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Добірка наукової літератури з теми "Logic, paraconsistency, inconsistent information"

Автор: Grafiati

Опубліковано: 10 грудня 2022

Оновлено: 28 січня 2023

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Статті в журналах з теми "Logic, paraconsistency, inconsistent information"

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. "Inconsistency-Tolerant Multi-Agent Calculus." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 22, no. 06 (December 2014): 815–29. http://dx.doi.org/10.1142/s0218488514500433.

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Verifying and specifying multi-agent systems in an appropriate inconsistency-tolerant logic are of growing importance in Computer Science since computer systems are generally used by or composed of inconsistency-tolerant multi-agents. In this paper, an inconsistency-tolerant logic for representing multi-agents is introduced as a Gentzen-type sequent calculus. This logic (or calculus) has multiple negation connectives that correspond to each agent, and these negation connectives have the property of paraconsistency that guarantees inconsistency-tolerance. The logic proposed is regarded as a modified generalization of trilattice logics, which are known to be useful for expressing fine-grained truth-values in computer networks. The completeness, cut-elimination and decidability theorems for the proposed logic (or sequent calculus) are proved as the main results of this paper.

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Cocos, Cristian, Fahim Imam, and Wendy MacCaull. "Ontology Merging and Reasoning Using Paraconsistent Logics." International Journal of Knowledge-Based Organizations 2, no. 4 (October 2012): 35–51. http://dx.doi.org/10.4018/ijkbo.2012100103.

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Dealing with the inconsistencies that might arise during the ontology merging process constitutes a major challenge. The explosive nature of classical logic requires any logic-based merging effort to dissolve possible contradictions, and thus maintain consistency. In many cases, however, inconsistent information may be useful for intelligent reasoning activities. In healthcare systems, for example, inconsistent information may be required to provide a full clinical perspective, and thus any information loss is undesirable. The authors present a 4-valued logic-based merging system that exhibits inconsistency-tolerant behavior to avoid information loss.

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Grooters, Diana, and Henry Prakken. "Two Aspects of Relevance in Structured Argumentation: Minimality and Paraconsistency." Journal of Artificial Intelligence Research 56 (June 15, 2016): 197–245. http://dx.doi.org/10.1613/jair.5058.

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This paper studies two issues concerning relevance in structured argumentation in the context of the ASPIC+ framework, arising from the combined use of strict and defeasible inference rules. One issue arises if the strict inference rules correspond to classical logic. A longstanding problem is how the trivialising effect of the classical Ex Falso principle can be avoided while satisfying consistency and closure postulates. In this paper, this problem is solved by disallowing chaining of strict rules, resulting in a variant of the ASPIC+ framework called ASPIC*, and then disallowing the application of strict rules to inconsistent sets of formulas. Thus in effect Rescher & Manor's paraconsistent notion of weak consequence is embedded in ASPIC*. Another issue is minimality of arguments. If arguments can apply defeasible inference rules, then they cannot be required to have subset-minimal premises, since defeasible rules based on more information may well make an argument stronger. In this paper instead minimality is required of applications of strict rules throughout an argument. It is shown that under some plausible assumptions this does not affect the set of conclusions. In addition, circular arguments are in the new ASPIC* framework excluded in a way that satisfies closure and consistency postulates and that generates finitary argumentation frameworks if the knowledge base and set of defeasible rules are finite. For the latter result the exclusion of chaining of strict rules is essential. Finally, the combined results of this paper are shown to be a proper extension of classical-logic argumentation with preferences and defeasible rules.

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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.

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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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HUNTER, ANTHONY. "Reasoning with inconsistency in structured text." Knowledge Engineering Review 15, no. 4 (December 2000): 317–37. http://dx.doi.org/10.1017/s0269888900002046.

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Reasoning with inconsistency involves some compromise on classical logic. There is a range of proposals for logics (called paraconsistent logics) for reasoning with inconsistency each with pros and cons. Selecting an appropriate paraconsistent logic for an application depends upon the requirements of the application. Here we review paraconsistent logics for the potentially significant application area of technology for structured text. Structured text is a general concept that is implicit in a variety of approaches to handling information. Syntactically, an item of structured text is a number of grammatically simple phrases together with a semantic label for each phrase. Items of structured text may be nested within larger items of structured text. The semantic labels in a structured text are meant to parameterize a stereotypical situation, and so a particular item of structured text is an instance of that stereotypical situation. Much information is potentially available as structured text, including tagged text in XML, text in relational and object-oriented databases, and the output from information extraction systems in the form of instantiated templates. In this review paper, we formalize the concept of structured text, and then focus on how we can identify inconsistency in items of structured text, and reason with these inconsistencies. Then we review key approaches to paraconsistent reasoning, and discuss the application of them to reasoning with inconsistency in structured text.

