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Journal articles on the topic 'Three-valued logic'

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Published: 9 March 2023

Last updated: 31 July 2025

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1

Kooi, Barteld, and Allard Tamminga. "Three-valued Logics in Modal Logic." Studia Logica 101, no. 5 (2012): 1061–72. http://dx.doi.org/10.1007/s11225-012-9420-0.

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2

Oliveira, Kleidson Êglicio Carvalho da Silva. "Paraconsistent Logic Programming in Three and Four-Valued Logics." Bulletin of Symbolic Logic 28, no. 2 (2022): 260. http://dx.doi.org/10.1017/bsl.2021.34.

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AbstractFrom the interaction among areas such as Computer Science, Formal Logic, and Automated Deduction arises an important new subject called Logic Programming. This has been used continuously in the theoretical study and practical applications in various fields of Artificial Intelligence. After the emergence of a wide variety of non-classical logics and the understanding of the limitations presented by first-order classical logic, it became necessary to consider logic programming based on other types of reasoning in addition to classical reasoning. A type of reasoning that has been well stu

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3

Devyatkin, Leonid Yu. "On the three-valued expansions of Kleene's logic." Logical Investigations 29, no. 2 (2023): 59–88. http://dx.doi.org/10.21146/2074-1472-2023-29-2-59-88.

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The paper is devoted to one of the most famous three-valued systems – Kleene's logic. The expressive capabilities of Kleene's logic and its three-valued expansions are described. We present two results. First, all possible three-valued expansions of Kleene's logic are found up to equivalence with respect to the mutual definability of connectives. It is shown that there are only twelve such expansions. This list includes both logics already known in the literature and completely new ones. For the found expansions, we describe the structure of the lattice ordered relative to the expressive power

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4

Томова, Н. Е. "Natural three-valued logics and classical logic." Logical Investigations 19 (April 9, 2013): 344–52. http://dx.doi.org/10.21146/2074-1472-2013-19-0-344-352.

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In this paper implicative fragments of natural three- valued logic are investigated. It is proved that some fragments are equivalent by set of tautologies to implicative fragment of classical logic. It is also shown that some natural three-valued logics verify all tautologies of classical propositional logic.

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5

Vauzeilles, J., and A. Strauss. "Intuitionistic three-valued logic and logic programming." RAIRO - Theoretical Informatics and Applications 25, no. 6 (1991): 557–87. http://dx.doi.org/10.1051/ita/1991250605571.

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6

Giuntini, Roberto. "Three-valued Brouwer-zadeh logic." International Journal of Theoretical Physics 32, no. 10 (1993): 1875–87. http://dx.doi.org/10.1007/bf00979508.

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7

Delahaye, J. P., and V. Thibau. "Programming in three-valued logic." Theoretical Computer Science 78, no. 1 (1991): 189–216. http://dx.doi.org/10.1016/0304-3975(51)90008-4.

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8

Тамминга, А. "Correspondence analysis for strong three-valued logic." Logical Investigations 20 (May 8, 2014): 253–66. http://dx.doi.org/10.21146/2074-1472-2014-20-0-253-266.

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I apply Kooi and Tamminga’s (2012) idea of correspondence analysis for many-valued logics to strong three-valued logic (K3). First, I characterize each possible single entry in the truth-table of a unary or a binary truth-functional operator that could be added to K3 by a basic inference scheme. Second, I define a class of natural deduction systems on the basis of these charac- terizing basic inference schemes and a natural deduction system for K3. Third, I show that each of the resulting natural deduction systems is sound and complete with respect to its particular semantics. Among other thin

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9

Takagi, Tsubasa. "Translation from Three-Valued Quantum Logic to Modal Logic." International Journal of Theoretical Physics 60, no. 1 (2021): 366–77. http://dx.doi.org/10.1007/s10773-020-04701-z.

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AbstractWe translate the three-valued quantum logic into modal logic, and prove 3-equivalence between the valuation of the three-valued logic and a kind of Kripke model in regard to this translation. To prove 3-equivalence, we introduce an observable-dependent logic, which is a fragment of the many-valued quantum logic. Compared to the Birkhoff and von Neumann’s quantum logic, some notions about observables, the completeness relation for example, in quantum mechanics can be utilized if the observable-dependent logic is employed.

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10

Morikawa, Osamu. "Some modal logics based on a three-valued logic." Notre Dame Journal of Formal Logic 30, no. 1 (1988): 130–37. http://dx.doi.org/10.1305/ndjfl/1093635000.

