Relevant bibliographies by topics / Paraconsistent modal logics

Academic literature on the topic 'Paraconsistent modal logics'

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Published: 8 June 2024

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Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Journal articles on the topic "Paraconsistent modal logics":

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Rivieccio, Umberto. "Paraconsistent Modal Logics." Electronic Notes in Theoretical Computer Science 278 (November 2011): 173–86. http://dx.doi.org/10.1016/j.entcs.2011.10.014.

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Avron, Arnon, and Anna Zamansky. "Paraconsistency, self-extensionality, modality." Logic Journal of the IGPL 28, no. 5 (November 27, 2018): 851–80. http://dx.doi.org/10.1093/jigpal/jzy064.

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Abstract Paraconsistent logics are logics that, in contrast to classical and intuitionistic logic, do not trivialize inconsistent theories. In this paper we take a paraconsistent view on two famous modal logics: B and S5. We use for this a well-known general method for turning modal logics to paraconsistent logics by defining a new (paraconsistent) negation as $\neg \varphi =_{Def} \sim \Box \varphi$ (where $\sim$ is the classical negation). We show that while that makes both B and S5 members of the well-studied family of paraconsistent C-systems, they differ from most other C-systems in having the important replacement property (which means that equivalence of formulas implies their congruence). We further show that B is a very robust C-system in the sense that almost any axiom which has been considered in the context of C-systems is either already a theorem of B or its addition to B leads to a logic that is no longer paraconsistent. There is exactly one notable exception, and the result of adding this exception to B leads to the other logic studied here, S5.
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ROBLES, GEMMA, and JOSÉ M. MÉNDEZ. "PARACONSISTENT LOGICS INCLUDED IN LEWIS’ S4." Review of Symbolic Logic 3, no. 3 (July 23, 2010): 442–66. http://dx.doi.org/10.1017/s1755020310000109.

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As is known, a logic S is paraconsistent if the rule ECQ (E contradictione quodlibet) is not a rule of S. Not less well known is the fact that Lewis’ modal logics are not paraconsistent. Actually, Lewis vindicates the validity of ECQ in a famous proof currently known as the “Lewis’ proof” or “Lewis’ argument.” This proof essentially leans on the Disjunctive Syllogism as a rule of inference. The aim of this paper is to define a series of paraconsistent logics included in S4 where the Disjunctive Syllogism is valid only as a rule of proof.
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Oliveira, Kleidson Êglicio Carvalho da Silva. "Paraconsistent Logic Programming in Three and Four-Valued Logics." Bulletin of Symbolic Logic 28, no. 2 (June 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 studied is the paraconsistent, that is, the reasoning that tolerates contradictions. However, although there are many paraconsistent logics with different types of semantics, their application to logic programming is more delicate than it first appears, requiring an in-depth study of what can or cannot be transferred directly from classical first-order logic to other types of logic.Based on studies of Tarcisio Rodrigues on the foundations of Paraconsistent Logic Programming (2010) for some Logics of Formal Inconsistency (LFIs), this thesis intends to resume the research of Rodrigues and place it in the specific context of LFIs with three- and four-valued semantics. This kind of logics are interesting from the computational point of view, as presented by Luiz Silvestrini in his Ph.D. thesis entitled “A new approach to the concept of quase-truth” (2011), and by Marcelo Coniglio and Martín Figallo in the article “Hilbert-style presentations of two logics associated to tetravalent modal algebras” [Studia Logica (2012)]. Based on original techniques, this study aims to define well-founded systems of paraconsistent logic programming based on well-known logics, in contrast to the ad hoc approaches to this question found in the literature.Abstract prepared by Kleidson Êglicio Carvalho da Silva Oliveira.E-mail: kecso10@yahoo.com.brURL: http://repositorio.unicamp.br/jspui/handle/REPOSIP/322632
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Odintsov, Sergei P., and Heinrich Wansing. "Disentangling FDE-Based Paraconsistent Modal Logics." Studia Logica 105, no. 6 (September 23, 2017): 1221–54. http://dx.doi.org/10.1007/s11225-017-9753-9.