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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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Dubois, Didier, and Henri Prade. "Inconsistency Management from the Standpoint of Possibilistic Logic." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 23, Suppl. 1 (December 2015): 15–30. http://dx.doi.org/10.1142/s0218488515400024.

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Uncertainty and inconsistency pervade human knowledge. Possibilistic logic, where propositional logic formulas are associated with lower bounds of a necessity measure, handles uncertainty in the setting of possibility theory. Moreover, central in standard possibilistic logic is the notion of inconsistency level of a possibilistic logic base, closely related to the notion of consistency degree of two fuzzy sets introduced by L. A. Zadeh. Formulas whose weight is strictly above this inconsistency level constitute a sub-base free of any inconsistency. However, several extensions, allowing for a paraconsistent form of reasoning, or associating possibilistic logic formulas with information sources or subsets of agents, or extensions involving other possibility theory measures, provide other forms of inconsistency, while enlarging the representation capabilities of possibilistic logic. The paper offers a structured overview of the various forms of inconsistency that can be accommodated in possibilistic logic. This overview echoes the rich representation power of the possibility theory framework.

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Nakayama, Yotaro, Seiki Akama, and Tetsuya Murai. "Bilattice Logic for Rough Sets." Journal of Advanced Computational Intelligence and Intelligent Informatics 24, no. 6 (November 20, 2020): 774–84. http://dx.doi.org/10.20965/jaciii.2020.p0774.

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Rough set theory is studied to manage uncertain and inconsistent information. Because Pawlak’s decision logic for rough sets is based on the classical two-valued logic, it is inconvenient for handling inconsistent information. We propose a bilattice logic as the deduction basis for the decision logic of rough sets to address inconsistent and ambiguous information. To enhance the decision logic to bilattice semantics, we introduce Variable Precision Rough Set (VPRS). As a deductive basis for bilattice decision logic, we define a consequence relation for Belnap’s four-valued semantics and provide a bilattice semantic tableau TB4 for a deduction system. We demonstrate the soundness and completeness of TB4 and enhance it with weak negation.

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Більше джерел

Дисертації з теми "Logic, paraconsistency, inconsistent information"

Wong, Paul, and paul wong@anu edu au. "Reasoning with Inconsistent Information." The Australian National University. Research School of Information Sciences and Engineering, 2004. http://thesis.anu.edu.au./public/adt-ANU20090611.152017.

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In this thesis we are concerned with developing formal and representational mechanisms for reasoning with inconsistent information. Strictly speaking there are two conceptually distinct senses in which we are interested in reasoning with inconsistent information. In one sense, we are interested in using logical deduction to draw inferences in a symbolic system. More specifically, we are interested in mechanisms that can continue to perform deduction in a reasonable manner despite the threat of inconsistencies as a direct result of errors or misrepresentations. So in this sense we are interested in inconsistency-tolerant or paraconsistent deduction. ¶ However, not every case of inconsistent description is a case of misrepresentation. In many practical situations, logically inconsistent descriptions may be deployed as representations for problems that are inherently conflicting. The issue of error or misrepresentation is irrelevant in these cases. Rather the main concern in these cases is to provide meaningful analyses of the underlying structure and properties of our logical representation which in turn informs us about the salient features of the problem under consideration. So in this second sense, we are interested in deploying logic as a representation to model situations involving conflict. ¶ In this thesis we adopt a novel framework to unify both logic-as-deduction and logic-as-representation approaches to reasoning with inconsistent information. From a preservational view point, we take deduction as a process by which metalogical properties are preserved from premises to conclusions. Thus methodologically we may begin by identifying inconsistency-tolerant deduction mechanisms and then investigate what additional properties of inconsistent premises are preserved by these mechanisms; or alternatively we may begin by identifying properties of inconsistent logical descriptions and investigate which deductive mechanisms can preserve these properties. We view these as two aspects of the same investigation. A key assumption in this work is that adequate analyses of inconsistencies require provisions to quantitatively measure and compare inconsistent logical representations. While paraconsistent logics have enjoyed considerable success in recent years, proper quantitative analysis of inconsistencies seems to have lapsed behind to some extent. In this thesis well explore different ways in which we can compare and measure inconsistencies. We hope to show that both inference and analysis can fruitfully be brought to bear on the issue of inconsistency handling under the same methodological scheme.

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Weber, Stefan. "Investigations in Belnap's Logic of Inconsistent and Unknown Information." Doctoral thesis, Universitätsbibliothek Leipzig, 2004. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-36489.