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11

SEGERBERG, KRISTER. "Some Modal Logics based on a Three-valued Logic." Theoria 33, no. 1 (2008): 53–71. http://dx.doi.org/10.1111/j.1755-2567.1967.tb00610.x.

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12

Pkhakadze, Sopo, and Hans Tompits. "Sequent-Type Calculi for Three-Valued and Disjunctive Default Logic." Axioms 9, no. 3 (2020): 84. http://dx.doi.org/10.3390/axioms9030084.

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Default logic is one of the basic formalisms for nonmonotonic reasoning, a well-established area from logic-based artificial intelligence dealing with the representation of rational conclusions, which are characterised by the feature that the inference process may require to retract prior conclusions given additional premisses. This nonmonotonic aspect is in contrast to valid inference relations, which are monotonic. Although nonmonotonic reasoning has been extensively studied in the literature, only few works exist dealing with a proper proof theory for specific logics. In this paper, we intr

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13

Konikowska, Beata, Andrzej Tarlecki, and Andrzej Blikle. "A Three-Valued Logic for Software Specification and Validation. Tertium tamen datur." Fundamenta Informaticae 14, no. 4 (1991): 411–53. http://dx.doi.org/10.3233/fi-1991-14403.

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Different calculi of partial or three-valued predicates have been used and studied by several authors in the context of software specification, development and validation. This paper offers a critical survey on the development of three-valued logics based on such calculi. In the first part of the paper we review two three-valued predicate calculi, based on, respectively, McCarthy’s and Kleene’s propositional connectives and quantifiers, and point out that in a three-valued logic one should distinguish between two notions of validity: strong validity (always true) and weak validity (never false

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14

Ma, Minghui, and Yuanlei Lin. "A Three-Valued Fregean Quantification Logic." Journal of Philosophical Logic 48, no. 2 (2018): 409–23. http://dx.doi.org/10.1007/s10992-018-9469-y.

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15

Yon, Yong Ho. "Many Valued Logic of Gödel and Łukasiewicz." Liberal Arts Innovation Center 12 (July 31, 2023): 265–80. http://dx.doi.org/10.54698/kl.2023.12.265.

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Gödel and Łukasiewicz proposed the three-valued logic by adding the third logical situation, which includes uncertainty and ambiguity, to the classical two logical values, true or false. These logical systems were generalized to the many types of many valued logics, and especially, Gödel’s many valued logic was developed to Heyting algebra and Łukasiewicz’s one to lattice implication algebra. In this paper, we introduce the many valued logics of Gödel and Łukasiewicz, and Heyting’s algebra and lattice implication algebra that are generalizations of Gödel’s and Łukasiewicz’s logic, respectively

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16

Font, Josep M., and Massoud Moussavi. "Note on a six-valued extension of three-valued logic." Journal of Applied Non-Classical Logics 3, no. 2 (1993): 173–87. http://dx.doi.org/10.1080/11663081.1993.10510806.

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17

Bezerra, Edson Vinícius. "Society semantics for four-valued Łukasiewicz logic." Logic Journal of the IGPL 28, no. 5 (2018): 892–911. http://dx.doi.org/10.1093/jigpal/jzy066.

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AbstractWe argue that many-valued logics (MVLs) can be useful in analysing informational conflicts by using society semantics (SSs). This work concentrates on four-valued Łukasiewicz logic. SSs were proposed by Carnielli and Lima-Marques (1999, Advances in Contemporary Logic and Computer Science, 235, 33–52) to deal with conflicts of information involving rational agents that make judgements about propositions according to a given logic within a society, where a society is understood as a collection $\mathcal{A}$ of agents. The interesting point of such semantics is that a new logic can be obt

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18

Martínez-Fernández, José, and Genoveva Martí. "The representation of gappy sentences in four-valued semantics." Semiotica 2021, no. 240 (2021): 145–63. http://dx.doi.org/10.1515/sem-2021-0011.

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Abstract Three-valued logics are standardly used to formalize gappy languages, i.e., interpreted languages in which sentences can be true, false or neither. A three-valued logic that assigns the same truth value to all gappy sentences is, in our view, insufficient to capture important semantic differences between them. In this paper we will argue that there are two different kinds of pathologies that should be treated separately and we defend the usefulness of a four-valued logic to represent adequately these two types of gappy sentences. Our purpose is to begin the formal exploration of the f

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19

Blikle, Andrzej. "Three-Valued Predicates for Software Specification and Validation." Fundamenta Informaticae 14, no. 4 (1991): 387–410. http://dx.doi.org/10.3233/fi-1991-14402.

