Статті в журналах: "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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2

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.

3

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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CARNIELLI, WALTER, MARCELO E. CONIGLIO, RODRIGO PODIACKI, and TARCÍSIO RODRIGUES. "ON THE WAY TO A WIDER MODEL THEORY: COMPLETENESS THEOREMS FOR FIRST-ORDER LOGICS OF FORMAL INCONSISTENCY." Review of Symbolic Logic 7, no. 3 (June 3, 2014): 548–78. http://dx.doi.org/10.1017/s1755020314000148.

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AbstractThis paper investigates the question of characterizing first-orderLFIs (logics of formal inconsistency) by means of two-valued semantics.LFIs are powerful paraconsistent logics that encode classical logic and permit a finer distinction between contradictions and inconsistencies, with a deep involvement in philosophical and foundational questions. Although focused on just one particular case, namely, the quantified logicQmbC, the method proposed here is completely general for this kind of logics, and can be easily extended to a large family of quantified paraconsistent logics, supplying a sound and complete semantical interpretation for such logics. However, certain subtleties involving term substitution and replacement, that are hidden in classical structures, have to be taken into account when one ventures into the realm of nonclassical reasoning. This paper shows how such difficulties can be overcome, and offers detailed proofs showing that a smooth treatment of semantical characterization can be given to all such logics. Although the paper is well-endowed in technical details and results, it has a significant philosophical aside: it shows how slight extensions of classical methods can be used to construct the basic model theory of logics that are weaker than traditional logic due to the absence of certain rules present in classical logic. Several such logics, however, as in the case of theLFIs treated here, are notorious for their wealth of models precisely because they do not make indiscriminate use of certain rules; these models thus require new methods. In the case of this paper, by just appealing to a refined version of the Principle of Explosion, or Pseudo-Scotus, some new constructions and crafty solutions to certain nonobvious subtleties are proposed. The result is that a richer extension of model theory can be inaugurated, with interest not only for paraconsistency, but hopefully to other enlargements of traditional logic.

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Kamide, Norihiro, and Daiki Koizumi. "Method for Combining Paraconsistency and Probability in Temporal Reasoning." Journal of Advanced Computational Intelligence and Intelligent Informatics 20, no. 5 (September 20, 2016): 813–27. http://dx.doi.org/10.20965/jaciii.2016.p0813.

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Computation tree logic (CTL) is known to be one of the most useful temporal logics for verifying concurrent systems by model checking technologies. However, CTL is not sufficient for handling inconsistency-tolerant and probabilistic accounts of concurrent systems. In this paper, a paraconsistent (or inconsistency-tolerant) probabilistic computation tree logic (PpCTL) is derived from an existing probabilistic computation tree logic (pCTL) by adding a paraconsistent negation connective. A theorem for embedding PpCTL into pCTL is proven, thereby indicating that we can reuse existing pCTL-based model checking algorithms. A relative decidability theorem for PpCTL, wherein the decidability of pCTL implies that of PpCTL, is proven using this embedding theorem. Some illustrative examples involving the use of PpCTL are also presented.

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Schwind, Nicolas, Sébastien Konieczny, and Ramón Pino Pérez. "On Paraconsistent Belief Revision in LP." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 5 (June 28, 2022): 5879–87. http://dx.doi.org/10.1609/aaai.v36i5.20532.

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Belief revision aims at incorporating, in a rational way, a new piece of information into the beliefs of an agent. Most works in belief revision suppose a classical logic setting, where the beliefs of the agent are consistent. Moreover, the consistency postulate states that the result of the revision should be consistent if the new piece of information is consistent. But in real applications it may easily happen that (some parts of) the beliefs of the agent are not consistent. In this case then it seems reasonable to use paraconsistent logics to derive sensible conclusions from these inconsistent beliefs. However, in this context, the standard belief revision postulates trivialize the revision process. In this work we discuss how to adapt these postulates when the underlying logic is Priest's LP logic, in order to model a rational change, while being a conservative extension of AGM/KM belief revision. This implies, in particular, to adequately adapt the notion of expansion. We provide a representation theorem and some examples of belief revision operators in this setting.

14

Béziau, Jean-Yves. "Paraconsistent logic from a modal viewpoint." Journal of Applied Logic 3, no. 1 (March 2005): 7–14. http://dx.doi.org/10.1016/j.jal.2004.07.009.

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Huang, Shasha, Jing Hao, and Dang Luo. "Incoherency Problems in a Combination of Description Logics and Rules." Journal of Applied Mathematics 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/604753.

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A paraconsistent semantics has been presented for hybrid MKNF knowledge bases—a combination method for description logics and rules. However, it is invalid when incoherency occurs in the knowledge base. In this paper, we introduce a semi-S5semantics for hybrid MKNF knowledge bases on the basis of nine-valued lattice, such that it is paraconsistent for incoherent knowledge base. It is shown that a semi-S5model can be computed via a fixpoint operator and is in fact a paraconsistent MKNF model when the knowledge base is incoherent. Moreover, we apply six-valued lattice to hybrid MKNF knowledge bases and present a suspicious semantics to distinguish different trust level information. At last, we investigate the relationship between suspicious semantics and paraconsistent semantics.