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Карниэлли, У. "Formal polynomials, heuristics and proofs in logic." Logical Investigations 16 (April 7, 2010): 280–94. http://dx.doi.org/10.21146/2074-1472-2010-16-0-280-294.

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This note surveys some previous results on the role of formal polynomials as a representation method for logical derivation in classical and non-classical logics, emphasizing many-valued logics, paraconsistent logics and modal logics. It also discusses the potentialities of formal polynomials as heuristic devices in logic and for expressing certain meta-logical properties, as well as pointing to some promising generalizations towards algebraic geometry.
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Маркин, В. И. "What trends in non-classical logic were anticipated by Nikolai Vasiliev?" Logical Investigations 19 (April 9, 2013): 122–35. http://dx.doi.org/10.21146/2074-1472-2013-19-0-122-135.

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In this paper we discuss a question about the trends in non-classical logic that were exactly anticipated by Niko- lai Vasiliev. We show the influence of Vasiliev’s Imaginary logic on paraconsistent logic. Metatheoretical relations between Vasiliev’s logical systems and many-valued predicate logics are established. We also make clear that Vasiliev has developed a sketch of original system of intensional logic and expressed certain ideas of modal and temporal logics.
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McGinnis, Casey. "Tableau Systems for Some Paraconsistent Modal Logics." Electronic Notes in Theoretical Computer Science 143 (January 2006): 141–57. http://dx.doi.org/10.1016/j.entcs.2005.05.028.

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Béziau, Jean-Yves. "Many-valuedness from a universal logic perspective." Logical Investigations 26, no. 1 (August 6, 2020): 78–90. http://dx.doi.org/10.21146/2074-1472-2020-26-1-78-90.

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We start by presenting various ways to define and to talk about many-valued logic(s). We make the distinction between on the one hand the class of many-valued logics and on the other hand what we call “many-valuedness”: the meta-theory of many-valued logics and the related meta-theoretical framework that is useful for the study of any logical systems. We point out that universal logic, considered as a general theory of logical systems, can be seen as an extension of many-valuedness. After a short story of many-valuedness, stressing that it is present since the beginning of the history of logic in Ancient Greece, we discuss the distinction between dichotomy and polytomy and the possible reduction to bivalence. We then examine the relations between singularity and universality and the connection of many-valuedness with the universe of logical systems. In particular, we have a look at the interrelationship between modal logic, 3-valued logic and paraconsistent logic. We go on by dealing with philosophical aspects and discussing the applications of many-valuedness. We end with some personal recollections regarding Alexander Karpenko, from our first meeting in Ghent, Belgium in 1997, up to our last meeting in Saint Petersburg, Russia in 2016.
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Coscarelli, Bruno Costa. "Model Theory in a Paraconsistent Environment." Bulletin of Symbolic Logic 27, no. 2 (June 2021): 216. http://dx.doi.org/10.1017/bsl.2021.33.

