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<p>In this article, we add a diamond to the box-based propositional language of intuitionistic doxastic logic <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11229_2025_5226_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbf{IEL}^{-}\)</EquationSource> </InlineEquation> and intuitionistic epistemic logic <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11229_2025_5226_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbf{IEL}\)</EquationSource> </InlineEquation> introduced by Artemov and Protopopescu. The main results of this article are the proofs of completeness with respect to their appropriate relational semantics of the resulting intuitionistic doxastic logic <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11229_2025_5226_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="34" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbf{L}_{\mathbf{dox}}\)</EquationSource> </InlineEquation> and intuitionistic epistemic logic <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11229_2025_5226_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbf{L}_{\mathbf{epi}}\)</EquationSource> </InlineEquation>.</p>

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Intuitionistic epistemic logic with two modal operators

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月24日

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  • Philippe Balbiani

摘要

In this article, we add a diamond to the box-based propositional language of intuitionistic doxastic logic \(\mathbf{IEL}^{-}\) and intuitionistic epistemic logic \(\mathbf{IEL}\) introduced by Artemov and Protopopescu. The main results of this article are the proofs of completeness with respect to their appropriate relational semantics of the resulting intuitionistic doxastic logic \(\mathbf{L}_{\mathbf{dox}}\) and intuitionistic epistemic logic \(\mathbf{L}_{\mathbf{epi}}\) .