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BAGAI, RAJIV, and RAJSHEKHAR SUNDERRAMAN. "COMPUTING THE WELL-FOUNDED MODEL OF DEDUCTIVE DATABASES." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 04, no. 02 (April 1996): 157–75. http://dx.doi.org/10.1142/s021848859600010x.

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The well-founded model is one of the most popular models of general logic programs, i.e. logic programs with negation in the bodies of clauses. We present a method for constructing this model for general deductive databases, which are logic programs without any function symbols. The method adopts paraconsistent relations as the semantic objects associated with the predicate symbols of the database. Paraconsistent relations are a generalization of ordinary relations in that they allow manipulation of incomplete as well as inconsistent information. The first step in the model construction method is to transform the database clauses into paraconsistent relation definitions involving these operators. The second step is to build the well-founded model iteratively. Algorithms for both steps are presented and their termination and correctness is also established.

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Esser, Olivier. "A Strong Model of Paraconsistent Logic." Notre Dame Journal of Formal Logic 44, no. 3 (July 2003): 149–56. http://dx.doi.org/10.1305/ndjfl/1091030853.

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Apostoli, Peter. "Modal Aggregation and the Theory of Paraconsistent Filters." Mathematical Logic Quarterly 42, no. 1 (1996): 175–90. http://dx.doi.org/10.1002/malq.19960420115.

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Mendonça, Bruno R., and Walter A. Carnielli. "Fraïssé’s theorem for logics of formal inconsistency." Logic Journal of the IGPL 28, no. 5 (November 29, 2018): 1060–72. http://dx.doi.org/10.1093/jigpal/jzy073.

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Abstract We prove that the minimal Logic of Formal Inconsistency (LFI) $\mathsf{QmbC}$ (basic quantified logic of formal inconsistency) validates a weaker version of Fraïssé’s theorem (FT). LFIs are paraconsistent logics that relativize the Principle of Explosion only to consistent formulas. Now, despite the recent interest in LFIs, their model-theoretic properties are still not fully understood. Our aim in this paper is to investigate the situation. Our interest in FT has to do with its fruitfulness; the preservation of FT indicates that a number of other classical semantic properties can be also salvaged in LFIs. Further, given that FT depends on truth-functionality (a property that, in general, fails in LFIs), whether full FT holds for $\mathsf{QmbC}$ becomes a challenging question.

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João Inácio da Silva Filho. "Application of Shannon Entropy in the Construction of a Paraconsistent Model of the Atom." JOURNAL OF ADVANCES IN PHYSICS 18 (October 11, 2020): 78–113. http://dx.doi.org/10.24297/jap.v18i.8873.

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In this paper, we present a model of the atom that is based on a nonclassical logic called paraconsistent logic (PL), which has the main property of accepting the contradiction in logical interpretations without the conclusions being annulled. The proposed model is constructed with an extension of PL called paraconsistent annotated logic with annotation of two values (PAL2v), which is associated with an interlaced lattice of four vertices. We use the logarithmic function of the Shannon entropy H(s) to construct the paraconsistent equations and thus adopt a probabilistic model for representations in quantum physics. Through analyses of the interlaced lattice, comparative values are obtained for some of the phenomena and effects of quantum mechanics, such as superposition of states, wave functions, and equations that determine the energy levels of the atomic shells of an atom. At the end of this article, we use the hydrogen atom as a basis for the representation of the PAL2v model, where the values of the energy levels in six orbital shells are obtained. As an example, we present a possible method of applying the PAL2v model to the use of Raman spectroscopy signals in the detection of lubricating mineral oil quality.

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Martinez, Angel Antonio Gonzalez, Irenilza de Alencar Nääs, Thayla Morandi Ridolfi de Carvalho-Curi та Jair Minoro Abe. "Applying Paraconsistent Annotated Logic Eτ for Optimizing Broiler Housing Conditions". AgriEngineering 6, № 2 (6 травня 2024): 1252–65. http://dx.doi.org/10.3390/agriengineering6020071.

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Broilers are particularly sensitive to heat stress, which can impair growth, and lower conversion efficiency and survival rates. Under a climate change scenario, maintaining optimal thermal conditions within broiler houses becomes more complex and energy-intensive. Climate change can worsen air quality issues inside broiler houses by increasing the concentration of harmful gases, and proper mechanical ventilation systems are essential for diluting and removing these gases. The present study aimed to develop and validate a model for the ideal broiler housing strategy by applying the Paraconsistent Annotated Evidential Logic Eτ. A database from four broiler houses in a commercial farm, rearing 157,700 birds from the 1st to the 42nd day of growth, was used in the research. All environmental data were recorded weekly inside the houses, and on day 42, flock mortality, overall feed-to-gain ratio, and body weight were calculated and registered. The Cohen’s Kappa statistics for each environmental parameter classification compared to the paraconsistent classification. Results indicated that temperature shows good agreement, relative humidity shows slight agreement, air velocity presents a good agreement, CO2 concentration has a slight agreement, and NH3 concentration is classified by slight agreement. The environmental and productivity variables as a function of the broiler age using the extreme True paraconsistent state indicate the model validation. The paraconsistent analysis presented the ideal scenario for broilers’ growth, maintaining the environmental variables level within a particular threshold and providing greater profit to broiler farmers.

