Journal of Applied Non-Classical Logics最新文献

{"title":"Expressiveness of SETAFs and support-free ADFs under 3-valued semantics","authors":"Wolfgang Dvorák, Atefeh Keshavarzi Zafarghandi, Stefan Woltran","doi":"10.1080/11663081.2023.2244361","DOIUrl":"https://doi.org/10.1080/11663081.2023.2244361","url":null,"abstract":"AbstractGeneralising the attack structure in argumentation frameworks (AFs) has been studied in different ways. Most prominently, the binary attack relation of Dung frameworks has been extended to the notion of collective attacks. The resulting formalism is often termed SETAFs. Among the generalisations of AFs, abstract dialectical frameworks (ADFs) allow for a systematic and flexible generalisation of AFs in which different kinds of logical relations, e.g. attack and support, among arguments can be represented. Restricting the logical relations among arguments leads to different subclasses of ADFs of interest. In this work, we consider so-called support-free ADFs that allow for all kinds of attacks but no support or other relations and SETADFs that embed SETAFs in the ADF setting. The aim of this paper is to shed light on the relation between these two different approaches. To this end, we investigate and compare the expressiveness of SETAFs and support-free ADFs under the lens of 3-valued semantics. Our results show that it is only the presence of unsatisfiable acceptance conditions in support-free ADFs that discriminates the two approaches.Keywords: Abstract argumentation frameworksabstract dialectical frameworkscollective attack Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 We note this concept does not allow for auxiliary arguments that simulate certain behaviours, see e.g. Modgil and Bench-Capon (Citation2011).2 As discussed in Polberg (Citation2017), in general, SETAFs translate to bipolar ADFs that contain attacking and redundant links. However, when we first remove redundant attacks from the SETAF we obtain a SFADF.3 Recent work Dvořák et al. (Citation2021a) studies different types of symmetry in SETAFs. Our notion of symmetry corresponds the notion of primal-symmetric SETAFs without self-attacks in Dvořák et al. (Citation2021a)Additional informationFundingThis research has been supported by Austrian Science Fund (FWF) through projects I2854, P30168. The second researcher is supported by 1- the Netherlands Organisation for Scientific Research (NWO) through the Hybrid Intelligence Gravitation Programme, And 2- the Netherlands eScience Center project “The Eye of theBeholder”.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135396947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Morphologic for knowledge dynamics: revision, fusion and abduction","authors":"I. Bloch, J. Lang, Ramón Pino Pérez, C. Uzcátegui","doi":"10.1080/11663081.2023.2244360","DOIUrl":"https://doi.org/10.1080/11663081.2023.2244360","url":null,"abstract":"Several tasks in artificial intelligence require the ability to find models about knowledge dynamics. They include belief revision, fusion and belief merging, and abduction. In this paper, we exploit the algebraic framework of mathematical morphology in the context of propositional logic and define operations such as dilation or erosion of a set of formulas. We derive concrete operators, based on a semantic approach, that have an intuitive interpretation and that are formally well behaved, to perform revision, fusion and abduction. Computation and tractability are addressed, and simple examples illustrate the main results.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"45 1","pages":"421 - 466"},"PeriodicalIF":0.0,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80751771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Logical connectives for two-state semantics","authors":"Marta Cialdea Mayer, L. F. D. Cerro","doi":"10.1080/11663081.2023.2244362","DOIUrl":"https://doi.org/10.1080/11663081.2023.2244362","url":null,"abstract":"In this note we define a new two-state logic, called 2neg-logic (logic with two negations) and compare its expressive power with other two-state logics, such as the logic of here-and-there, contingency logic, and bi-state logic.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"34 1","pages":"520 - 536"},"PeriodicalIF":0.0,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78380934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Admissible generalisation of temporal sequences as chronicles","authors":"Thomas Guyet","doi":"10.1080/11663081.2023.2244717","DOIUrl":"https://doi.org/10.1080/11663081.2023.2244717","url":null,"abstract":"Machine learning is the art of generalising a set of examples. Beside the efficiency of the algorithms, the challenge is to define generalisations that make sense for a data scientist. In this article, we consider generalisations of temporal sequences as chronicles. A chronicle is a temporal model that represents a situation occurring in temporal sequences, i.e. a series of event types with timestamps. A chronicle is a collection of event types with metric temporal constraints on their delays of occurrence. Generalising sequences by a set of event types can intuitively be the smallest set of events that occur in all sequences. A question arises with the generalisation of metric temporal constraints. In this article, we study the admissibility of these generalisations by deriving the notion of rule admissibility to the generalisation as chronicles. Through formalisation, new insights about the notions of chronicles may lead to conceive original chronicle mining algorithms.