A note on the intuitionistic logic of false belief

TL;DR

This paper explores the intuitionistic logic of false belief, analyzing its properties and interpretations using neighborhood semantics, and discusses foundational issues like monotonicity, soundness, and completeness.

Contribution

It extends the classical logic of false belief into an intuitionistic framework with neighborhood semantics, providing new insights and formal systems.

Findings

Analysis of monotonicity of forcing in the intuitionistic setting

Results on soundness and completeness of the proposed logic

Development of simple systems modeling confirmation of beliefs

Abstract

In this paper we analyse logic of false belief in intuitionistic setting. This logic, studied in its classical version by Steinsvold, Fan, Gilbert and Venturi, describes the following situation: a formula F is not satisfied in a given world, but we still believe in it (or we think that it should be accepted). Another interpretations are also possible: e.g. that we do not accept F but it is imposed on us by a kind of council or advisory board. From the mathematical point of view, the idea is expressed by an adequate form of modal operator W which is interpreted in relational frames with neighborhoods. We discuss monotonicity of forcing, soundness, completeness and several other issues. We present also some simple systems in which confirmation of previously accepted formula is modelled.