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Shalack, Vladimir I. "On the origins of logical pluralism." Philosophy Journal 15, no. 4 (November 29, 2022): 88–97. http://dx.doi.org/10.21146/2072-0726-2022-15-4-88-97.

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The article presents a brief analysis of how the existence of various logics became possible. This is shown on the example of such well-known logical theories as syllogistics, temporal, multivalued, intuitionistic, paraconsistent and quantum logics. Each of them arose not on someone’s whim, but to solve specific problems. They are based on the most general ontological assumptions about the subject area under study. In formal logic ontological assumptions are refined in the concept of a model structure. Since it is impossible to talk about logic in isolation from the language used, the most general epistemic assumptions about the nature of the relationship of linguistic expressions to those objects of extralinguistic reality that they represent are also accepted. One of the most important of these relationships is the concept of the truth of sentences, which was first formulated by Plato and Aristotle. Taking certain ontological and epistemic assumptions depending on the problem being solved, we obtain different logics. Process logic is primarily characterized by special ontological assumptions that are fundamentally different from the assumptions of other currently existing logics. The ontology of processes is an ontology of developing processes, not things. Historically, it was most vividly described in the writings of Heraclitus. In the overwhelming majority of modern approaches to the description of processes, we see attempts to reduce them to sequences of states, which devalues the very concept of a process, just as a cinematic picture of the flow of time devalues the concept of time. Since logics are built on the basis of various ontological and epistemic assumptions, they are inherently theories of these accepted assumptions, and not universal reasoning tools that don’t depend on the characteristics of the study area and the categories of linguistic expressions. Universal logic is possible if one rises from the level of specific languages to a higher level of sign theory.

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GAO, TIANTIAN, PAUL FODOR, and MICHAEL KIFER. "Paraconsistency and word puzzles." Theory and Practice of Logic Programming 16, no. 5-6 (September 2016): 703–20. http://dx.doi.org/10.1017/s1471068416000326.

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AbstractWord puzzles and the problem of their representations in logic languages have received considerable attention in the last decade (Ponnuruet al. 2004; Shapiro 2011; Baral and Dzifcak 2012; Schwitter 2013). Of special interest is the problem of generating such representations directly from natural language (NL) or controlled natural language (CNL). An interesting variation of this problem, and to the best of our knowledge, scarcely explored variation in this context, is when the input information is inconsistent. In such situations, the existing encodings of word puzzles produce inconsistent representations and break down. In this paper, we bring the well-known type of paraconsistent logics, calledAnnotated Predicate Calculus(APC) (Kifer and Lozinskii 1992), to bear on the problem. We introduce a new kind of non-monotonic semantics for APC, calledconsistency preferred stable modelsand argue that it makes APC into a suitable platform for dealing with inconsistency in word puzzles and, more generally, in NL sentences. We also devise a number of general principles to help the user choose among the different representations of NL sentences, which might seem equivalent but, in fact, behave differently when inconsistent information is taken into account. These principles can be incorporated into existing CNL translators, such as Attempto Controlled English (ACE) (Fuchset al. 2008) and PENG Light (White and Schwitter 2009). Finally, we show that APC with the consistency preferred stable model semantics can be equivalently embedded in ASP with preferences over stable models, and we use this embedding to implement this version of APC in Clingo (Gebseret al. 2011) and its Asprin add-on (Brewkaet al. 2015).

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Kamide, Norihiro, and Yoni Zohar. "Modal extension of ideal paraconsistent four-valued logic and its subsystem." Annals of Pure and Applied Logic 171, no. 10 (December 2020): 102830. http://dx.doi.org/10.1016/j.apal.2020.102830.

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Iakovleva, Varvara. "Penalty Logic: Paraconsistency and Applications." Логико-философские штудии, no. 1 (September 15, 2021): 110–11. http://dx.doi.org/10.52119/lphs.2021.34.37.007.

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Penalty logic is a non-classical non-monotonic logic which allows us to demonstrate the power of belief, the level of truth or the reliability of data that we are using. This logic can be useful to model human reasoning or to replace the penalty function in the sphere of Machine Learning. We can also talk about paraconsistency of this logic and suggest the definition of contradiction without negation.

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López Astorga, Miguel. "Jaina logic: a model-based analysis of the seven predications." Círculo de Lingüística Aplicada a la Comunicación 95 (September 18, 2023): 207–14. http://dx.doi.org/10.5209/clac.77136.

