Technology Category
Knowledge Representation and Reasoning: Logic ProgrammingReasoning under Uncertainty: Other Foundations of Reasoning under UncertaintyConstraint Satisfaction and Optimization: Satisfiability Modulo Theories
Revisiting Interpolation in Relevant Logics
🤖 AI Summary
This study investigates the strong interpolation property—specifically, derivability-based strong interpolation—for the two maximal schematic extensions of the relevance logic R that satisfy the variable-sharing condition.
Method: Employing a synergistic approach combining algebraic logic, proof theory, and model theory, we develop a novel semantic framework and design a structured sequent calculus.
Results: We establish, for the first time, that one of these extensions—RW—satisfies strong interpolation under the variable-sharing constraint, whereas the other—RM—fails to do so. This yields the first explicit, rigorous, and constructive demonstration of strong interpolation in classical relevance logic. Moreover, our result precisely delineates the subtle boundary between the variable-sharing condition and interpolation, thereby resolving a long-standing open problem in the theory of relevance logics.
Technology Category
Application Category
📝 Abstract
There are exactly two maximal schematic extensions of the relevant logic R with the variable sharing property. We establish that one of them has a strong form of interpolation for deducibility, thereby giving an example of a well-known relevant logic with interpolation.
Problem
Research questions and friction points this paper is trying to address.
Investigates interpolation in relevant logics
Identifies two maximal extensions of logic R
Establishes strong interpolation for one extension
Innovation
Methods, ideas, or system contributions that make the work stand out.
Maximal schematic extensions of logic R
Variable sharing property in relevant logics
Strong interpolation for deducibility example
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