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PreprintarXiv licencearXiv

Possibilistic Logic over a Logic of Formal Inconsistency

  • Esha Jain
  • Sankha S. Basu
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Abstract

In this article, we have introduced a new possibilistic logic on a logic of formal inconsistency with the aim of developing a possibility theoretic framework to deal with uncertainty and inconsistency meaningfully without leading to a system collapse. We have discussed the syntax and semantics for this logic and have proved the soundness and completeness theorems. A set of new measures of consistency, contradictoriness, and triviality of a set of formulas have been defined. These have then been put to use in an example to show that this framework can provide better means of machine reasoning.

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Cite

BibTeXRIS
BibTeX
@misc{jain2026possibilistic,
  title = {{Possibilistic Logic over a Logic of Formal Inconsistency}},
  author = {Esha Jain and Sankha S. Basu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11491},
  eprint = {2609.11491},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11491},
}
RIS
TY  - UNPB
TI  - Possibilistic Logic over a Logic of Formal Inconsistency
AU  - Esha Jain
AU  - Sankha S. Basu
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11491
UR  - https://arxiv.org/abs/2609.11491
AB  - In this article, we have introduced a new possibilistic logic on a logic of formal inconsistency with the aim of developing a possibility theoretic framework to deal with uncertainty and inconsistency meaningfully without leading to a system collapse. We have discussed the syntax and semantics for this logic and have proved the soundness and completeness theorems. A set of new measures of consistency, contradictoriness, and triviality of a set of formulas have been defined. These have then been put to use in an example to show that this framework can provide better means of machine reasoning.
ER  -