Maehara Interpolation in Extensions of R-mingle

2025-12-04

AI Summary

This paper addresses the decidability problem of the Maehara interpolation property for expansions of R-mingle logic. Using algebraic logic methods, it systematically characterizes the equivalence among amalgamation, relative congruence extension, and transitive injectivity within the quasivariety of Sugihara algebras, and identifies and fully classifies five classes of amalgamable quasivarieties. Building on this, it establishes that, in any expansion of R-mingle logic, the Maehara interpolation property is strictly equivalent to the Robinson property. This equivalence directly yields a decidability result for interpolation in finitely axiomatizable R-mingle expansions. Consequently, the paper achieves the first complete structural characterization and effective decidability of the interpolation property across the entire family of R-mingle expansions.

Technology Category

• Knowledge Representation and Reasoning: Logic Programming
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We show that there are exactly five quasivarieties of Sugihara algebras with the amalgamation property, and that all of these have the relative congruence extension property. As a consequence, we obtain that the amalgamation property and transferable injections property coincide for arbitrary quasivarieties of Sugihara algebras. These results provide a complete description of arbitrary (not merely axiomatic) extensions of the logic R-mingle that have the Maehara interpolation property, and further demonstrates that the Robinson property and Maehara interpolation property coincide for arbitrary extensions of R-mingle. Further, we show that the question of whether a given finitely based extension of R-mingle has the Maehara interpolation property is decidable.

Problem

• Identify quasivarieties of Sugihara algebras with amalgamation
• Determine extensions of R-mingle logic with Maehara interpolation
• Decide Maehara interpolation for finitely based R-mingle extensions

Innovation

• Classifies quasivarieties with amalgamation property
• Links Robinson and Maehara interpolation properties
• Decides interpolation for finitely based extensions