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Journal of Applied Non-Classical Logics最新文献

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Exactly true and non-falsity logics meeting infectious ones 真假逻辑完全符合传染性逻辑
Journal of Applied Non-Classical Logics Pub Date : 2020-04-02 DOI: 10.1080/11663081.2020.1751573
A. Belikov, Y. Petrukhin
{"title":"Exactly true and non-falsity logics meeting infectious ones","authors":"A. Belikov, Y. Petrukhin","doi":"10.1080/11663081.2020.1751573","DOIUrl":"https://doi.org/10.1080/11663081.2020.1751573","url":null,"abstract":"In this paper, we study logical systems which represent entailment relations of two kinds. We extend the approach of finding ‘exactly true’ and ‘non-falsity’ versions of four-valued logics that emerged in series of recent works [Pietz & Rivieccio (2013). Nothing but the truth. Journal of Philosophical Logic, 42(1), 125–135; Shramko (2019). Dual-Belnap logic and anything but falsehood. Journal of Logics and their Applications, 6, 413–433; Shramko et al. (2017). First-degree entailment and its relatives. Studia Logica, 105(6), 1291–1317] to the case of infectious logics, namely to the case of Deutsch's logic introduced in Deutsch [Relevant analytic entailment. The Relevance Logic Newsletter, 2(1), 26–44; The completeness of S. Studia Logica, 38(2), 137–147]. The particular systems obtained in this way are and . We present them in the form of sequent calculi and prove corresponding soundness and completeness theorems. We illuminate the connection between , and two well-known systems, strong Kleene three-valued logic and Priest's Logic of Paradox . This connection allows us to investigate the characterisation of the entailment relations associated with and as well as to introduce the notion of ‘infectious analogue’ of a certain logic. We also study implicative extensions of and and prove soundness and completeness theorems for them as well.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"412 1","pages":"122 - 93"},"PeriodicalIF":0.0,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76473000","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}
引用次数: 5
On searching explanatory argumentation graphs 关于寻找解释性论证图
Journal of Applied Non-Classical Logics Pub Date : 2020-04-02 DOI: 10.1080/11663081.2020.1766248
Régis Riveret
{"title":"On searching explanatory argumentation graphs","authors":"Régis Riveret","doi":"10.1080/11663081.2020.1766248","DOIUrl":"https://doi.org/10.1080/11663081.2020.1766248","url":null,"abstract":"Cases or examples can be often explained by the interplay of arguments in favour or against their outcomes. This paper addresses the problem of finding explanations for a collection of cases where an explanation is a labelled argumentation graph consistent with the cases, and a case is represented as a statement labelling. The focus is on semi-abstract argumentation graphs specifying attack and subargument relations between arguments, along with particular complete argument labellings taken from probabilistic argumentation where arguments can be excluded. The framework and computational considerations lead to an iterated local iterative deepening depth-first search to collect ‘interesting’ semi-abstract argumentation graphs consistent with a collection of statement labellings. Finally, the framework is illustrated and evaluated with a proof-of-concept implementation.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"1 1","pages":"123 - 192"},"PeriodicalIF":0.0,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77389597","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}
引用次数: 5
Reconstructor: a computer program that uses three-valued logics to represent lack of information in empirical scientific contexts 重构器:一种计算机程序，它使用三值逻辑来表示经验科学背景下信息的缺乏
Journal of Applied Non-Classical Logics Pub Date : 2020-01-02 DOI: 10.1080/11663081.2019.1703467
A. Roffé
{"title":"Reconstructor: a computer program that uses three-valued logics to represent lack of information in empirical scientific contexts","authors":"A. Roffé","doi":"10.1080/11663081.2019.1703467","DOIUrl":"https://doi.org/10.1080/11663081.2019.1703467","url":null,"abstract":"ABSTRACT In this article, I develop three conceptual innovations within the area of formal metatheory, and present a computer program, called Reconstructor, that implements those developments. The first development consists in a methodology for testing formal reconstructions of scientific theories, which involves checking both whether translations of paradigmatically successful applications into models satisfy the formalisation of the laws, and also whether unsuccessful applications do not. I show how Reconstructor can help carry this out, since it allows the end-user to specify a formal language, input axioms and models formulated in that language, and then ask if the models satisfy the axioms. The second innovation is the introduction of incomplete models (for which the denotation of some terms is missing) into scientific metatheory, in order to represent cases of missing information. I specify the paracomplete semantics built into Reconstructor to deal with sentences where denotation failures occur. The third development consists in a new way of explicating the structuralist notion of a determination method, by equating them with algorithms. This allows determination methods to be loaded into Reconstructor and then executed within a model to find out the value of a previously non-denoting term (i.e. it allows the formal reconstruction to make predictions). This, in turn, can help test the reconstruction in a different way. Finally, I conclude with some suggestions about additional uses the program may have.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"3 1","pages":"68 - 91"},"PeriodicalIF":0.0,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88483459","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}