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A relevant part of Jainism is its logic. Jaina logic gives tools to communicate and argue. However, it is problematic from the western perspective: it seems to be a paraconsistent system, that is, a system in which a fact and the denial of that very fact can be true at once. Those difficulties have been overtaken from interpretations that ignore classical standard logic and assess Jaina logic from a point of view more linked to reasoning and the real use of natural language. One of those interpretations have resorted to the theory of mental models, and that interpretation is the one the present paper develops. This is because the theory of mental models has been updated and, hence, any relation provided between Jaina logic and this last theory should be updated as well.

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LÖWE, BENEDIKT, and SOURAV TARAFDER. "GENERALIZED ALGEBRA-VALUED MODELS OF SET THEORY." Review of Symbolic Logic 8, no. 1 (January 12, 2015): 192–205. http://dx.doi.org/10.1017/s175502031400046x.

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AbstractWe generalize the construction of lattice-valued models of set theory due to Takeuti, Titani, Kozawa and Ozawa to a wider class of algebras and show that this yields a model of a paraconsistent logic that validates all axioms of the negation-free fragment of Zermelo-Fraenkel set theory.

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Méndez, José M., and Gemma Robles. "Strengthening Brady’s Paraconsistent 4-Valued Logic BN4 with Truth-Functional Modal Operators." Journal of Logic, Language and Information 25, no. 2 (March 1, 2016): 163–89. http://dx.doi.org/10.1007/s10849-016-9237-8.

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Da Silva Filho, João Inácio, Raphael Adamelk Bispo de Oliveira, Marcos Carneiro Rodrigues, Hyghor Miranda Côrtes, Alexandre Rocco, Mauricio Conceição Mario, Dorotéa Vilanova Garcia, et al. "Predictive Controller Based on Paraconsistent Annotated Logic for Synchronous Generator Excitation Control." Energies 16, no. 4 (February 15, 2023): 1934. http://dx.doi.org/10.3390/en16041934.

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This study presents a new Model Predictive Controller (MPC), built with algorithms based on Paraconsistent Annotated Logic (PAL), with application examples in the excitation control of a synchronous generator. PAL is a non-classical evidential and propositional logic that is associated with a Hasse lattice, and which presents the property of accepting the contradiction in its foundations. In this research, the algorithm was constructed with a version of the PAL that works with two information signals in the degrees of evidence format and, therefore, is called Paraconsistent Annotated Logic with annotation of two values (PAL2v). For the validation of the algorithmic structure, the computational tool MATLAB® Release 2012b, The MathWorks, Inc., Natick, MA, United States was used. Simulations were performed which compared the results obtained with PPC-PAL2v to those obtained in essays with the AVR (Automatic Voltage Regulator) controls in conjunction with the PSS (Power System Stabilizer) and the conventional MPC of fixed weights. The comparative results showed the PPC-PAL2v to display superior performance in the action of the excitation control of the synchronous generator, with a great efficiency in response to small signals.

30

Priest, Graham. "Contradiction and the Instant of Change Revisited." Vivarium 55, no. 1-3 (July 14, 2017): 217–26. http://dx.doi.org/10.1163/15685349-12341337.

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Instantaneous changes may well be thought to give rise to contradiction. If one endorses an explosive logic, where contradictions entail everything, this is entirely unacceptable. However, if one deploys a paraconsistent logic, which keeps contradictions under control, one may give perfectly coherent and precise models of such changes. In In Contradiction the author showed how and he explored the philosophical implications of the model. Here, the author revisits the issue in the light of a recent critique by Greg Littmann.

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Sedlár, Igor, and Vít Punčochář. "From positive PDL to its non-classical extensions." Logic Journal of the IGPL 27, no. 4 (May 28, 2019): 522–42. http://dx.doi.org/10.1093/jigpal/jzz017.

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AbstractWe provide a complete binary implicational axiomatization of the positive fragment of propositional dynamic logic (PDL). The intended application of this result are completeness proofs for non-classical extensions of positive PDL. Two examples are discussed in this article, namely, a paraconsistent extension with modal De Morgan negation and a substructural extension with the residuated operators of the non-associative Lambek calculus. Informal interpretations of these two extensions are outlined.

32

Chen, Donghuo, and Jinzhao Wu. "Model Checking Temporal Aspects of Inconsistent Concurrent Systems Based on Paraconsistent Logic." Electronic Notes in Theoretical Computer Science 157, no. 1 (May 2006): 23–38. http://dx.doi.org/10.1016/j.entcs.2006.01.021.

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33

Rusu, Andrei, and Elena Rusu. "On some classes of formulas in S5 which are pre-complete relative to existential expressibility." Computer Science Journal of Moldova 31, no. 3(93) (December 2023): 395–408. http://dx.doi.org/10.56415/csjm.v31.21.

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Existential expressibility for all k-valued functions was proposed by A. V. Kuznetsov and later was investigated in more details by S. S. Marchenkov. In the present paper, we consider existential expressibility in the case of formulas defined by a logical calculus and find out some conditions for a system of formulas to be closed relative to existential expressibility. As a consequence, it has been established some pre-complete as to existential expressibility classes of formulas in some finite extensions of the paraconsistent modal logic S5.