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Nuel Belnap schlug 1977 eine vierwertige Logik vor, die -- im Gegensatz zur klassischen Logik -- die Faehigkeit haben sollte, sowohl mit widerspruechlicher als auch mit fehlender Information umzugehen. Diese Logik hat jedoch den Nachteil, dass sie Saetze der Form "wenn ..., dann ..." nicht ausdruecken kann. Ausgehend von dieser Beobachtung analysieren wir die beiden nichtklassischen Aspekte, Widerspruechlichkeit und fehlende Information, indem wir eine dreiwertige Logik entwickeln, die mit widerspruechlicher Information umgehen kann und eine Modallogik, die mit fehlender Information umgehen kann. Beide Logiken sind nicht monoton. Wir untersuchen Eigenschaften, wie z.B. Kompaktheit, Entscheidbarkeit, Deduktionstheoreme und Berechnungkomplexitaet dieser Logiken. Es stellt sich heraus, dass die dreiwertige Logik, nicht kompakt und ihre Folgerungsmenge im Allgemeinen nicht rekursiv aufzaehlbar ist. Beschraenkt man sich hingegen auf endliche Formelmengen, so ist die Folgerungsmenge rekursiv entscheidbar, liegt in der Klasse $\Sigma_2^P$ der polynomiellen Zeithierarchie und ist DIFFP-schwer. Wir geben ein auf semantischen Tableaux basierendes, korrektes und vollstaendiges Berechnungsverfahren fuer endliche Praemissenmengen an. Darueberhinaus untersuchen wir Abschwaechungen der Kompaktheitseigenschaft. Die nichtmonotone auf S5-Modellen basierende Modallogik stellt sich als nicht minder komplex heraus. Auch hier untersuchen wir eine sinnvolle Abschwaechung der Kompaktheitseigenschaft. Desweiteren studieren wir den Zusammenhang zu anderen nichtmonotonen Modallogiken wie Moores autoepistemischer Logik (AEL) und McDermotts NML-2. Wir zeigen, dass unsere Logik zwischen AEL und NML-2 liegt. Schliesslich koppeln wir die entworfene Modallogik mit der dreiwertigen Logik. Die dabei enstehende Logik MKT ist eine Erweiterung des nichtmonotonen Fragments von Belnaps Logik. Wir schliessen unsere Betrachtungen mit einem Vergleich von MKT und verschiedenen informationstheoretischen Logiken, wie z.B. Nelsons N und Heytings intuitionistischer Logik ab.

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Weber, Stefan. "Investigations in Belnap's logic of inconsistent and unknown information." [S.l. : s.n.], 1998. http://dol.uni-leipzig.de/pub/1998-13.

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Bakhtiarinoodeh, Zeinab. "The Dynamics of Incomplete and Inconsistent Information : Applications of logic, algebra and coalgebra." Thesis, Université de Lorraine, 2017. http://www.theses.fr/2017LORR0208/document.

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Cette thèse est structurée autour de deux axes d’études : (1) développer des logiques épistémiques formalisant la prise en compte de nouvelles données en présence d'informations incomplètes ou incohérentes ; (2) caractériser les notions de bisimulation sur les modèles de ces nouvelles logiques. Les logiques modales utilisées pour formaliser des raisonnements dans le cadre d’informations incomplètes et incohérentes, telle que la logique modale de contingence, sont généralement plus faibles que les logiques modales standards. Nos travaux se basent sur des méthodes logiques, algébriques et co-algébriques
In this Ph.D. dissertation we investigate reasoning about information change in the presence of incomplete or inconsistent information, and the characterisation of notions of bisimulation on models encoding such reasoning patterns. Modal logics for incomplete and inconsistent information are typically weaker than the standard modal logics, such as the modal logic of contingency. We use logical, algebraic and co-algebraic methods to achieve our aims. The dissertation consists of two main parts. The first part focusses on reasoning about information change, and the second part focusses on expressivity and bisimulation. In the following, we give an overview of the contents of this dissertation

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Wong, Paul. "Reasoning with Inconsistent Information." Phd thesis, 2004. http://hdl.handle.net/1885/49368.

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Weber, Stefan [Verfasser]. "Investigations in Belnap's logic of inconsistent and unknown information / eingereicht von Stefan Weber." 1998. http://d-nb.info/959118233/34.

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Книги з теми "Logic, paraconsistency, inconsistent information"

João Inácio da Silva Filho. Uncertainty treatment using paraconsistent logic: Introducing paraconsistent artificial neural networks. Amsterdam: IOS Press, 2010.

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A, Carnielli Walter, Coniglio Marcelo E. 1963-, and D'Ottaviano, Itala M. L., 1944-, eds. Paraconsistency: The logical way to the inconsistent : proceedings of the world congress held in São Paulo. New York: Marcel Dekker, 2002.