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Partial functions, hence also partial predicates, cannot be avoided in algorithms. However, in spite of the fact that partial functions have been formally introduced into the theory of software very early, partial predicates are still not quite commonly recognized. In many programming- and software-specification languages partial Boolean expressions are treated in a rather simplistic way: the evaluation of a Boolean sub-expression to an error leads to the evaluation of the hosting Boolean expression to an error and, in the consequence, to the abortion of the whole program. This technique is kn

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20

Feldman, Norman. "The cylindric algebras of three-valued logic." Journal of Symbolic Logic 63, no. 4 (1998): 1201–17. http://dx.doi.org/10.2307/2586647.

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In this paper we consider the three-valued logic used by Kleene [6] in the theory of partial recursive functions. This logic has three truth values: true (T), false (F), and undefined (U). One interpretation of U is as follows: Suppose we have two partially recursive predicates P(x) and Q(x) and we want to know the truth value of P(x) ∧ Q(x) for a particular x0. If x0 is in the domain of definition of both P and Q, then P(x0) ∧ Q(x0) is true if both P(x0) and Q(x0) are true, and false otherwise. But what if x0 is not in the domain of definition of P, but is in the domain of definition of Q? Th

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21

Bigaj, Tomasz. "Three-valued Logic, Indeterminacy and Quantum Mechanics." Journal of Philosophical Logic 30, no. 2 (2001): 97–119. http://dx.doi.org/10.1023/a:1017571731461.

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22

TÖRNEBOHM, HÅKAN. "On truth, implication, and three-valued logic." Theoria 22, no. 3 (2008): 185–98. http://dx.doi.org/10.1111/j.1755-2567.1956.tb01181.x.

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23

FISHER, MARK. "A three-valued calculus for deontic logic." Theoria 27, no. 3 (2008): 107–18. http://dx.doi.org/10.1111/j.1755-2567.1961.tb00019.x.

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24

Qi, Guilin, Peter Milligan, and Paul Sage. "Incidence Calculus on Łukasiewicz's Three-valued Logic." Fundamenta Informaticae 68, no. 4 (2005): 357–78. https://doi.org/10.3233/fun-2005-68404.

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Incidence calculus is a probabilistic logic which possesses both numerical and symbolic approaches. However, Liu in [5] pointed out that the original incidence calculus had some drawbacks and she established a generalized incidence calculus theory (GICT) based on Łukasiewicz's three-valued logic to improve it. In a GICT, an incidence function is defined to relate each proposition ϕ in the axioms of the theory to a set of possible worlds in which ϕ has truth value true. But the incidence function only represents those absolute true states of propositions, so it can not deal with the uncertain s

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25

Marchenkov, S. S. "Positively closed classes of three-valued logic." Journal of Applied and Industrial Mathematics 8, no. 2 (2014): 256–66. http://dx.doi.org/10.1134/s1990478914020124.

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26

Libkin, Leonid. "SQL’s Three-Valued Logic and Certain Answers." ACM Transactions on Database Systems 41, no. 1 (2016): 1–28. http://dx.doi.org/10.1145/2877206.

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27

NAISH, LEE. "A three-valued semantics for logic programmers." Theory and Practice of Logic Programming 6, no. 5 (2006): 509–38. http://dx.doi.org/10.1017/s1471068406002742.

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This paper describes a simpler way for programmers to reason about the correctness of their code. The study of semantics of logic programs has shown strong links between the model theoretic semantics (truth and falsity of atoms in the programmer's interpretation of a program), procedural semantics (for example, SLD resolution) and fixpoint semantics (which is useful for program analysis and alternative execution mechanisms). Most of this work assumes that intended interpretations are two-valued: a ground atom is true (and should succeed according to the procedural semantics) or false (and shou

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28

Bergstra, Jan A., and Alban Ponse. "Kleene's three-valued logic and process algebra." Information Processing Letters 67, no. 2 (1998): 95–103. http://dx.doi.org/10.1016/s0020-0190(98)00083-0.

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29

Leszczyńska-Jasion, Dorota, and Paweł Łupkowski. "Erotetic Search Scenarios and Three-Valued Logic." Journal of Logic, Language and Information 25, no. 1 (2015): 51–76. http://dx.doi.org/10.1007/s10849-015-9233-4.