引用次数: 2
The logic of modal changes LMC 模态的逻辑改变了LMC
Journal of Applied Non-Classical Logics Pub Date : 2020-01-02 DOI: 10.1080/11663081.2020.1717267
Marcin Łyczak
{"title":"The logic of modal changes LMC","authors":"Marcin Łyczak","doi":"10.1080/11663081.2020.1717267","DOIUrl":"https://doi.org/10.1080/11663081.2020.1717267","url":null,"abstract":"ABSTRACT The logic of change formulated by K. Świętorzecka, has its motivation coming from the Aristotelian theory of substantial change which is undrstood as a transformation consisting in the disappearing and becoming of individual substances. The transition: becoming/disapearing (and conversely) is expressed in by the primitive operator C, to be read: it changes that …, and it is mapped by the progressively expanding language. We are interested in attributive changes of individual substances. We consider a formalism with two non-normal and not mutually definable operators of possible and necessary change, inspired by Aristotelian distinction of accidental and essential attributes. From we adopt the idea that temporal concepts are defined via change operators, and the idea of an expanding language. In what follows, We axiomatise our new logic and describe its semantics, giving the proof of its completeness. We compare our formalism with selected modal logics.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"1 1","pages":"50 - 67"},"PeriodicalIF":0.0,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88329983","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}
引用次数: 2
Axiomatization of non-associative generalisations of Hájek's BL and psBL Hájek的BL和psBL的非联想概括的公理化
Journal of Applied Non-Classical Logics Pub Date : 2020-01-02 DOI: 10.1080/11663081.2019.1703468
Y. Petrukhin
{"title":"Axiomatization of non-associative generalisations of Hájek's BL and psBL","authors":"Y. Petrukhin","doi":"10.1080/11663081.2019.1703468","DOIUrl":"https://doi.org/10.1080/11663081.2019.1703468","url":null,"abstract":"ABSTRACT In this paper, we consider non-associative generalisations of Hájek's logics BL and psBL. As it was shown by Cignoli, Esteva, Godo, and Torrens, the former is the logic of continuous t-norms and their residua. Botur introduced logic naBL which is the logic of non-associative continuous t-norms and their residua. Thus, naBL can be viewed as a non-associative generalisation of BL. However, Botur has not presented axiomatization of naBL. We fill this gap by constructing an adequate Hilbert-style calculus for naBL. Although, as was shown by Flondor, Georgescu, and Iorgulescu, there are no non-commutative continuous t-norms, Hájek's psBL can be viewed as BL's non-commutative generalisation. We present the logic psnaBL of psnaBL-algebras which can be viewed as naBL's non-commutative generalisation as well as psBL's non-associative generalisation and BL's both non-commutative and non-associative generalisation.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"53 1","pages":"1 - 15"},"PeriodicalIF":0.0,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80849609","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}
引用次数: 1
On recent applications of paraconsistent logic: an exploratory literature review 副协调逻辑的最新应用:探索性文献综述
Journal of Applied Non-Classical Logics Pub Date : 2019-10-02 DOI: 10.1080/11663081.2019.1656393
A. Zamansky
{"title":"On recent applications of paraconsistent logic: an exploratory literature review","authors":"A. Zamansky","doi":"10.1080/11663081.2019.1656393","DOIUrl":"https://doi.org/10.1080/11663081.2019.1656393","url":null,"abstract":"ABSTRACT This paper aims to empirically explore the state of practical applications of paraconsistent logics. To this end, we performed an exploratory literature review, analysing papers published between the years 2015 and 2018. Paraconsistent formalisms based on annotated logics are practically the sole type of approach we found to be applied in engineering applications. The engineering problems solved by paraconsistent approaches were mainly in the fields of signal and image processing and decision support. The results of our exploratory review indicate that recent developments in the theory of paraconsistency have not yet been adopted for applications.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"15 1","pages":"382 - 391"},"PeriodicalIF":0.0,"publicationDate":"2019-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77309905","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}
引用次数: 6
Polynomial semantics for modal logics 模态逻辑的多项式语义
Journal of Applied Non-Classical Logics Pub Date : 2019-10-02 DOI: 10.1080/11663081.2019.1676004
J. C. Agudelo, Santiago Echeverri-Valencia