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AbstractThe purpose of this thesis is to develop a paraconsistent Model Theory. The basis for such a theory was launched by Walter Carnielli, Marcelo Esteban Coniglio, Rodrigo Podiack, and Tarcísio Rodrigues in the article ‘On the Way to a Wider Model Theory: Completeness Theorems for First-Order Logics of Formal Inconsistency’ [The Review of Symbolic Logic, vol. 7 (2014)].Naturally, a complete theory cannot be fully developed in a single work. Indeed, the goal of this work is to show that a paraconsistent Model Theory is a sound and worthy possibility. The pursuit of this goal is divided in three tasks: The first one is to give the theory a philosophical meaning. The second one is to transpose as many results from the classical theory to the new one as possible. The third one is to show an application of the theory to practical science.The response to the first task is a Paraconsistent Reasoning System. The start point is that paraconsistency is an epistemological concept. The pursuit of a deeper understanding of the phenomenon of paraconsistency from this point of view leads to a reasoning system based on the Logics of Formal Inconsistency. Models are regarded as states of knowledge and the concept of isomorphism is reformulated so as to give raise to a new concept that preserves a portion of the whole knowledge of each state. Based on this, a notion of refinement is created which may occur from inside or from outside the state.In order to respond to the second task, two important classical results, namely the Omitting Types Theorem and Craig’s Interpolation Theorem are shown to hold in the new system and it is also shown that, if classical results in general are to hold in a paraconsistent system, then such a system should be in essence how it was developed here.Finally, the response to the third task is a proposal of what a Paraconsistent Logic Programming may be. For that, the basis for a paraconsistent PROLOG is settled in the light of the ideas developed so far.Abstract prepared by Bruno Costa Coscarelli.E-mail: brunocostacoscarelli@gmail.comURL: http://repositorio.unicamp.br/jspui/handle/REPOSIP/331697
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Journal articles

Dissertations / Theses on the topic "Paraconsistent modal logics":

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KOZHEMIACHENKO, Daniil. "Paraconsistent and fuzzy modal logics for reasoning about uncertainty." Electronic Thesis or Diss., Bourges, INSA Centre Val de Loire, 2023. http://www.theses.fr/2023ISAB0014.

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Ce manuscrit est dédié à l'étude des logiques modales floues qui formalisent le raisonnement (paraconsistant) sur l'incertitude. Ici, l'interprétation d'«information (données) incertain(es)» inclut toute combinaison des trois propriétés suivantes. Premièrement, l'information peur être quantifiée, i.e., la proposition est associée à un degré de vérité plutôt qu'une valeur de vérité. Deuxièmement, l'information peut être incomplète. Troisièmement, l'information peut être contradictoire.Toutes les logiques étudiees se divisent en deux groupes. Les plus «traditionnelles» dont la sémantique est construite sur des modèles de Kripke où les formules (et parfois, même des relations d'accessibilité) prennent des valeurs dans [0,1] constituent le premier groupe. Le second groupe contient des logiques dites «bi-stratifiées». Ici, le langage est composé de trois parties: la strate intérieure, la strate extérieure, et la modalité non-nichante. On interprète la modalité comme une mesure sur l'univers (e.g., une mesure de probabilité, fonction de croyance, fonction de plausibilité, etc.) correspondante au degré de (in)certitude de l'agent dans une proposition donnée. Le raisonnement sur cette (in)certitude est conduit dans la strate extérieure. Les cadres dans des logiques bi-stratifiées sont alors des ensembles munis de mesures.Chacun de ces deux genres de logiques correspond à l'une des façons d'interpréter l'incertitude. Dans le cas moins formel, nous utiliserons les logiques avec la sémantique de Kripke. Dans le cas plus formel où l'on assume que le degré de certitude se comporte comme une mesure d'incertitude concrète, nous utiliserons les logiques bi-stratifiées
This dissertation is devoted to the study of fuzzy modal logics that formalise (paraconsistent) reasoning about uncertainty. The understanding of ‘uncertain information (data)’ here includes any combination of the following three characteristics. First, the information can be graded, i.e., the statement is equipped with a truth degree rather than a truth value. Second, the information can be incomplete. Third, the information can be contradictory.All the logics in question can be divided into two kinds. First, the more ‘traditional’ modal logics defined on [0,1]-valued Kripke models (possibly, with fuzzy accessibility relations) whose language includes modal operators interpreted as infima and suprema of values in the accessible states.The second kind of logics contains so-called ‘two-layered’ logics. In this framework, the language is divided into three parts: the inner layer, the outer layer, and the non-nesting modality. The idea is to use the inner-layer language to describe events, interpret the modality as a measure on the set of events (e.g., as a probability function, belief function, plausibility, etc.) corresponding to the degree of the agent's (un)certainty in a given event, and then reason about this (un)certainty in the outer-layer language. A frame in a two-layered logic is, thus, a set with a measure defined thereon.These two kinds of logics correspond to two ways of interpreting uncertainty. In the less formal one, we will be using the logics with the Kripke-frame semantics. In the more formal case where the degree of one's certainty or belief is assumed to behave as a concrete uncertainty measure, we will use the two-layered logics
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Costa, Diana Filipa de Pinho. "Paraconsistency in hybrid logic." Master's thesis, Universidade de Aveiro, 2014. http://hdl.handle.net/10773/13305.

