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Journal of Applied Non-Classical Logics最新文献

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Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix II. Only one designated value Kleene强三值矩阵自然隐含展开式的Belnap-Dunn语义。只有一个指定值
Journal of Applied Non-Classical Logics Pub Date : 2019-07-03 DOI: 10.1080/11663081.2019.1644079
G. Robles, Francisco Salto, J. Méndez
{"title":"Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix II. Only one designated value","authors":"G. Robles, Francisco Salto, J. Méndez","doi":"10.1080/11663081.2019.1644079","DOIUrl":"https://doi.org/10.1080/11663081.2019.1644079","url":null,"abstract":"ABSTRACT This paper is a sequel to ‘Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix with two designated values’, where a ‘bivalent’ Belnap-Dunn semantics is provided for all the expansions referred to in its title. The aim of the present paper is to carry out a parallel investigation for all natural implicative expansions of Kleene's strong 3-valued matrix now with only one designated value.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"33 1","pages":"307 - 325"},"PeriodicalIF":0.0,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77555001","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
Axiomatic and dual systems for constructive necessity, a formally verified equivalence 构造必要性的公理化和对偶系统，正式验证的等价性
Journal of Applied Non-Classical Logics Pub Date : 2019-07-03 DOI: 10.1080/11663081.2019.1647653
Lourdes Del Carmen González-Huesca, F. E. Miranda-Perea, P. S. Linares-Arévalo
{"title":"Axiomatic and dual systems for constructive necessity, a formally verified equivalence","authors":"Lourdes Del Carmen González-Huesca, F. E. Miranda-Perea, P. S. Linares-Arévalo","doi":"10.1080/11663081.2019.1647653","DOIUrl":"https://doi.org/10.1080/11663081.2019.1647653","url":null,"abstract":"ABSTRACT We present a proof of the equivalence between two deductive systems for constructive necessity, namely an axiomatic characterisation inspired by Hakli and Negri's system of derivations from assumptions for modal logic , a Hilbert-style formalism designed to ensure the validity of the deduction theorem, and the judgmental reconstruction given by Pfenning and Davies by means of a natural deduction approach that makes a distinction between valid and true formulae, constructively. Both systems and the proof of their equivalence are formally verified using the state-of-the-art proof assistant Coq. The proof approach taken throughout the paper unveils the use of some alternative proof methods that allow for a smooth transition from the high-level mathematical proofs to their mechanised counterparts.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"1 1","pages":"255 - 287"},"PeriodicalIF":0.0,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84085873","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
Subordination Tarski algebras 隶属Tarski代数
Journal of Applied Non-Classical Logics Pub Date : 2019-07-03 DOI: 10.1080/11663081.2019.1638080
S. Celani
{"title":"Subordination Tarski algebras","authors":"S. Celani","doi":"10.1080/11663081.2019.1638080","DOIUrl":"https://doi.org/10.1080/11663081.2019.1638080","url":null,"abstract":"ABSTRACT In this work we will study Tarski algebras endowed with a subordination, called subordination Tarski algebras. We will define the notion of round filters, and we will study the class of irreducible round filters and the maximal round filters, called ends. We will prove that the poset of all round filters is a lattice isomorphic to the lattice of the congruences that are compatible with the subordination. We will prove that every end is an irreducible round filter, and that in a topological subordination Tarski algebra A, every irreducible round filter is an end iff A is a monadic subordination Tarski algebra. As corollary of this result we have that the variety of monadic Tarski algebra can be characterised as the topological Tarski algebras where every irreducible open filter is a maximal open filter.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"20 1","pages":"288 - 306"},"PeriodicalIF":0.0,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84645633","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: 4
Indefinite abductive explanations 不确定溯因解释
Journal of Applied Non-Classical Logics Pub Date : 2019-06-04 DOI: 10.1080/11663081.2019.1624349
Luciano Caroprese, E. Zumpano
{"title":"Indefinite abductive explanations","authors":"Luciano Caroprese, E. Zumpano","doi":"10.1080/11663081.2019.1624349","DOIUrl":"https://doi.org/10.1080/11663081.2019.1624349","url":null,"abstract":"ABSTRACT This paper stems from previous works of the authors in which a new measure of the simplicity of an explanation based on its degree of arbitrariness is proposed: The more the explanation is arbitray, the less appealing it is, with explanations having no arbitrariness – called constrained – being the preferred ones. In previous works, as commonly done in the literature of abductive logic programming, a set of hypotheses is not an explanation, unless it is definite, i.e. it explains all the data belonging to the observation. In this paper, we follow a different perspective and