Matrix Modal Logics with Indeterminate Truth Values

Abstract

Andrey Kuznetsov*

This paper introduces non-relational Resolution Matrix Semantics (RMS) as an alternative framework for constructing systems of modal logic. The concept of non-relational semantics for modal logic, initially suggested by J. Kearns [1981] and later developed in various ways by different researchers serves as a foundational inspiration for this approach [1-5]. Y. Ivlev suggested defining modal operators based on informal reasoning tailored to their area of applicability—such as epistemology, ethics, or physics—rather than formal relational structures, introducing the notion of an interpretation quasi-function that assigns truth values in a context- dependent manner. His modal systems, while lacking an obvious correspondence to Kripkean systems, offered an intriguing informal, substantive perspective that prioritized practical interpretation over abstract world-relations.

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