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Mestrado em Matemática e Aplicações
The use of hybrid logics allows the description of relational structures, at the same time that allows establishing accessibility relations between states and, furthermore, nominating and making mention to what happens at speci c states. However, the information we collect is subject to inconsistencies, namely, the search for di erent information sources can lead us to pick up contradictions. Nowadays, by having so many means of dissemination available, that happens frequently. The aim of this work is to develop tools capable of dealing with contradictory information that can be described as hybrid logics' formulas. To build models, to compare inconsistency in di erent databases, and to see the applicability of this method in day-to-day life are the basis for the development of this dissertation.
O uso de lógicas híbridas permite a descrição de estruturas relacionais, ao mesmo tempo que permite estabelecer relações de acessibilidade entre estados, e, para além disso, nomear e fazer referência ao que acontece em estados específicos. No entanto, a informação que recolhemos está sujeita a inconsistências, isto é, a procura de diferentes fontes de informação pode levar a recolha de contradições. O que nos dias de hoje, com tantos meios de divulgação disponíveis, acontece frequentemente. O objetivo deste trabalho e desenvolver ferramentas capazes de lidar com informação contraditória que possa ser descrita através de fórmulas de lógicas híbridas. Construir modelos e comparar a inconsistência de diferentes bases de dados e ver a aplicabilidade deste método no dia-a-dia são a base para o desenvolvimento desta dissertação.
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Teles, Eugênia Ribeiro. "Uma Abordagem paraconsistente para o problema da consistência nos dilemas morais." Universidade Federal da Paraí­ba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/5619.

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This work deals with the question of logical consistency inside the context of moral dilemmas or, more specifically, genuine moral dilemmas, which are situations where someone has a conflict between two obligatory actions guided by the same moral principle. In other words, it is a situation where there are two moral obligations which should be satisfied, but since they are incompatible, while sometimes one is the negation of the other, they cannot be both accomplished. When we formalize moral dilemmas along with some deontic principles, the result is a contradiction. Inside the framework of classical deontic logic, due to its limitation of dealing with paradoxes of such kind, the existence of moral dilemmas is taken as something absurd, as an affront to rationality. Thus, given the inconsistency, the solution would be to deny the existence of the dilemmas, which has been the most widespread solution, or to deny the deontic principles involved in the inconsistency. We do not agree with these two solutions. Instead, we propose to weaken the rationalist argumentation based on the existence of dialetheias and on the suggestion of dealing with moral dilemmas inside a paraconsistent framework, in such a way that the existence of inconsistence would not be a reason any more to deny the existence of such dilemmas.
RESUMOO presente trabalho aborda a questão da consistência lógica dentro do contexto dos dilemas morais; mais especificamente dilemas morais genuínos, que são situações nas quais uma pessoa tem o conflito entre duas ações obrigatórias guiadas pelo mesmo princípio. Ou seja, existem duas obrigações que deveriam ser satisfeitas, mas por se tratarem de ações incompatíveis, em que uma é a negação da outra, não podem ambas ser praticadas. Quando se faz a formalização do dilema moral conjuntamente com alguns princípios deônticos o resultado é uma contradição. Dentro do framework da Lógica Deôntica clássica, por causa de sua limitação em tratar com paradoxos devido a alguns princípios clássicos, a existência dos dilemas morais é tida como algo absurdo ou uma afronta à racionalidade. Assim, dada à inconsistência, a solução seria negar a existência dos dilemas ou negar os princípios deônticos envolvidos na inconsistência. A solução mais propagada foi a negação da existência dos dilemas. Entretanto, discordando dessa solução, tentamos enfraquecer a argumentação racionalista com base na ideia de dialetéias e consequentemente sugerindo que, se os dilemas morais forem tratados em um framework paraconsistente a inconsistência não seria motivo suficiente para negar a existência desses dilemas.

