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A Note on the Intuitionistic Logic of False Belief

100%

Witczak T.

Bulletin of the Section of Logic

2022

tom 51

nr 1

57-71

In this paper we analyse logic of false belief in the intuitionistic setting. This logic, studied in its classical version by Steinsvold, Fan, Gilbert and Venturi, describes the following situation: a formula $\varphi$ 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 $\varphi$ 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 $\mathsf{W}$ which is interpreted in relational frames with neighborhoods. We discuss monotonicity of forcing, soundness, completeness and several other issues. Finally, we mention the fact that it is possible to investigate intuitionistic logics of unknown truths.

Topological and Multi-Topological Frames in the Context of Intuitionistic Modal Logic

100%

Witczak T.

Bulletin of the Section of Logic

2019

tom 48

nr 3

187-205

We present three examples of topological semantics for intuitionistic modal logic with one modal operator □. We show that it is possible to treat neighborhood models, introduced earlier, as topological or multi-topological. From the neighborhood point of view, our method is based on differences between properties of minimal and maximal neighborhoods. Also we propose transformation of multitopological spaces into the neighborhood structures.

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2 Bulletin of the Section of Logic

2 Witczak T.

1 2021

1 2019

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A Note on the Intuitionistic Logic of False Belief

Topological and Multi-Topological Frames in the Context of Intuitionistic Modal Logic