Studia Logica最新文献_第5页

Proof-Theoretic Aspects of Paraconsistency with Strong Consistency Operator 带强一致性操作符的准一致性的证明论方面

IF 0.7 3区数学

Studia Logica Pub Date : 2024-01-13 DOI: 10.1007/s11225-023-10089-8

Victoria Arce Pistone, Martín Figallo

{"title":"Proof-Theoretic Aspects of Paraconsistency with Strong Consistency Operator","authors":"Victoria Arce Pistone, Martín Figallo","doi":"10.1007/s11225-023-10089-8","DOIUrl":"https://doi.org/10.1007/s11225-023-10089-8","url":null,"abstract":"In order to develop efficient tools for automated reasoning with inconsistency (theorem provers), eventually making Logics of Formal inconsistency (LFI) a more appealing formalism for reasoning under uncertainty, it is important to develop the proof theory of the first-order versions of such LFIs. Here, we intend to make a first step in this direction. On the other hand, the logic Ciore was developed to provide new logical systems in the study of inconsistent databases from the point of view of LFIs. An interesting fact about Ciore is that it has a strong consistency operator, that is, a consistency operator which (forward/backward) propagates inconsistency. Also, it turns out to be an algebraizable logic (in the sense of Blok and Pigozzi) that can be characterized by means of a 3-valued logical matrix. Recently, a first-order version of Ciore, namely QCiore, was defined preserving the spirit of Ciore, that is, without introducing unexpected relationships between the quantifiers. Besides, some important model-theoretic results were obtained for this logic. In this paper we study some proof–theoretic aspects of both Ciore and QCiore respectively. In first place, we introduce a two-sided sequent system for Ciore. Later, we prove that this system enjoys the cut-elimination property and apply it to derive some interesting properties. Later, we extend the above-mentioned system to first-order languages and prove completeness and cut-elimination property using the well-known Shütte’s technique.","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":"73 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139463990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An $$omega $$ -Rule for the Logic of Provability and Its Models 可证明性逻辑及其模型的 $$omega $$ 规则

IF 0.7 3区数学

Studia Logica Pub Date : 2024-01-09 DOI: 10.1007/s11225-023-10090-1

Katsumi Sasaki, Yoshihito Tanaka

{"title":"An $$omega $$ -Rule for the Logic of Provability and Its Models","authors":"Katsumi Sasaki, Yoshihito Tanaka","doi":"10.1007/s11225-023-10090-1","DOIUrl":"https://doi.org/10.1007/s11225-023-10090-1","url":null,"abstract":"In this paper, we discuss semantical properties of the logic (textbf{GL}) of provability. The logic (textbf{GL}) is a normal modal logic which is axiomatized by the the Löb formula ( Box (Box psupset p)supset Box p ), but it is known that (textbf{GL}) can also be axiomatized by an axiom (Box psupset Box Box p) and an (omega )-rule ((Diamond ^{*})) which takes countably many premises (phi supset Diamond ^{n}top ) ((nin omega )) and returns a conclusion (phi supset bot ). We show that the class of transitive Kripke frames which validates ((Diamond ^{*})) and the class of transitive Kripke frames which strongly validates ((Diamond ^{*})) are equal, and that the following three classes of transitive Kripke frames, the class which validates ((Diamond ^{*})), the class which weakly validates ((Diamond ^{*})), and the class which is defined by the Löb formula, are mutually different, while all of them characterize (textbf{GL}). This gives an example of a proof system P and a class C of Kripke frames such that P is sound and complete with respect to C but the soundness cannot be proved by simple induction on the height of the derivations in P. We also show Kripke completeness of the proof system with ((Diamond ^{*})) in an algebraic manner. As a corollary, we show that the class of modal algebras which is defined by equations (Box xle Box Box x) and (bigwedge _{nin omega }Diamond ^{n}1=0) is not a variety.","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":"121 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139412978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Nelson Conuclei and Nuclei: The Twist Construction Beyond Involutivity 纳尔逊的 "核 "与 "核"：超越不可逆性的扭曲构造

IF 0.7 3区数学

Studia Logica Pub Date : 2024-01-09 DOI: 10.1007/s11225-023-10088-9

引用次数: 0

Combining Intuitionistic and Classical Propositional Logic: Gentzenization and Craig Interpolation 直觉逻辑与古典命题逻辑的结合：根岑化和克雷格插值法