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"31 1","pages":"641 - 653"},"PeriodicalIF":0.0,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90153123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Natural deduction calculi for classical and intuitionistic S5","authors":"S. Guerrini, A. Masini, M. Zorzi","doi":"10.1080/11663081.2023.2233750","DOIUrl":"https://doi.org/10.1080/11663081.2023.2233750","url":null,"abstract":"We propose an indexed natural deduction system for the modal logic , ideally following Wansing's previous work in the context of tableaux sequents. The system, given both in the classical and intuitionistic versions (called and respectively), is designed to match as much as possible the structure and properties of the standard system of natural deduction for first-order logic, exploiting the formal analogy between modalities and quantifiers. We study a (syntactical) normalization theorem for both and and its main consequences, the sub-formula principle and the consistency theorem. In particular, we propose an intuitionistic encoding of classical (via a suitable extension of the Gödel translation for first-order classical logic). Moreover, via the BHK interpretation of intuitionistic proofs, we propose a suitable Curry–Howard isomorphism for . By translation into the natural deduction system given by Galmiche and Salhi in [(2010b). Label-free proof systems for intuitionistic modal logic is5. In E. M. Clarke & A. Voronkov (Eds.), Logic for programming, artificial intelligence, and reasoning (pp. 255–271). Springer Berlin Heidelberg.], we prove the equivalence of w.r.t. an Hilbert-style axiomatization of . However, when considering the sheer provability of labelled formulas, our system is comparable to the one presented by Simpson in [(1993). The proof theory and semantics of intuitionistic modal logic [PhD thesis], University of Edinburgh, UK.]. Nevertheless, it remains uncertain whether it is feasible to establish a translation between the corresponding derivations.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"22 1","pages":"165 - 205"},"PeriodicalIF":0.0,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87622101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nested sequents for intermediate logics: the case of Gödel-Dummett logics","authors":"Tim S. Lyon","doi":"10.1080/11663081.2023.2233346","DOIUrl":"https://doi.org/10.1080/11663081.2023.2233346","url":null,"abstract":"We present nested sequent systems for propositional Gödel-Dummett logic and its first-order extensions with non-constant and constant domains, built atop nested calculi for intuitionistic logics. To obtain nested systems for these Gödel-Dummett logics, we introduce a new structural rule, called the linearity rule, which (bottom-up) operates by linearising branching structure in a given nested sequent. In addition, an interesting feature of our calculi is the inclusion of reachability rules, which are special logical rules that operate by propagating data and/or checking if data exists along certain paths within a nested sequent. Such rules require us to generalise our nested sequents to include signatures (i.e. finite collections of variables) in the first-order cases, thus giving rise to a generalisation of the usual nested sequent formalism. Our calculi exhibit favourable properties, admitting the height-preserving invertibility of every logical rule and the (height-preserving) admissibility of a large collection of structural and reachability rules. We prove all of our systems sound and cut-free complete, and show that syntactic cut-elimination obtains for the intuitionistic systems. We conclude the paper by discussing possible extensions and modifications, putting forth an array of structural rules that could be used to provide a sizable class of intermediate logics with cut-free nested sequent systems.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"13 1","pages":"121 - 164"},"PeriodicalIF":0.0,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87815761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Defeasible linear temporal logic","authors":"Anasse Chafik, Fahima Cheikh, Jean-François Condotta, I. Varzinczak","doi":"10.1080/11663081.2023.2209494","DOIUrl":"https://doi.org/10.1080/11663081.2023.2209494","url":null,"abstract":"After the seminal work of Kraus, Lehmann and Magidor (formally known as the KLM approach) on conditionals and preferential models, many aspects of defeasibility in more complex formalisms have been studied in recent years. Examples of these aspects are the notion of typicality in description logic and defeasible necessity in modal logic. We discuss a new aspect of defeasibility that can be expressed in the case of temporal logic, which is the normality in an execution. In this contribution, we take Linear Temporal Logic ( ) as case study for this defeasible aspect. has found extensive applications in Computer Science and Artificial Intelligence, notably as a formal framework for representing and verifying computer systems that vary over time. However, some systems may presents exceptions at some innocuous time points where they can be tolerated, or conversely, exceptions at other crucial time points where they need to be addressed. In order to ensure the reliability of such systems, we study a preferential extension of , called defeasible linear temporal logic ( ). In the first part of this paper, we show how semantics of KLM's preferential models can be integrated with . We also discuss the addition of non-monotonic temporal operators as a way to formalise defeasible properties of these systems. The second part of this paper is a study of the satisfiability problem of sentences. Based on Sistla and Clarke's work on the complexity of the classical language, we show the bounded-model property of two fragments of language. Moreover, we provide a procedure to check the satisfiability of sentences in both of these fragments.