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Mario, Mauricio Conceição, Dorotéa Vilanova Garcia, João Inácio da Silva Filho, Landulfo Silveira Júnior, and Heraldo Silveira Barbuy. "Characterization and classification of numerical data patterns using Annotated Paraconsistent Logic and the effect of contradiction." Research, Society and Development 10, no. 13 (October 22, 2021): e283101320830. http://dx.doi.org/10.33448/rsd-v10i13.20830.

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This work describes the development of a computational mathematical model that uses Annotated Paraconsistent Logic - APL and a concept derived from it, the effect of contradiction, to identify patterns in numerical data for pattern classification purposes. The APL admits paraconsistent and paracomplete logical principles, which allow the manipulation of inconsistent and contradictory data, and its use allowed the identification and quantization of the attribute related to the contradiction. To validate the model, series of Raman spectroscopies obtained after exposure of proteins, lipids and nucleic acids, collected from cutaneous tissue cell samples previously examined for the detection of cancerous lesions, identified as basal carcinoma, melanoma and normal, were used. Initially, the attributes related to contradiction, derivative and median obtained from spectroscopies were identified and quantified. A machine learning process with approximately 31.6% of each type of samples detects a sequence of spectroscopies capable of characterizing and classifying the type of lesion through the chosen attributes. Approximately 68.4% of the samples are used for classification tests. The proposed model identified a segment of spectroscopies where the classification of test samples had a hit rate of 76.92%. As a differential and innovation of this work, the use of APL principles in a complete process of training, learning and classification of patterns for numerical data sets stands out, with flexibility to choose the attributes used for the characterization of patterns, and a quantity of samples of about one third of the total required for characterization.

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Apostoli, Peter, and Bryson Brown. "A solution to the completeness problem for weakly aggregative modal logic." Journal of Symbolic Logic 60, no. 3 (September 1995): 832–42. http://dx.doi.org/10.2307/2275759.

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We are accustomed to regarding K as the weakest modal logic admitting of a relational semantics in the style made popular by Kripke. However, in a series of papers which demonstrates a startling connection between modal logic and the theory of paraconsistent inference, Ray Jennings and Peter Schotch have developed a generalized relational frame theory which articulates an infinite hierarchy of sublogics of K, each expressing a species of “weakly aggregative necessity”. Recall that K is axiomatized, in the presence of N and RM, by the schema of “binary aggregation”For each n ≥ 1, the weakly aggregative modal logic Kn is axiomatized by replacing K with the schema of “n-ary aggregation”which is an n-ary relaxation, or weakening, of K. Note that K1 = K.In [3], the authors claim without proof that Kn is determined by the class of frames F = (W, R), where W is a nonempty set and R is an (n + 1)-ary relation on W, under the generalization of Kriple's truth condition according to which □α is true at a point w in W if and only if α is true at one of x1,…,xn for all x1,…, xn in W such that Rw, x1,…, xn.

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Puga, Leila Z., Newton C. A. Da Costa, and Roberto J. Vernengo. "Lógicas normativas, moral y derecho." Crítica (México D. F. En línea) 23, no. 69 (December 13, 1991): 27–59. http://dx.doi.org/10.22201/iifs.18704905e.1991.811.

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The relationships between moral and legal codes, that is, between specific normative sets, is a traditional problem of ethics, politics and law philosophy. Deontic logics have provided some instruments for a deeper analysis of those relations. The authors try to analyze the logical consequences of the adoption of different axiomaticallogical systems, where deontic modalities are introduced as expressing different senses of moral or legal obligation, prohibition, permission, etc. It tums out, as a result of the analysis , that sorne very traditional thesis about the relationships between law and moral presuppose different logical requirements, some of which are not only interesting from a pure formal point of view, but also as an essay in a rational analysis of normative discourse. Different types of logics, specially sorne called bidimensional deontic systems, are investigated, as sorne mixed alethic-deontic and paraconsistent systems are sketched, Contraintuitive consequences and paradoxes deriving Crom those logical presuppositions are described and their consequences in ethical thinking are underlined. The paper' s purpose is to attain a better understanding of sorne informal ethical notions through the construction of formal systems expressing with sorne precision the very vague notions that sometimes are behind accepted legal or moral conceptions. Thus, the authors think, it would be possible a progressive aproximation to a better analysis of sorne important presuppositions of ethical discourse, a discourse where morals and law have an essential part to play. [Roberto Vemengo]

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Da Silva Filho, João Inácio. "Undulatory Theory with Paraconsistent Logic (Part I): Quantum Logical Model with Two Wave Functions." Journal of Quantum Information Science 06, no. 03 (2016): 143–80. http://dx.doi.org/10.4236/jqis.2016.63012.

