Bridging the Semantic Gap: A Unified Framework for Non-Classical Logics via Sheaf-Theoretic Representations
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2025
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| _version_ | 1866901622474407936 |
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| author | Revista, Zen MATH, 10 |
| author_facet | Revista, Zen MATH, 10 |
| contents | This paper introduces a novel sheaf-theoretic framework designed to bridge the semantic gap between diverse non-classical logics. By representing logical systems as sheaves over suitable topological spaces, we offer a unified perspective that reveals underlying structural similarities and facilitates the transfer of techniques between different logical paradigms. Specifically, we explore how this framework can be applied to intuitionistic logic, modal logic, and fuzzy logic, demonstrating its versatility and potential for uncovering new relationships and insights. The framework allows for a more nuanced understanding of the semantic foundations of these logics, leading to new avenues for automated reasoning, knowledge representation, and the development of hybrid logical systems. This approach not only provides a powerful tool for analyzing and comparing different logics but also paves the way for constructing more expressive and flexible logical formalisms for a wide range of applications. |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17833666 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Bridging the Semantic Gap: A Unified Framework for Non-Classical Logics via Sheaf-Theoretic Representations Revista, Zen MATH, 10 This paper introduces a novel sheaf-theoretic framework designed to bridge the semantic gap between diverse non-classical logics. By representing logical systems as sheaves over suitable topological spaces, we offer a unified perspective that reveals underlying structural similarities and facilitates the transfer of techniques between different logical paradigms. Specifically, we explore how this framework can be applied to intuitionistic logic, modal logic, and fuzzy logic, demonstrating its versatility and potential for uncovering new relationships and insights. The framework allows for a more nuanced understanding of the semantic foundations of these logics, leading to new avenues for automated reasoning, knowledge representation, and the development of hybrid logical systems. This approach not only provides a powerful tool for analyzing and comparing different logics but also paves the way for constructing more expressive and flexible logical formalisms for a wide range of applications. |
| title | Bridging the Semantic Gap: A Unified Framework for Non-Classical Logics via Sheaf-Theoretic Representations |
| url | https://doi.org/10.5281/zenodo.17833666 |