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- W4200630724 abstract "We provide a sound and complete proof system for an extension of Kleene's ternary logic to predicates. The concept of theory is extended with, for each function symbol, a formula that specifies when the function is defined. The notion of is defined is extended to terms and formulas via a straightforward recursive algorithm. The is defined formulas are constructed so that they themselves are always defined. The completeness proof relies on the Henkin construction. For each formula, precisely one of the formula, its negation, and the negation of its is defined formula is true on the constructed model. Many other ternary logics in the literature can be reduced to ours. Partial functions are ubiquitous in computer science and even in (in)equation solving at schools. Our work was motivated by an attempt to explain, precisely in terms of logic, typical informal methods of reasoning in such applications." @default.
- W4200630724 created "2021-12-31" @default.
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- W4200630724 date "2021-12-08" @default.
- W4200630724 modified "2023-10-16" @default.
- W4200630724 title "A Completeness Proof for A Regular Predicate Logic with Undefined Truth Value" @default.
- W4200630724 doi "https://doi.org/10.48550/arxiv.2112.04436" @default.
- W4200630724 hasPublicationYear "2021" @default.
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