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38

K., Veerasamy, and E. J. Thomson Fredrik. "Intelligent Farming based on Uncertainty Expert System with Butterfly Optimization Algorithm for Crop Recommendation." Journal of Internet Services and Information Security 13, no. 4 (December 2, 2023): 158–69. http://dx.doi.org/10.58346/jisis.2023.i4.011.

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Meeting the current population's food demands has become challenging, given the rising population, frequent climate fluctuations, and limited resources. Smart farming, also known as precision agriculture, has emerged as an advanced approach to tackle modern challenges in crop production. At the heart of this cutting-edge technology is machine learning, serving as the driving force behind its implementation. Though, there are many algorithms are available in crop prediction process, the problem of predicting vague information is still a challenging issue. Unfortunately, existing algorithms mostly avoids the complicated instances in crop recommendation dataset by not handling them effectively, due to imbalance class distribution. Hence in this research work to conduct an intelligent farming, two different uncertain theories are adopted to handle the issue of vagueness in appropriate recommendation of crop by considering soil fertility and climatic condition. The proposed is developed based on uncertainty expert system with both neutrosophicalparaconsistent inference model. The neutrosophic inference model is integrated with the paraconsistent logic to overcome the problem of uncertainty in prediction of appropriate crop by representing the factors in terms of certainty degree and contradiction degree. The rule generated by paraconsistent model is validated to improve the accuracy of crop prediction by fusing the knowledge of butterfly optimization algorithm. The nectar searching behavior of the butterflies are used for searching potential rules as a validation process. With the pruned rules generated by uncertainty expert model, the suitable crop is predicted more accurately compared to the other existing prediction models.

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Dos Santos, Denis Medeiros, João Inácio da Silva Filho, Carlos Teofilo Salinas Sedano, and Mauricio Conceição Mario. "Desenvolvimento de um Modelo em Lógica Paraconsistente para Monitoração de Bombas Centrifugas durante a Operação de uma Refinaria de Petróleo / Development of a Paraconsistent Logic Model for Monitoring Centrifugal Pumps during the Operation of an Oil Refinery." Brazilian Journal of Development 7, no. 12 (December 29, 2021): 118653–73. http://dx.doi.org/10.34117//bjdv7n12-568.

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40

Zamberlan, Miguel Fabrício, and Carolina Yukari Veludo Watanabe. "The adoption of an indicator panel in educational management to decision-making support." International Journal for Innovation Education and Research 8, no. 6 (June 1, 2020): 266–90. http://dx.doi.org/10.31686/ijier.vol8.iss6.2411.

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The use of technology to assist in the performance of daily activities and to carry out communication between individuals has become a necessary task in the face of technological advances. In the context of public institutions, the insertion of technology is also based on the possibilities of making the activities of this sector more efficient and better quality, in addition to allowing greater transparency and accessibility of information for society. For public managers, the information and communication technology tools allow for a more accurate assessment of the variables and possibilities involved in a decision-making process and, thus, to make better decisions in a sector whose main customer is society (users). Therefore, this paper aimed to analyze the use and acceptance of a decision support tool in a public educational institution called the Indicators Panel. For this, the Unified Theory of Acceptance and Use of Technology (UTAUT) was used, and the results were measured using the paraconsistent logic. The results indicate that it is possible to consider the use and acceptance of the decision support system in the public educational institution by reducing the propositions of the UTAUT Model in three factors: Usability, Performance, and Relationship. Regarding the UTAUT Model, it was found that the moderating variables of gender, age, and experience do not significantly influence the adoption of the decision support system. It is important to note that managers point the tool as very important for the development of their activities and emphasize that ease of use is one of the main points for the adoption of technology.

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Mruczek-Nasieniewska, Krystyna, Yaroslav Petrukhin, and Vasilyi Shangin. "On Paracomplete Versions of Jaśkowski's Discussive Logic." Bulletin of the Section of Logic, January 4, 2024. http://dx.doi.org/10.18778/0138-0680.2024.01.

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Jaśkowski's discussive (discursive) logic D2 is historically one of the first paraconsistent logics, i.e., logics which 'tolerate' contradictions. Following Jaśkowski's idea to define his discussive logic by means of the modal logic S5 via special translation functions between discussive and modal languages, and supporting at the same time the tradition of paracomplete logics being the counterpart of paraconsistent ones, we present a paracomplete discussive logic D2p.

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CARNIELLI, WALTER, MARCELO E. CONIGLIO, and DAVID FUENMAYOR. "LOGICS OF FORMAL INCONSISTENCY ENRICHED WITH REPLACEMENT: AN ALGEBRAIC AND MODAL ACCOUNT." Review of Symbolic Logic, July 2, 2021, 1–36. http://dx.doi.org/10.1017/s1755020321000277.