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30

Radzikowska, Anna. "A three-valued approach to default logic." Journal of Applied Non-Classical Logics 6, no. 2 (1996): 149–90. http://dx.doi.org/10.1080/11663081.1996.10510876.

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31

Nota, G., S. Orefice, G. Pacini, F. Ruggiero, and G. Tortora. "Legality concepts for three-valued logic programs." Theoretical Computer Science 120, no. 1 (1993): 45–68. http://dx.doi.org/10.1016/0304-3975(93)90244-n.

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32

Teusink, Frank. "Three-valued completion for abductive logic programs." Theoretical Computer Science 165, no. 1 (1996): 171–200. http://dx.doi.org/10.1016/0304-3975(96)00044-8.

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33

García Olmedo, Francisco M., and Antonio J. Rodríguez Salas. "Algebraization of the Three-valued BCK-logic." MLQ 48, no. 2 (2002): 163–78. http://dx.doi.org/10.1002/1521-3870(200202)48:2<163::aid-malq163>3.0.co;2-b.

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34

Marchenkov, S. S. "Implicatively Implicit Extensions in Three-Valued Logic." Moscow University Computational Mathematics and Cybernetics 48, no. 1 (2024): 7–14. http://dx.doi.org/10.3103/s0278641924010035.

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35

Przymusinski, Teodor. "Well-Founded Semantics Coincides with Three-Valued Stable Semantics1." Fundamenta Informaticae 13, no. 4 (1990): 445–63. http://dx.doi.org/10.3233/fi-1990-13404.

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We introduce 3-valued stable models which are a natural generalization of standard (2-valued) stable models. We show that every logic program P has at least one 3-valued stable model and that the well-founded model of any program P [Van Gelder et al., 1990] coincides with the smallest 3-valued stable model of P. We conclude that the well-founded semantics of an arbitrary logic program coincides with the 3-valued stable model semantics. The 3-valued stable semantics is closely related to non-monotonic formalisms in AI. Namely, every program P can be translated into a suitable autoepistemic (res

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36

Akama, Seiki, and Yasunori Nagata. "Prior’s Three-Valued Modal Logic Q and its Possible Applications." Journal of Advanced Computational Intelligence and Intelligent Informatics 11, no. 1 (2007): 105–10. http://dx.doi.org/10.20965/jaciii.2007.p0105.

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Prior proposed a three-valued modal logic Q as a “correct” modal logic from his philosophical motivations. Unfortunately, Prior’s Q and many-valued modal logic have been neglected in the tradition of many-valued and modal logic. In this paper, we introduce a version of three-valued Kripke semantics for Q, which aims to establish Prior’s ideas based on possible worlds. We investigate formal properties of Q and prove the completeness theorem of Q. We also compare our approach with others and suggest possible applications.

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37

NAISH, LEE, and HARALD SØNDERGAARD. "Truth versus information in logic programming." Theory and Practice of Logic Programming 14, no. 6 (2013): 803–40. http://dx.doi.org/10.1017/s1471068413000069.

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AbstractThe semantics of logic programs was originally described in terms of two-valued logic. Soon, however, it was realised that three-valued logic had some natural advantages, as it provides distinct values not only for truth and falsehood but also for “undefined”. The three-valued semantics proposed by Fitting (Fitting, M. 1985. A Kripke–Kleene semantics for logic programs. Journal of Logic Programming 2, 4, 295–312) and Kunen (Kunen, K. 1987. Negation in logic programming. Journal of Logic Programming 4, 4, 289–308) are closely related to what is computed by a logic program, the third tru

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38

Polkowski, Lech. "A Note on 3-valued Rough Logic Accepting Decision Rules." Fundamenta Informaticae 61, no. 1 (2004): 37–45. https://doi.org/10.3233/fun-2004-61104.

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Rough sets carry, intuitively, a 3-valued logical structure related to the three regions into which any rough set x divides the universe., viz., the lower definable set i(x), the upper definable set c(x), and the boundary region c(x)\setminus i(x) witnessing the vagueness of associated knowledge. In spite of this intuition, the currently known way of relating rough sets and 3-valued logics is only via 3-valued Łukasiewicz algebras (Pagliani) that endow spaces of disjoint representations of rough sets with its structure. Here, we point to a 3-valued rough logic RL of unary predicates in which v

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39

Fitting, Melvin, and Marion Ben-Jacob. "Stratified, Weak Stratified, and Three-Valued Semantics1." Fundamenta Informaticae 13, no. 1 (1990): 19–33. http://dx.doi.org/10.3233/fi-1990-13104.

