Preservation of admissible rules when combining logics

TL;DR

This paper demonstrates that the meet-combination of various logics preserves admissible rules, structural completeness, and decidability, providing a basis for combined logics with practical examples.

Contribution

It establishes that admissible rules are conservatively preserved under meet-combination and offers a method to derive bases for the combined logic from component logics.

Findings

Admissible rules are preserved in meet-combination.

Structural completeness is maintained in combined logics.

Decidability of admissible rules remains unaffected.

Abstract

Admissible rules are shown to be conservatively preserved by the meet-combination of a wide class of logics. A basis is obtained for the resulting logic from bases given for the component logics. Structural completeness and decidability of the set of admissible rules are also shown to be preserved, the latter with no penalty on the time complexity. Examples are provided for the meet-combination of intermediate and modal logics.