What question did this study set out to answer?

The aim is to study weak mixed algebras and develop a corresponding logic system with binary operators.

January 17, 2026Open Access

A Mixed Logic With Binary Operators

Key Points

The aim is to study weak mixed algebras and develop a corresponding logic system with binary operators.
Introduced the concept of weak mixed algebras with binary operators.
Developed a logic system with two binary modalities.
Proved soundness and completeness of the logic with respect to specific frames.
Demonstrated a new logic that effectively utilizes weak mixed algebras.
Established an embedding theorem that resolves a previously open problem.

Abstract

Abstract In previous work 4 we introduced and examined the class of betweenness algebras. In the current article we study a larger class of algebras with binary operators of possibility and sufficiency, the weak mixed algebras . Furthermore, we develop a system of logic with two binary modalities, sound and complete with respect to the class of frames closely related to the aforementioned algebras, and we prove an embedding theorem which solves an open problem from 4.

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Cite This Study

DÜNTSCH et al. (Thu,) studied this question.

synapsesocial.com/papers/696b2672d2a12237a9349ad9 https://doi.org/https://doi.org/10.1017/jsl.2025.10175

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