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Abstract It is customary to expect from a logical system that it can be algebraizable, in the sense that an algebraic companion of the deductive machinery can always be found. Since the inception of da Costa’s paraconsistent calculi, algebraic equivalents for such systems have been sought. It is known, however, that these systems are not self-extensional (i.e., they do not satisfy the replacement property). More than this, they are not algebraizable in the sense of Blok–Pigozzi. The same negative results hold for several systems of the hierarchy of paraconsistent logics known as Logics of Formal Inconsistency (LFIs). Because of this, several systems belonging to this class of logics are only characterizable by semantics of a non-deterministic nature. This paper offers a solution for two open problems in the domain of paraconsistency, in particular connected to algebraization of LFIs, by extending with rules several LFIs weaker than $C_1$ , thus obtaining the replacement property (that is, such LFIs turn out to be self-extensional). Moreover, these logics become algebraizable in the standard Lindenbaum–Tarski’s sense by a suitable variety of Boolean algebras extended with additional operations. The weakest LFI satisfying replacement presented here is called RmbC, which is obtained from the basic LFI called mbC. Some axiomatic extensions of RmbC are also studied. In addition, a neighborhood semantics is defined for such systems. It is shown that RmbC can be defined within the minimal bimodal non-normal logic $\mathbf {E} {\oplus } \mathbf {E}$ defined by the fusion of the non-normal modal logic E with itself. Finally, the framework is extended to first-order languages. RQmbC, the quantified extension of RmbC, is shown to be sound and complete w.r.t. the proposed algebraic semantics.

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Ramos, Jaime, João Rasga, and Cristina Sernadas. "Labelled proof systems for existential reasoning." Logic Journal of the IGPL, January 30, 2024. http://dx.doi.org/10.1093/jigpal/jzad030.

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Abstract Usually in logic, proof systems are defined having in mind proving properties like validity and semantic consequence. It seems worthwhile to address the problem of having proof systems where satisfiability is a primitive notion in the sense that a formal derivation means that a finite set of formulas is satisfiable. Moreover, it would be useful to cover within the same framework as many logics as possible. We consider Kripke semantics where the properties of the constructors are provided by valuation constraints as the common ground of those logics. This includes for instance intuitionistic logic, paraconsistent Nelson’s logic ${\textsf{N4}}$, paraconsistent logic ${\textsf{imbC}}$ and modal logics among others. After specifying a logic by those valuation constraints, we show how to induce automatically and from scratch an existential proof system for that logic. The rules of the proof system are shown to be invertible. General results of soundness and completeness are proved and then applied to the logics at hand.

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Degauquier, Vincent. "Useful Four-Valued Extension of the Temporal Logic KtT4." Bulletin of the Section of Logic 47, no. 1 (March 30, 2018). http://dx.doi.org/10.18778/0138-0680.47.1.02.

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The temporal logic KtT4 is the modal logic obtained from the minimal temporal logic Kt by requiring the accessibility relation to be reflexive (which corresponds to the axiom T) and transitive (which corresponds to the axiom 4). This article aims, firstly, at providing both a model-theoretic and a proof-theoretic characterisation of a four-valued extension of the temporal logic KtT4 and, secondly, at identifying some of the most useful properties of this extension in the context of partial and paraconsistent logics.

45

Bílková, Marta, Sabine Frittella, and Daniil Kozhemiachenko. "Fuzzy bi-Gödel modal logic and its paraconsistent relatives." Journal of Logic and Computation, March 31, 2024. http://dx.doi.org/10.1093/logcom/exae011.

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Abstract We present an axiomatization of the fuzzy bi-Gödel modal logic ${\textbf{K}\textsf{biG}}^{\textsf{f}}$ formulated in the language containing $\triangle $ (Baaz Delta operator) and treating $-\!-\!< $ (co-implication) as the defined connective. We also consider two paraconsistent relatives of ${\textbf{K}\textsf{biG}}^{\textsf{f}}$ — $\textbf{K}\textsf{G}^{2\pm \textsf{f}}$ and $\textsf{G}^{2\pm \textsf{f}}_{\blacksquare ,\blacklozenge }$. These logics are defined on fuzzy frames with two valuations $e_{1}$ and $e_{2}$ standing for the support of truth and falsity, respectively, and equipped with two fuzzy relations$R^{+}$ and $R^{-}$ used to determine supports of truth and falsity of modal formulas. We construct embeddings of $\textbf{K}\textsf{G}^{2\pm \textsf{f}}$ and $\textsf{G}^{2\pm \textsf{f}}_{\blacksquare ,\blacklozenge }$ into ${\textbf{K}\textsf{biG}}^{\textsf{f}}$ and use them to obtain the characterization of $\textbf{K}\textsf{G}^{2}$- and $\textsf{G}^{2}_{\blacksquare ,\blacklozenge }$-definable frames. Moreover, we study the transfer of ${\textbf{K}\textsf{biG}}^{\textsf{f}}$ formulas into $\textbf{K}\textsf{G}^{2\pm \textsf{f}}$, i.e., formulas that are ${\textbf{K}\textsf{biG}}^{\textsf{f}}$-valid on mono-relational frames $\mathfrak{F}$ and $\mathfrak{F}^{\prime}$ iff they are $\textbf{K}\textsf{G}^{2\pm \textsf{f}}$-valid on their bi-relational counterparts. Finally, we establish $\textsf{PSpace}$-completeness of all considered logics.

