A taxonomy for controlling (in)consistency
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911609039880192 |
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| author | Coniglio, Marcelo E. Ongaratto, Rafael |
| author_facet | Coniglio, Marcelo E. Ongaratto, Rafael |
| contents | In this article, the hierarchy of LFIs L$_n^k$, Logics of Controlled Consistency (LCC), is introduced. Inspired by da Costa's original C$_n$ systems, this hierarchy can represent different degrees of paraconsistent commitment and different related notions of consistency, inconsistency, and negation associated with each two-dimensional level of these logics. In one dimension, the logics become increasingly more paraconsistent by allowing the consistency operator to behave inconsistently up to a fixed iteration. In another dimension, the negation is increasingly strengthened. Initially, we present these logics with a swap structure semantics, showing their soundness and completeness. Some well-known LFIs are shown to be particular cases of LCCs. With some examples, we show how these different logics represent different types of paraconsistent commitment: from skepticism to dogmastism, these logics have the multiplicity to represent these different philosophical positions. Furthermore, the development of the hierarchy in a general manner allows pragmatism to take place when considering the different types of paraconsistent commitment. Each level we go up in this direction we get a stronger family of logics. Furthermore, we also present an extension of an LCC, a 5-valued LFI called LFI3, a sublogic of LFI1. LFI3 presents a paradigmatic case for the development of many-valued LFIs that have more than three values. Using a technique that combines Karnaugh Maps and Twist Structures, we give an axiomatization and a semantical account of LFI3. Finally, using RNmatrices, we give a general semantical account of the L$_n^k$ family of logics, and we also prove its soundness and completeness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18766 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A taxonomy for controlling (in)consistency Coniglio, Marcelo E. Ongaratto, Rafael Logic in Computer Science 03B53, 03B50 In this article, the hierarchy of LFIs L$_n^k$, Logics of Controlled Consistency (LCC), is introduced. Inspired by da Costa's original C$_n$ systems, this hierarchy can represent different degrees of paraconsistent commitment and different related notions of consistency, inconsistency, and negation associated with each two-dimensional level of these logics. In one dimension, the logics become increasingly more paraconsistent by allowing the consistency operator to behave inconsistently up to a fixed iteration. In another dimension, the negation is increasingly strengthened. Initially, we present these logics with a swap structure semantics, showing their soundness and completeness. Some well-known LFIs are shown to be particular cases of LCCs. With some examples, we show how these different logics represent different types of paraconsistent commitment: from skepticism to dogmastism, these logics have the multiplicity to represent these different philosophical positions. Furthermore, the development of the hierarchy in a general manner allows pragmatism to take place when considering the different types of paraconsistent commitment. Each level we go up in this direction we get a stronger family of logics. Furthermore, we also present an extension of an LCC, a 5-valued LFI called LFI3, a sublogic of LFI1. LFI3 presents a paradigmatic case for the development of many-valued LFIs that have more than three values. Using a technique that combines Karnaugh Maps and Twist Structures, we give an axiomatization and a semantical account of LFI3. Finally, using RNmatrices, we give a general semantical account of the L$_n^k$ family of logics, and we also prove its soundness and completeness. |
| title | A taxonomy for controlling (in)consistency |
| topic | Logic in Computer Science 03B53, 03B50 |
| url | https://arxiv.org/abs/2604.18766 |