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Computer Science > Logic in Computer Science

arXiv:2203.09321 (cs)
[Submitted on 17 Mar 2022]

Title:Non-commutative propositional logic with short-circuited biconditional and NAND

Authors:Dalia Papuc, Alban Ponse
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Abstract:Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. In programming, short-circuit evaluation is widely used, with left-sequential conjunction and disjunction as primitive connectives. We consider left-sequential, non-commutative propositional logic, also known as MSCL (memorising short-circuit logic), and start from a previously published, equational axiomatisation. First, we extend this logic with a left-sequential version of the biconditional connective, which allows for an elegant axiomatisation of MSCL. Next, we consider a left-sequential version of the NAND operator (the Sheffer stroke) and again give a complete, equational axiomatisation of the corresponding variant of MSCL. Finally, we consider these logical systems in a three-valued setting with a constant for `undefined', and again provide completeness results.
Comments: 21 pages, 6 tables
Subjects: Logic in Computer Science (cs.LO)
MSC classes: 03C90
ACM classes: F.3.1; F.3.2
Cite as: arXiv:2203.09321 [cs.LO]
  (or arXiv:2203.09321v1 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.2203.09321

Submission history

From: Alban Ponse [view email]
[v1] Thu, 17 Mar 2022 13:51:55 UTC (19 KB)
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