Boolean Algebra -- Driven Sepsis Diagnosis

Abstract

Sepsis remains a diagnostic challenge due to its heterogeneous molecular signatures and complex immune responses. In this study, we develop a logical data analysis framework based on Boolean polynomial rings. This method constructs an ideal ℐ of selection criteria that isolate empty subsets of previously analyzed patient data. This approach enables the derivation of interpretable classification rules based on biomarker profiles. We demonstrate that logical data analysis identifies distinct logical patterns for positive and negative sepsis classification. For instance, elevated levels of GLP-1 and MyD88 are associated with septic states in our dataset, whereas high TRAIL and low MyD88 concentrations may suggest a non-septic condition. Importantly, a new way to integrate expert knowledge to filter out potential overfitting or dataset-specific artifacts is shown. Our findings highlight the utility of logics in generating transparent, biologically plausible rules for a data-based and expert-based understanding of sepsis. Moreover, we show how data analysis can benefit from algebraic structures.

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BibTeX RIS

BibTeX

@misc{weber2026boolean,
  title = {{Boolean Algebra -- Driven Sepsis Diagnosis}},
  author = {Marcus Weber and Kai Kappert and Marco Reidelbach and Ambros Gleixner and Konstantin Fackeldey and Wolfgang Bauer},
  howpublished = {arXiv},
  year = {2026},
  month = may,
  doi = {10.48550/arxiv.2605.29686},
  eprint = {2605.29686},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.29686},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Boolean Algebra -- Driven Sepsis Diagnosis
AU  - Marcus Weber
AU  - Kai Kappert
AU  - Marco Reidelbach
AU  - Ambros Gleixner
AU  - Konstantin Fackeldey
AU  - Wolfgang Bauer
PY  - 2026
DA  - 2026/05/28
PB  - arXiv
DO  - 10.48550/arxiv.2605.29686
UR  - https://arxiv.org/abs/2605.29686
AB  - Sepsis remains a diagnostic challenge due to its heterogeneous molecular signatures and complex immune responses. In this study, we develop a logical data analysis framework based on Boolean polynomial rings. This method constructs an ideal ℐ of selection criteria that isolate empty subsets of previously analyzed patient data. This approach enables the derivation of interpretable classification rules based on biomarker profiles. We demonstrate that logical data analysis identifies distinct logical patterns for positive and negative sepsis classification. For instance, elevated levels of GLP-1 and MyD88 are associated with septic states in our dataset, whereas high TRAIL and low MyD88 concentrations may suggest a non-septic condition. Importantly, a new way to integrate expert knowledge to filter out potential overfitting or dataset-specific artifacts is shown. Our findings highlight the utility of logics in generating transparent, biologically plausible rules for a data-based and expert-based understanding of sepsis. Moreover, we show how data analysis can benefit from algebraic structures.
ER  -

Abstract

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