define the concept of indefinite constrained explanations, i.e. constrained explanations that are not definite, but admit some indefiniteness. An indefinite constrained explanation captures the intuition of the existence of an explanation (indefinite explanation) that would best explain the given evidence, while not making arbitrary choices (constrained explanation). The main contribution of the paper is the study of abduction in indefinite deductive theories: specifically, the paper studies the framework of abductive logic programming extended with integrity constraints in the setting in which both the initial knowledge base and the abductive explanations are indefinite (may contain occurrences of null values) and the domain is possibly infinite. Furthermore, the paper discusses the complexity of problems concerning indefinite (constrained) explanations.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"20 1","pages":"233 - 254"},"PeriodicalIF":0.0,"publicationDate":"2019-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87548167","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: 4
A logic for best explanations 最佳解释的逻辑
Journal of Applied Non-Classical Logics Pub Date : 2019-03-31 DOI: 10.1080/11663081.2019.1591108
Jared Millson, Christian Straßer
{"title":"A logic for best explanations","authors":"Jared Millson, Christian Straßer","doi":"10.1080/11663081.2019.1591108","DOIUrl":"https://doi.org/10.1080/11663081.2019.1591108","url":null,"abstract":"ABSTRACT Efforts to formalize qualitative accounts of inference to the best explanation (IBE) confront two obstacles: the imprecise nature of such accounts and the unusual logical properties that explanations exhibit, such as contradiction-intolerance and irreflexivity. This paper aims to surmount these challenges by utilising a new, more precise theory that treats explanations as expressions that codify defeasible inferences. To formalise this account, we provide a sequent calculus in which IBE serves as an elimination rule for a connective that exhibits many of the properties associated with the behaviour of the English expression ‘That…best explains why…’. We first construct a calculus that encodes these properties at the level of the turnstile, i.e. as a metalinguistic expression for classes of defeasible consequence relations. We then show how this calculus can be conservatively extended over a language that contains a best-explains-why operator.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"60 1","pages":"184 - 231"},"PeriodicalIF":0.0,"publicationDate":"2019-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79112873","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
Monoidal logics: completeness and classical systems 一元逻辑:完备性与经典系统
Journal of Applied Non-Classical Logics Pub Date : 2019-03-28 DOI: 10.1080/11663081.2018.1547513
Clayton Peterson
{"title":"Monoidal logics: completeness and classical systems","authors":"Clayton Peterson","doi":"10.1080/11663081.2018.1547513","DOIUrl":"https://doi.org/10.1080/11663081.2018.1547513","url":null,"abstract":"ABSTRACT Monoidal logics were introduced as a foundational framework to analyze the proof theory of logical systems. Inspired by Lambek's seminal work in categorical logic, the objective is to define logical systems in order to make explicit their categorical (monoidal) structure. In this setting, logical connectives can be proven to be functors with specific properties. Accordingly, monoidal logics allow a classification of logical systems in function of their categorical structure and the functorial properties of their connectives. As they stand, however, strong parallels can be made between monoidal logics and the broader proof-theoretical framework of display logics. In this paper, we extend the results presented in Peterson ((2016). A comparison between monoidal and substructural logics. Journal of Applied Non-Classical Logics, 26(2), 126–159) and we show that monoidal logics are sound and complete with respect to associative display logics, thus providing a completeness result with regards to the algebraic semantics of display and substructural logics. In addition, we discuss the notions of classical and intuitionistic systems. Starting from Lambek's and Grishin's analyses, we explore the role played by partial De Morgan dualities and discuss the necessary and sufficient conditions required for the definitions of classical and intuitionistic deductive systems.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"32 1","pages":"121 - 151"},"PeriodicalIF":0.0,"publicationDate":"2019-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88541381","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
n-valued maximal paraconsistent matrices n值最大副相容矩阵
Journal of Applied Non-Classical Logics Pub Date : 2019-02-27 DOI: 10.1080/11663081.2019.1578602
A. Trybus