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"24 1","pages":"1 - 51"},"PeriodicalIF":0.0,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87143076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fragments of quasi-Nelson: residuation","authors":"U. Rivieccio","doi":"10.1080/11663081.2023.2203312","DOIUrl":"https://doi.org/10.1080/11663081.2023.2203312","url":null,"abstract":"Quasi-Nelson logic (QNL) was recently introduced as a common generalisation of intuitionistic logic and Nelson's constructive logic with strong negation. Viewed as a substructural logic, QNL is the axiomatic extension of the Full Lambek Calculus with Exchange and Weakening by the Nelson axiom, and its algebraic counterpart is a variety of residuated lattices called quasi-Nelson algebras. Nelson's logic, in turn, may be obtained as the axiomatic extension of QNL by the double negation (or involutivity) axiom, and intuitionistic logic as the extension of QNL by the contraction axiom. A recent series of papers by the author and collaborators initiated the study of fragments of QNL, which correspond to subreducts of quasi-Nelson algebras. In the present paper we focus on fragments that contain the connectives forming a residuated pair (the monoid conjunction and the so-called strong Nelson implication), these being the most interesting ones from a substructural logic perspective. We provide quasi-equational (whenever possible, equational) axiomatisations for the corresponding classes of algebras, obtain twist representations for them, study their congruence properties and take a look at a few notable subvarieties. Our results specialise to the involutive case, yielding characterisations of the corresponding fragments of Nelson's logic and their algebraic counterparts.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"88 1","pages":"52 - 119"},"PeriodicalIF":0.0,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76261501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Bayesian approach to forward and inverse abstract argumentation problems","authors":"Hiroyuki Kido, B. Liao","doi":"10.1080/11663081.2022.2144830","DOIUrl":"https://doi.org/10.1080/11663081.2022.2144830","url":null,"abstract":"This paper studies a fundamental mechanism by which conflicts between arguments are drawn from sentiments regarding acceptability of the arguments. Given sets of arguments, an inverse abstract argumentation problem seeks attack relations between arguments such that acceptability semantics interprets each argument in the sets of arguments as being acceptable in each of the attack relations. It is an inverse problem of the traditional problem we refer to as the forward abstract argumentation problem. Given an attack relation, the forward abstract argumentation problem seeks sets of arguments such that acceptability semantics interprets each argument in the sets of arguments as being acceptable in the attack relation. We give a probabilistic model of argumentation-theoretic inference. It is a generative model formalising the process by which acceptability semantics interprets acceptability of arguments in a given attack relation. We show that it gives a broad view of solutions to the forward and inverse abstract argumentation problems. Specifically, solutions to the inverse and forward abstract argumentation problems are shown to be equivalent to a maximum likelihood estimate and maximum likelihood prediction, respectively, which are both available with the generative model. In addition, they are shown to be special cases of the posterior distribution and the evidence, respectively, which are both obtained by probabilistic inference on the generative model. We report an experiment result and application example of the generative model in the inverse problems.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"1 1","pages":"273 - 304"},"PeriodicalIF":0.0,"publicationDate":"2022-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89838312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A set-theoretic proof of the representation of MV-algebras by sheaves","authors":"Alejandro Estrada, Y. Poveda","doi":"10.1080/11663081.2023.2190007","DOIUrl":"https://doi.org/10.1080/11663081.2023.2190007","url":null,"abstract":"ABSTRACT In this paper, we provide a set-theoretic proof of the general representation theorem for MV-algebras, which was developed by Dubuc and Poveda in 2010. The theorem states that every MV-algebra is isomorphic to the MV-algebra of all global sections of its prime spectrum. We avoid using topos theory and instead rely on basic concepts from MV-algebras, topology and set theory.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"111 1","pages":"317 - 334"},"PeriodicalIF":0.0,"publicationDate":"2022-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82175922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}