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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.14821 |
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| _version_ | 1866912627328811008 |
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| author | Bergstra, Jan A. Ponse, Alban |
| author_facet | Bergstra, Jan A. Ponse, Alban |
| contents | Three-valued conditional logic (CL) is defined by Guzmán and Squier (1990), and based on McCarthy's noncommutative connectives, axiomatises a short-circuit logic (SCL) that defines more identities than three-valued MSCL (Memorising SCL, which also has a two-valued variant). This follows from the fact that the definable connective that prescribes full left-sequential conjunction is commutative in CL. We show that in CL, the full left-sequential connectives and negation define Bochvar's three-valued strict logic. We observe that CL also has a two-valued variant of which the full left-sequential connectives and negation define a commutative logic that is weaker than propositional logic because the absorption laws do not hold.
Next, we show that the original, equational axiomatisation of CL is not independent and give several alternative, independent axiomatisations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_14821 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Conditional logic as a short-circuit logic Bergstra, Jan A. Ponse, Alban Logic in Computer Science 03C90 F.3.1; F.3.2 Three-valued conditional logic (CL) is defined by Guzmán and Squier (1990), and based on McCarthy's noncommutative connectives, axiomatises a short-circuit logic (SCL) that defines more identities than three-valued MSCL (Memorising SCL, which also has a two-valued variant). This follows from the fact that the definable connective that prescribes full left-sequential conjunction is commutative in CL. We show that in CL, the full left-sequential connectives and negation define Bochvar's three-valued strict logic. We observe that CL also has a two-valued variant of which the full left-sequential connectives and negation define a commutative logic that is weaker than propositional logic because the absorption laws do not hold. Next, we show that the original, equational axiomatisation of CL is not independent and give several alternative, independent axiomatisations. |
| title | Conditional logic as a short-circuit logic |
| topic | Logic in Computer Science 03C90 F.3.1; F.3.2 |
| url | https://arxiv.org/abs/2304.14821 |