{"title":"Polynomial semantics for modal logics","authors":"J. C. Agudelo, Santiago Echeverri-Valencia","doi":"10.1080/11663081.2019.1676004","DOIUrl":"https://doi.org/10.1080/11663081.2019.1676004","url":null,"abstract":"ABSTRACT It is shown here that the modal logic K and any extension of it with a finite number of axioms can be characterised by a polynomial semantics. Moreover, some comments are made about the possibility of using algebraic computation to determine deducibility on these logics.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"8 1","pages":"430 - 449"},"PeriodicalIF":0.0,"publicationDate":"2019-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84013382","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}
引用次数: 1
Logical dual concepts based on mathematical morphology in stratified institutions: applications to spatial reasoning 分层制度中基于数学形态学的逻辑对偶概念:在空间推理中的应用
Journal of Applied Non-Classical Logics Pub Date : 2019-09-27 DOI: 10.1080/11663081.2019.1668678
M. Aiguier, I. Bloch
{"title":"Logical dual concepts based on mathematical morphology in stratified institutions: applications to spatial reasoning","authors":"M. Aiguier, I. Bloch","doi":"10.1080/11663081.2019.1668678","DOIUrl":"https://doi.org/10.1080/11663081.2019.1668678","url":null,"abstract":"ABSTRACT Several logical operators are defined as dual pairs, in different types of logics. Such dual pairs of operators also occur in other algebraic theories, such as mathematical morphology. Based on this observation, this paper proposes to define, at the abstract level of institutions, a pair of abstract dual and logical operators as morphological erosion and dilation. Standard quantifiers and modalities are then derived from these two abstract logical operators. These operators are studied both on sets of states and sets of models. To cope with the lack of explicit set of states in institutions, the proposed abstract logical dual operators are defined in an extension of institutions, the stratified institutions, which take into account the notion of open sentences, whose satisfaction is parametrised by sets of states. A hint on the potential interest of the proposed framework for spatial reasoning is also provided.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"97 4 1","pages":"392 - 429"},"PeriodicalIF":0.0,"publicationDate":"2019-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83355453","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}
引用次数: 11
Modelling last-act attempted crime in criminal law 刑法中最后行为未遂的建模
Journal of Applied Non-Classical Logics Pub Date : 2019-08-07 DOI: 10.1080/11663081.2019.1647652
Jiraporn Pooksook, P. M. Dung, K. Satoh, G. Sartor
{"title":"Modelling last-act attempted crime in criminal law","authors":"Jiraporn Pooksook, P. M. Dung, K. Satoh, G. Sartor","doi":"10.1080/11663081.2019.1647652","DOIUrl":"https://doi.org/10.1080/11663081.2019.1647652","url":null,"abstract":"ABSTRACT In the court of law, a person can be punished for attempting to commit a crime. An open issue in the study of Artificial Intelligence and Law is whether the law of attempts could be formally modelled. There are distinct legal rules for determining attempted crime whereas the last-act rule (also called proximity rule) represents the strictest approach. In this paper, we provide a formal model of the last-act rule using structured argumentation.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"32 1","pages":"327 - 357"},"PeriodicalIF":0.0,"publicationDate":"2019-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91154555","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}
引用次数: 1
Two proofs of the algebraic completeness theorem for multilattice logic 多格逻辑代数完备性定理的两个证明
Journal of Applied Non-Classical Logics Pub Date : 2019-08-05 DOI: 10.1080/11663081.2019.1647654
Oleg M. Grigoriev, Y. Petrukhin
{"title":"Two proofs of the algebraic completeness theorem for multilattice logic","authors":"Oleg M. Grigoriev, Y. Petrukhin","doi":"10.1080/11663081.2019.1647654","DOIUrl":"https://doi.org/10.1080/11663081.2019.1647654","url":null,"abstract":"Abstract Shramko [(2016). Truth, falsehood, information and beyond: The American plan generalized. In K. Bimbo (Ed.), J. Michael Dunn on information based logics, outstanding contributions to logic (pp. 191–212). Dordrecht: Springer] formulated multilattice logic and the algebraic completeness theorem for it. However, the proof has not been presented. In this paper, we consider Kamide and Shramko's multilattice logic [Kamide & Shramko (2017a). Embedding from multilattice logic into classical logic and vice versa. Journal of Logic and Computation, 27(5), 1549–1575] which is an extension of Shramko's original multilattice logic by several implications and coimplications. Using the technique of algebraic embedding, we show that Kamide and Shramko's sequent calculus for multilattice logic is sound and complete with respect to multilattices. Moreover, we introduce yet another algebraic semantics for this logic based on the notion of a De Morgan multilattice. Using Lindenbaum-Tarski algebras, we show that is sound and complete with respect to De Morgan multilattices. Besides, we modify Kamide and Shramko's notion of modal multilattice [Kamide & Shramko (2017b). Modal multilattice logic. Logica Universalis, 11(3), 317–343], i.e. we present the concept of De Morgan modal multilattice. We prove that Kamide and Shramko's modal multilattice logic (Kamide & Shramko, 2017b) is adequate with respect to De Morgan modal multilattices.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"70 1","pages":"358 - 381"},"PeriodicalIF":0.0,"publicationDate":"2019-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77194832","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}
引用次数: 2
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