{"title":"n-valued maximal paraconsistent matrices","authors":"A. Trybus","doi":"10.1080/11663081.2019.1578602","DOIUrl":"https://doi.org/10.1080/11663081.2019.1578602","url":null,"abstract":"ABSTRACT The articles Maximality and Refutability Skura [(2004). Maximality and refutability. Notre Dame Journal of Formal Logic, 45, 65–72] and Three-valued Maximal Paraconsistent Logics Skura and Tuziak [(2005). Three-valued maximal paraconsistent logics. In Logika (Vol. 23). Wydawnictwo Uniwersytetu Wrocławskiego] introduced a simple method of proving maximality (in the two distinguished senses) of a given paraconsistent matrix. This method stemmed from the so-called refutation calculus, where the focus in on rejecting rather than accepting formulas. The article A Generalisation of a Refutation-related Method in Paraconsistent Logics Trybus [(2018). A generalisation of a refutation-related method in paraconsistent logics. Logic and Logical Philosophy, 27(2). doi:10.12775/LLP.2018.002] was a first step towards generalising the method. In it, a number of 3-valued paraconsistent matrices were shown maximal. In this article we extend these results to cover a number of n-valued (n>2) paraconsistent matrices using the same method.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"12 1","pages":"171 - 183"},"PeriodicalIF":0.0,"publicationDate":"2019-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78369388","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: 0
A family of metainferential logics 一组元间逻辑
Journal of Applied Non-Classical Logics Pub Date : 2019-01-02 DOI: 10.1080/11663081.2018.1534486
F. Pailos
{"title":"A family of metainferential logics","authors":"F. Pailos","doi":"10.1080/11663081.2018.1534486","DOIUrl":"https://doi.org/10.1080/11663081.2018.1534486","url":null,"abstract":"ABSTRACT We will present 12 different mixed metainferential consequence relations. Each one of them is specified using two different inferential Tarskian or non-Tarskian consequence relations: or . We will show that it is possible to obtain a Tarskian logic with non-Tarskian inferential logics, but also a non-Tarskian logic with Tarskian inferential logics. Moreover, we will show how some of these metainferential logics work better than the corresponding inferential rivals. Finally, we will show how these logics prove that it is not enough to work with inferences as pairs of sets of formulas to obtain a contractive logic.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"24 1","pages":"120 - 97"},"PeriodicalIF":0.0,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85407249","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: 10
Semantical analysis of weak Kleene logics 弱Kleene逻辑的语义分析
Journal of Applied Non-Classical Logics Pub Date : 2019-01-02 DOI: 10.1080/11663081.2018.1547514
R. Ciuni, Massimiliano Carrara
{"title":"Semantical analysis of weak Kleene logics","authors":"R. Ciuni, Massimiliano Carrara","doi":"10.1080/11663081.2018.1547514","DOIUrl":"https://doi.org/10.1080/11663081.2018.1547514","url":null,"abstract":"ABSTRACT This paper presents a semantical analysis of the Weak Kleene Logics and from the tradition of Bochvar and Halldén. These are three-valued logics in which a formula takes the third value if at least one of its components does. The paper establishes two main results: a characterisation result for the relation of logical consequence in – that is, we individuate necessary and sufficient conditions for a set Δ of formulas to follow from a set Γ in – and a characterisation result for logical consequence in . The paper also investigates two subsystems of and and discusses the relevance of the results against existing background. Finally, the paper discusses some issues related to Weak Kleene Logics – in particular, their philosophical interpretation and the reading of conjunction and disjunction – and points at some open issues.","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"3 1","pages":"1 - 36"},"PeriodicalIF":0.0,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85380718","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: 17
Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix with two designated values 具有两个指定值的Kleene强三值矩阵自然隐含展开式的Belnap-Dunn语义
Journal of Applied Non-Classical Logics Pub Date : 2019-01-02 DOI: 10.1080/11663081.2018.1534487
G. Robles, J. Méndez
{"title":"Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix with two designated values","authors":"G. Robles, J. Méndez","doi":"10.1080/11663081.2018.1534487","DOIUrl":"https://doi.org/10.1080/11663081.2018.1534487","url":null,"abstract":"ABSTRACT A conditional is natural if it fulfils the three following conditions. (1) It coincides with the classical conditional when restricted to the classical values T and F; (2) it satisfies the Modus Ponens; and (3) it is assigned a designated value whenever the value assigned to its antecedent is less than or equal to the value assigned to its consequent. The aim of this paper is to provide a ‘bivalent’ Belnap-Dunn semantics for all natural implicative expansions of Kleene's strong 3-valued matrix with two designated elements. (We understand the notion ‘natural conditional’ according to N. Tomova, ‘A lattice of implicative extensions of regular Kleene's logics’, Reports on Mathematical Logic, 47, 173–182, 2012.)","PeriodicalId":38573,"journal":{"name":"Journal of Applied Non-Classical Logics","volume":"39 1","pages":"37 - 63"},"PeriodicalIF":0.0,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81508487","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: 17
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