On generalized Van-Benthem-type characterizations

TL;DR

This paper extends model-theoretic characterizations of intuitionistic logic to include broader classes of connectives, providing a unified framework for understanding their expressive powers over bounded lattices.

Contribution

It generalizes Van-Benthem-type characterizations to encompass finite sets of guarded and regular connectives of degrees 1 and 2.

Findings

Characterizes expressive power of guarded connectives of degree ≤1

Provides model-theoretic framework for regular connectives of degree 2

Extends previous intuitionistic logic characterizations

Abstract

The paper continues the line of model-theoretic characterizations for versions of intuitionistic logic previously achieved by the author, further generalizing them. This results in a model-theoretic characterization of expressive powers of arbitrary finite sets of guarded connectives of degree not exceeding 1 and regular connectives of degree 2 over the language of bounded lattices.