Kleene's Logic, Generalized
@article{Fitting1991KleenesLG, title={Kleene's Logic, Generalized}, author={Melvin Fitting}, journal={J. Log. Comput.}, year={1991}, volume={1}, pages={797-810}, url={https://api.semanticscholar.org/CorpusID:13400935} }
Kleene's well-known strong three-valued logic is shown to be one of a family of logics with similar mathematical properties that lend themselves well to semantical constructions based on fixpoint procedures, as in logic programming.
163 Citations
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Computer Science, Mathematics
This work introduces a guard connective into Belnap's logic and shows that by using it four-valued analogs of Kleene’s weak three-valued logic, and the asymmetric logic of Lisp are also available.
Natural Deduction for Fitting’s Four-Valued Generalizations of Kleene’s Logics
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Mathematics, Philosophy
In this paper, we present sound and complete natural deduction systems for Fitting’s four-valued generalizations of Kleene’s three-valued regular logics.
Natural Deduction for Fitting’s Four-Valued Generalizations of Kleene’s Logics
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Mathematics, Philosophy
In this paper, we present sound and complete natural deduction systems for Fitting’s four-valued generalizations of Kleene’s three-valued regular logics.
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Computer Science, Mathematics
This paper vindicates Belnap's thesis by showing that the logical role that the four-valued structure has among Ginsberg's well-known bilattices is similar to therole that the two-valued algebra has among Boolean algebras.
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Philosophy, Computer Science
This paper develops proof systems, which correspond to bilattices in an essential way, and introduces the notion of logical bilattices, which can be used for eecient inferences from possibly inconsistent data.
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Mathematics
The aim of this paper is to axiomatize the logics determined by all natural implicative expansions of MK3 and MK3 .
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Computer Science, Philosophy
This paper develops proof systems, which correspond to bilattice in an essential way, and introduces the notion of logical bilattices, which can be used for efficient inferences from possibly inconsistent data.
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Mathematics
It is proved, by using algebraic properties of the class of De Morgan algebras, that this semantically defined logic can be axiomatized as Belnap's “useful” four-valued logic.
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Computer Science, Mathematics
A family of preferential logics that are useful for handling information with different levels of uncertainty are introduced, and it is shown that the formalisms in this family can be embedded in corresponding four-valued logics with at most three uncertainty levels.
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