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Gouveia, Paula, João Rasga, and Cristina Sernadas. "Meet-Combination of Consequence Systems." Logic and Logical Philosophy, May 29, 2024, 1–36. http://dx.doi.org/10.12775/llp.2024.017.

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We extend meet-combination of logics for capturing the consequences that are common to both logics. With this purpose in mind we define meet-combination of consequence systems. This notion has the advantage of accommodating different ways of presenting the semantics and the deductive calculi. We consider consequence systems generated by a matrix semantics and consequence systems generated by Hilbert calculi. The meet-combination of consequence systems generated by matrix semantics is the consequence system generated by their product. On the other hand, the meet-combination of consequence systems generated by Hilbert calculi is the consequence system generated by their interconnection. We investigate preservation of several properties. Capitalizing on these results we show that interconnection provides an axiomatization for the product. Illustrations are given for intuitionistic and modal logics, Łukasiewicz logic and some paraconsistent logics.

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Skura, Tomasz. "Refutations and Proofs in the Paraconsistent Modal Logics: KN4 and KN4.D." Studia Logica, April 25, 2024. http://dx.doi.org/10.1007/s11225-024-10102-8.

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48

Figallo-Orellano, Aldo, Miguel Peréz-Gaspar, and Juan Manuel Ramírez-Contreras. "Paraconsistent and Paracomplete Logics Based on k-Cyclic Modal Pseudocomplemented De Morgan Algebras." Studia Logica, May 28, 2022. http://dx.doi.org/10.1007/s11225-022-10004-7.

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Mishra, Meha, and A. V. Ravishankar Sarma. "Tolerating Inconsistencies: A Study of Logic of Moral Conflicts." Bulletin of the Section of Logic, June 7, 2022. http://dx.doi.org/10.18778/0138-0680.2022.06.

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Moral conflicts are the situations which emerge as a response to deal with conflicting obligations or duties. In general, an agent in a state of moral conflict, ought to act on two or more events simultaneously, but fails to do all of them at once. An interesting case arises when an agent thinks that two obligations A and B are equally important, but yet fails to choose one obligation over the other. Despite the fact that the systematic study and the resolution of moral conflicts finds prominence in our linguistic discourse, standard deontic logic when used to represent moral conflicts, implies the impossibility of moral conflicts. This presents a conundrum for appropriate logic to address these moral conflicts. We frequently believe that there is a close connection between tolerating inconsistencies and conflicting moral obligations. In paraconsistent logics, we tolerate inconsistencies by treating them to be both true and false. In this paper, we analyze Graham Priest's paraconsistent logic LP, and extending our examination to the deontic extension of LP known as DLP. We illustrate our work with a classic example from the famous Indian epic Mahabharata, where the protagonist Arjuna faces a moral conflict in the battlefield of Kurukshetra. The paper aims to come up with a significant set of principles to accommodate Arjuna's moral conflict in paraconsistent deontic logics. Our analysis is expected to provide novel tools towards the logical representation of moral conflicts and to shed some light on the relationship between the actual world and the context-sensitive ideal world.

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CONIGLIO, MARCELO E., G. T. GOMEZ-PEREIRA, and MARTÍN FIGALLO. "SOME MODEL-THEORETIC RESULTS ON THE 3-VALUED PARACONSISTENT FIRST-ORDER LOGIC QCIORE." Review of Symbolic Logic, December 9, 2019, 1–38. http://dx.doi.org/10.1017/s1755020319000595.

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Abstract The 3-valued paraconsistent logic Ciore was developed by Carnielli, Marcos and de Amo under the name LFI2, in the study of inconsistent databases from the point of view of logics of formal inconsistency (LFIs). They also considered a first-order version of Ciore called LFI2*. The logic Ciore enjoys extreme features concerning propagation and retropropagation of the consistency operator: a formula is consistent if and only if some of its subformulas is consistent. In addition, Ciore is algebraizable in the sense of Blok and Pigozzi. On the other hand, the logic LFI2* satisfies a somewhat counter-intuitive property: the universal and the existential quantifier are inter-definable by means of the paraconsistent negation, as it happens in classical first-order logic with respect to the classical negation. This feature seems to be unnatural, given that both quantifiers have the classical meaning in LFI2*, and that this logic does not satisfy the De Morgan laws with respect to its paraconsistent negation. The first goal of the present article is to introduce a first-order version of Ciore (which we call QCiore) preserving the spirit of Ciore, that is, without introducing unexpected relationships between the quantifiers. The second goal of the article is to adapt to QCiore the partial structures semantics for the first-order paraconsistent logic LPT1 introduced by Coniglio and Silvestrini, which generalizes the semantic notion of quasi-truth considered by Mikeberg, da Costa and Chuaqui. Finally, some important results of classical Model Theory are obtained for this logic, such as Robinson’s joint consistency theorem, amalgamation and interpolation. Although we focus on QCiore, this framework can be adapted to other 3-valued first-order LFIs.

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