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We investigate the relationship between three-valued Kripke/Kleene semantics and stratified semantics for stratifiable logic programs. We first show these are compatible, in the sense that if the three-valued semantics assigns a classical truth value, the stratified approach will assign the same value. Next, the familiar fixed point semantics for pure Horn clause programs gives both smallest and biggest fixed points fundamental roles. We show how to extend this idea to the family of stratifiable logic programs, producing a semantics we call weak stratified. Finally, we show weak stratified sem

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40

Shan, Jing Yi, Zhi Xiang Yin, Xin Yu Tang, and Jing Jing Tang. "A DNA Computing Model for the AND Gate in Three-Valued Logical Circuit." Applied Mechanics and Materials 610 (August 2014): 764–68. http://dx.doi.org/10.4028/www.scientific.net/amm.610.764.

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Multiple-valued logic is an extended form of Boolean logic. In daily life, people often encounter the problem about the multiple-valued logic. With further study on Boolean logic, multiple-valued logic has been paid more and more attention by researchers. This paper achieves the operation of AND gate in three-valued logic by using the DNA hairpin structure. The experiment makes the DNA hairpin structure as the basic structure, and the molecular beacon as the input signal, and at last judges the logical results according to the intensity of fluorescence and gel electrophoresis. This method has

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41

Gehrke, Mai, Carol Walker, and Elbert Walker. "A Mathematical Setting for Fuzzy Logics." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 05, no. 03 (1997): 223–38. http://dx.doi.org/10.1142/s021848859700021x.

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The setup of a mathematical propositional logic is given in algebraic terms, describing exactly when two choices of truth value algebras give the same logic. The propositional logic obtained when the algebra of truth values is the real numbers in the unit interval equipped with minimum, maximum and -x=1-x for conjunction, disjunction and negation, respectively, is the standard propositional fuzzy logic. This is shown to be the same as three-valued logic. The propositional logic obtained when the algebra of truth values is the set {(a, b)|a≤ b and a,b∈[0,1]} of subintervals of the unit interval

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42

Konikowska, Beata. "A two-valued logic for reasoning about different types of consequence in Kleene's three-valued logic." Studia Logica 49, no. 4 (1990): 541–55. http://dx.doi.org/10.1007/bf00370164.

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43

Takano, Mitio. "Cut-free systems for three-valued modal logics." Notre Dame Journal of Formal Logic 33, no. 3 (1992): 359–68. http://dx.doi.org/10.1305/ndjfl/1093634401.

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44

Petrukhin, Ya I. "Natural deduction system for three-valued Heyting’s logic." Moscow University Mathematics Bulletin 72, no. 3 (2017): 133–36. http://dx.doi.org/10.3103/s002713221703007x.

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45

Barbosa, João, Mário Florido, and Vítor Santos Costa. "A Three-Valued Semantics for Typed Logic Programming." Electronic Proceedings in Theoretical Computer Science 306 (September 19, 2019): 36–51. http://dx.doi.org/10.4204/eptcs.306.10.

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46

Walker, E. A. "Stone algebras, conditional events, and three valued logic." IEEE Transactions on Systems, Man, and Cybernetics 24, no. 12 (1994): 1699–707. http://dx.doi.org/10.1109/21.328927.

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47

Marchenkov, Sergey S., and Anatoliy V. Chernyshev. "Basic positively closed classes in three-valued logic." Discrete Mathematics and Applications 28, no. 3 (2018): 157–65. http://dx.doi.org/10.1515/dma-2018-0015.

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Abstract Basic positively closed classes are intersections of positively precomplete classes. We prove that three-valued logic contains exactly 79 basic positively closed classes. Each class is described in terms of endomorphism semigroups.

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48

Besslich, Ph W., and E. A. Trachtenberg. "Three-valued quasi-linear transformation for logic synthesis." IEE Proceedings - Computers and Digital Techniques 143, no. 6 (1996): 391. http://dx.doi.org/10.1049/ip-cdt:19960466.

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49

Pynko, Alexej P. "Extensions of Hałkowska-Zajac's three-valued paraconsistent logic." Archive for Mathematical Logic 41, no. 3 (2002): 299–307. http://dx.doi.org/10.1007/s001530100115.

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50

Rubinson, Claude. "Nulls, three-valued logic, and ambiguity in SQL." ACM SIGMOD Record 36, no. 4 (2007): 13–17. http://dx.doi.org/10.1145/1361348.1361350.

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