Books on the topic "Paraconsistent modal logics":

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Burgess, John P. Logic and Philosophical Methodology. Edited by Herman Cappelen, Tamar Szabó Gendler, and John Hawthorne. Oxford University Press, 2016. http://dx.doi.org/10.1093/oxfordhb/9780199668779.013.30.

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This article explores the role of logic in philosophical methodology, as well as its application in philosophy. The discussion gives a roughly equal coverage to the seven branches of logic: elementary logic, set theory, model theory, recursion theory, proof theory, extraclassical logics, and anticlassical logics. Mathematical logic comprises set theory, model theory, recursion theory, and proof theory. Philosophical logic in the relevant sense is divided into the study of extensions of classical logic, such as modal or temporal or deontic or conditional logics, and the study of alternatives to classical logic, such as intuitionistic or quantum or partial or paraconsistent logics. The nonclassical consists of the extraclassical and the anticlassical, although the distinction is not clearcut.

Book chapters on the topic "Paraconsistent modal logics":

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Kudo, Yasuo, Tetsuya Murai, and Seiki Akama. "A Review on Rough Sets and Possible World Semantics for Modal Logics." In Towards Paraconsistent Engineering, 165–77. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-40418-9_8.

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Indrzejczak, Andrzej, and Yaroslav Petrukhin. "A Uniform Formalisation of Three-Valued Logics in Bisequent Calculus." In Automated Deduction – CADE 29, 325–43. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-38499-8_19.

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AbstractWe present a uniform characterisation of three-valued logics by means of bisequent calculus (BSC). It is a generalised form of sequent calculus (SC) where rules operate on the ordered pairs of ordinary sequents. BSC may be treated as the weakest kind of system in the rich family of generalised SC operating on items being some collections of ordinary sequents. This family covers several forms of hypersequent and nested sequent calculi introduced to provide decent SC for several non-classical logics. It seems that for many non-classical logics, including some many-valued, paraconsistent and modal logics, this reasonably modest generalization of standard SC is sufficient. In this paper we examine a variety of three-valued logics and show how they can be formalised in the framework of bisequent calculus. All provided systems are cut-free and satisfy the subformula property. Also the interpolation theorem is constructively proved for some logics.
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Besnard, Philippe, and Paul Wong. "Modal (Logic) Paraconsistency." In Lecture Notes in Computer Science, 540–51. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-45062-7_44.

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Bílková, Marta, Sabine Frittella, and Daniil Kozhemiachenko. "Paraconsistent Gödel Modal Logic." In Automated Reasoning, 429–48. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-10769-6_26.

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AbstractWe introduce a paraconsistent modal logic $$\mathbf {K}\mathsf {G}^2$$ K G 2 , based on Gödel logic with coimplication (bi-Gödel logic) expanded with a De Morgan negation $$\lnot $$ ¬ . We use the logic to formalise reasoning with graded, incomplete and inconsistent information. Semantics of $$\mathbf {K}\mathsf {G}^2$$ K G 2 is two-dimensional: we interpret $$\mathbf {K}\mathsf {G}^2$$ K G 2 on crisp frames with two valuations $$v_1$$ v 1 and $$v_2$$ v 2 , connected via $$\lnot $$ ¬ , that assign to each formula two values from the real-valued interval [0, 1]. The first (resp., second) valuation encodes the positive (resp., negative) information the state gives to a statement. We obtain that $$\mathbf {K}\mathsf {G}^2$$ K G 2 is strictly more expressive than the classical modal logic $$\mathbf {K}$$ K by proving that finitely branching frames are definable and by establishing a faithful embedding of $$\mathbf {K}$$ K into $$\mathbf {K}\mathsf {G}^2$$ K G 2 . We also construct a constraint tableau calculus for $$\mathbf {K}\mathsf {G}^2$$ K G 2 over finitely branching frames, establish its decidability and provide a complexity evaluation.
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Nasieniewski, Marek, and Andrzej Pietruszczak. "On Modal Logics Defining Jaśkowski’s D2-Consequence." In Paraconsistency: Logic and Applications, 141–61. Dordrecht: Springer Netherlands, 2012. http://dx.doi.org/10.1007/978-94-007-4438-7_9.