IF 0.7 3区数学

Studia Logica Pub Date : 2024-01-06 DOI: 10.1007/s11225-023-10067-0

{"title":"Combining Intuitionistic and Classical Propositional Logic: Gentzenization and Craig Interpolation","authors":"","doi":"10.1007/s11225-023-10067-0","DOIUrl":"https://doi.org/10.1007/s11225-023-10067-0","url":null,"abstract":"<h3>Abstract</h3> This paper studies a combined system of intuitionistic and classical propositional logic from proof-theoretic viewpoints. Based on the semantic treatment of Humberstone (J Philos Log 8:171–196, 1979) and del Cerro and Herzig (Frontiers of combining systems: FroCoS, Springer, 1996), a sequent calculus (textsf{G}(textbf{C}+textbf{J})) is proposed. An approximate idea of obtaining (textsf{G}(textbf{C}+textbf{J})) is adding rules for classical implication on top of the intuitionistic multi-succedent sequent calculus by Maehara (Nagoya Math J 7:45–64, 1954). However, in the semantic treatment, some formulas do not satisfy heredity, which leads to the necessity of a restriction on the right rule for intuitionistic implication to keep the soundness of the calculus. The calculus (textsf{G}(textbf{C}+textbf{J})) enjoys cut elimination and Craig interpolation, whose detailed proofs are described in this paper. Cut elimination enables us to show the decidability of this combination both directly and syntactically. This paper also employs a canonical model argument to establish the strong completeness of Hilbert system (mathbf {C+J}) proposed by del Cerro and Herzig (Frontiers of combining systems: FroCoS, Springer, 1996).","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":"6 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139375740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Quineanism, Noneism and Metaphysical Equivalence 奎因主义、无主义和形而上学等价性

IF 0.7 3区数学

Studia Logica Pub Date : 2023-12-09 DOI: 10.1007/s11225-023-10085-y

Bruno Jacinto, Javier Belastegui

引用次数: 0

Connexive Logic, Connexivity, and Connexivism: Remarks on Terminology 逻辑相联性、相联性和相联主义：术语说明

IF 0.7 3区数学

Studia Logica Pub Date : 2023-12-09 DOI: 10.1007/s11225-023-10082-1

Heinrich Wansing, Hitoshi Omori

引用次数: 0

The Logic ILP for Intuitionistic Reasoning About Probability 概率直觉推理的逻辑 ILP

IF 0.7 3区数学

Studia Logica Pub Date : 2023-12-09 DOI: 10.1007/s11225-023-10084-z

Angelina Ilić-Stepić, Zoran Ognjanović, Aleksandar Perović

引用次数: 0

Representability of Kleene Posets and Kleene Lattices Kleene Posets 和 Kleene Lattices 的可表示性

IF 0.7 3区数学

Studia Logica Pub Date : 2023-12-08 DOI: 10.1007/s11225-023-10080-3

Ivan Chajda, Helmut Länger, Jan Paseka

{"title":"Representability of Kleene Posets and Kleene Lattices","authors":"Ivan Chajda, Helmut Länger, Jan Paseka","doi":"10.1007/s11225-023-10080-3","DOIUrl":"https://doi.org/10.1007/s11225-023-10080-3","url":null,"abstract":"A Kleene lattice is a distributive lattice equipped with an antitone involution and satisfying the so-called normality condition. These lattices were introduced by J. A. Kalman. We extended this concept also for posets with an antitone involution. In our recent paper (Chajda, Länger and Paseka, in: Proceeding of 2022 IEEE 52th International Symposium on Multiple-Valued Logic, Springer, 2022), we showed how to construct such Kleene lattices or Kleene posets from a given distributive lattice or poset and a fixed element of this lattice or poset by using the so-called twist product construction, respectively. We extend this construction of Kleene lattices and Kleene posets by considering a fixed subset instead of a fixed element. Moreover, we show that in some cases, this generating poset can be embedded into the resulting Kleene poset. We investigate the question when a Kleene poset can be represented by a Kleene poset obtained by the mentioned construction. We show that a direct product of representable Kleene posets is again representable and hence a direct product of finite chains is representable. This does not hold in general for subdirect products, but we show some examples where it holds. We present large classes of representable and non-representable Kleene posets. Finally, we investigate two kinds of extensions of a distributive poset ({textbf{A}}), namely its Dedekind-MacNeille completion ({{,mathrm{textbf{DM}},}}({textbf{A}})) and a completion (G({textbf{A}})) which coincides with ({{,mathrm{textbf{DM}},}}({textbf{A}})) provided ({textbf{A}}) is finite. In particular we prove that if ({textbf{A}}) is a Kleene poset then its extension (G({textbf{A}})) is also a Kleene lattice. If the subset X of principal order ideals of ({textbf{A}}) is involution-closed and doubly dense in (G({textbf{A}})) then it generates (G({textbf{A}})) and it is isomorphic to ({textbf{A}}) itself.","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":"10 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138556262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On Pretabular Extensions of Relevance Logic 论关联逻辑的表前扩展

IF 0.7 3区数学

Studia Logica Pub Date : 2023-11-16 DOI: 10.1007/s11225-023-10081-2

Asadollah Fallahi, James Gordon Raftery

引用次数: 0

A Generalization of Beall’s Off-Topic Interpretation 比尔离题解释的概括

3区数学

Studia Logica Pub Date : 2023-11-14 DOI: 10.1007/s11225-023-10075-0

Yang Song, Hitoshi Omori, Jonas R. B. Arenhart, Satoshi Tojo

引用次数: 0