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Nguyễn, Ngọc Thanh. Advanced Methods for Inconsistent Knowledge Management (Advanced Information and Knowledge Processing). Springer, 2007.

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Частини книг з теми "Logic, paraconsistency, inconsistent information"

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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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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Weber, Zach. "Notes on Inconsistent Set Theory." In Paraconsistency: Logic and Applications, 315–28. Dordrecht: Springer Netherlands, 2012. http://dx.doi.org/10.1007/978-94-007-4438-7_17.

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Mares, Edwin D. "Information, Negation, and Paraconsistency." In Paraconsistency: Logic and Applications, 43–55. Dordrecht: Springer Netherlands, 2012. http://dx.doi.org/10.1007/978-94-007-4438-7_4.

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Verdée, Peter. "Strong Paraconsistency by Separating Composition and Decomposition in Classical Logic." In Logic, Language, Information and Computation, 272–92. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20920-8_26.

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Fominykh, Igor, and Michael Vinkov. "Paraconsistency of Argumentation Semantics for Stepping Theories of Active Logic." In Proceedings of the First International Scientific Conference “Intelligent Information Technologies for Industry” (IITI’16), 171–80. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-33609-1_15.

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Albanese, Massimiliano, Matthias Broecheler, John Grant, Maria Vanina Martinez, and V. S. Subrahmanian. "PLINI: A Probabilistic Logic Program Framework for Inconsistent News Information." In Lecture Notes in Computer Science, 347–76. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20832-4_23.

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Besnard, Philippe, and Anthony Hunter. "Quasi-classical logic: Non-trivializable classical reasoning from inconsistent information." In Symbolic and Quantitative Approaches to Reasoning and Uncertainty, 44–51. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/3-540-60112-0_6.

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Bernert, Marie, and Fano Ramparany. "A Belief Update System Using an Event Model for Location of People in a Smart Home." In Lecture Notes in Computer Science, 17–32. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72308-8_2.

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AbstractArtificial Intelligence applications often require to maintain a knowledge base about the observed environment. In particular, when the current knowledge is inconsistent with new information, it has to be updated. Such inconsistency can be due to erroneous assumptions or to changes in the environment. Here we considered the second case, and develop a knowledge update algorithm based on event logic that takes into account constraints according to which the environment can evolve. These constraints take the form of events that modify the environment in a well-defined manner. The belief update triggered by a new observation is thus explained by a sequence of events. We then apply this algorithm to the problem of locating people in a smart home and show that taking into account past information and move’s constraints improves location inference.

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Alonso-Jiménez, José A., Joaquín Borrego-Díaz, and Antonia M. Chávez-González. "Inconsistency, Logic Databases, and Ontologies." In Handbook of Research on Innovations in Database Technologies and Applications, 452–59. IGI Global, 2009. http://dx.doi.org/10.4018/978-1-60566-242-8.ch049.

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Nowadays, data management on the World Wide Web needs to consider very large knowledge databases (KDB). The larger is a KDB, the smaller the possibility of being consistent. Consistency in checking algorithms and systems fails to analyse very large KDBs, and so many have to work every day with inconsistent information. Database revision—transformation of the KDB into another, consistent database—is a solution to this inconsistency, but the task is computationally untractable. Paraconsistent logics are also a useful option to work with inconsistent databases. These logics work on inconsistent KDBs but prohibit non desired inferences. From a philosophical (logical) point of view, the paraconsistent reasoning is a need that the self human discourse practices. From a computational, logical point of view, we need to design logical formalisms that allow us to extract useful information from an inconsistent database, taking into account diverse aspects of the semantics that are “attached” to deductive databases reasoning (see Table 1). The arrival of the semantic web (SW) will force the database users to work with a KDB that is expressed by logic formulas with higher syntactic complexity than are classic logic databases.

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Тези доповідей конференцій з теми "Logic, paraconsistency, inconsistent information"

Arieli, Ofer, Kees van Berkel, and Christian Straßer. "Annotated Sequent Calculi for Paraconsistent Reasoning and Their Relations to Logical Argumentation." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/351.

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Анотація:

We introduce annotated sequent calculi, which are extensions of standard sequent calculi, where sequents are combined with annotations that represent their derivation statuses. Unlike in ordinary calculi, sequents that are derived in annotated calculi may still be retracted in the presence of conflicting sequents, thus inferences are made under stricter conditions. Conflicts in the resulting systems are handled like in adaptive logics and argumentation theory. The outcome is a robust family of proof systems for non-monotonic reasoning with inconsistent information, where revision considerations are fully integrated into the object level of the proofs. These systems are shown to be strongly connected to logical argumentation.

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