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Damásio, Carlos Viegas, and Luís Moniz Pereira. "A model theory for paraconsistent logic programming." In Progress in Artificial Intelligence, 377–86. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/3-540-60428-6_32.

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Sedlár, Igor, and Ondrej Majer. "Modelling Sources of Inconsistent Information in Paraconsistent Modal Logic." In New Essays on Belnap-­Dunn Logic, 293–310. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-31136-0_17.

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Jayakumar, Badrinath, and Rajshekhar Sunderraman. "Description Logic Programs: A Paraconsistent Relational Model Approach." In Lecture Notes in Computer Science, 139–57. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-27060-9_12.

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Başkent, Can. "Public Announcements and Inconsistencies: For a Paraconsistent Topological Model." In Logic, Epistemology, and the Unity of Science, 251–68. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-26506-3_9.

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Tarafder, Sourav. "Ordinals in an Algebra-Valued Model of a Paraconsistent Set Theory." In Logic and Its Applications, 195–206. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-45824-2_14.

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Conference papers on the topic "Paraconsistent modal logics":

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Kamide, Norihiro, and Yoni Zohar. "Finite Model Property for Modal Ideal Paraconsistent Four-Valued Logic." In 2019 IEEE 49th International Symposium on Multiple-Valued Logic (ISMVL). IEEE, 2019. http://dx.doi.org/10.1109/ismvl.2019.00029.

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Yan, Fei, Huanguo Zhang, Lina Wang, and Min Yang. "An improved intrusion detection model based on paraconsistent logic." In Asia-Pacific Optical Communications, edited by S. J. Ben Yoo, Gee-Kung Chang, Guangcheng Li, and Kwok-wai Cheung. SPIE, 2005. http://dx.doi.org/10.1117/12.574963.

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Kirilo, Caique Z., Jair M. Abe, Marcelo Nogueira, Kazumi Nakamatsu, Luiz Carlos Machi Lozano, and Luiz A. de Lima. "Evaluation Of Adherence To The Model Six Sigma Using Paraconsistent Logic." In 2018 Innovations in Intelligent Systems and Applications (INISTA). IEEE, 2018. http://dx.doi.org/10.1109/inista.2018.8466287.

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Pena, Eduardo H. M., Sylvio Barbon, Joel J. P. C. Rodrigues, and Mario Lemes Proenca. "Anomaly detection using digital signature of network segment with adaptive ARIMA model and Paraconsistent Logic." In 2014 IEEE Symposium on Computers and Communication (ISCC). IEEE, 2014. http://dx.doi.org/10.1109/iscc.2014.6912503.

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Porubay, Oksana. "MAKING MANAGEMENT DECISIONS OF THE ELECTRIC POWER SYSTEM USING THE PARACONSISTENCY LOGICAL MODEL OF THE EXPERT SYSTEM (PESPAL2V)." In CAD/EDA/SIMULATION IN MODERN ELECTRONICS 2021. Bryansk State Technical University, 2021. http://dx.doi.org/10.30987/conferencearticle_61c997ef1fd468.69147282.

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This article describes an expert system that is designed and developed for a certain and limited application of human knowledge. Equipped with an information base, it is able to make decisions based on reasonable knowledge. At the same time, the algorithms from which the computational program of the expert system consist, represent knowledge from the area they should analyze and help solve problems.

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