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Non-Classical Logic. Theory and Applications最新文献

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On the Expressive Power of the Normal Form for Branching-Time Temporal Logics 分支时间时态逻辑范式的表达能力
Non-Classical Logic. Theory and Applications Pub Date : 2022-04-14 DOI: 10.4204/EPTCS.358.19
A. Bolotov
{"title":"On the Expressive Power of the Normal Form for Branching-Time Temporal Logics","authors":"A. Bolotov","doi":"10.4204/EPTCS.358.19","DOIUrl":"https://doi.org/10.4204/EPTCS.358.19","url":null,"abstract":"With the emerging applications that involve complex distributed systems branching-time specifications are specifically important as they reflect dynamic and non-deterministic nature of such applications. We describe the expressive power of a simple yet powerful branching-time specification framework -- branching-time normal form (BNF), which has been developed as part of clausal resolution for branching-time temporal logics. We show the encoding of Buchi Tree Automata in the language of the normal form, thus representing, syntactically, tree automata in a high-level way. Thus we can treat BNF as a normal form for the latter. These results enable us (1) to translate given problem specifications into the normal form and apply as a verification method a deductive reasoning technique -- the clausal temporal resolution; (2) to apply one of the core components of the resolution method -- the loop searching to extract, syntactically, hidden invariants in a wide range of complex temporal specifications.","PeriodicalId":214417,"journal":{"name":"Non-Classical Logic. Theory and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117338875","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 van Benthem Theorem for Atomic and Molecular Logics 原子与分子逻辑中的范本瑟姆定理
Non-Classical Logic. Theory and Applications Pub Date : 2022-04-14 DOI: 10.4204/EPTCS.358.7
Guillaume Aucher
{"title":"A van Benthem Theorem for Atomic and Molecular Logics","authors":"Guillaume Aucher","doi":"10.4204/EPTCS.358.7","DOIUrl":"https://doi.org/10.4204/EPTCS.358.7","url":null,"abstract":"After recalling the definitions of atomic and molecular logics, we show how notions of bisimulation can be automatically defined from the truth conditions of the connectives of any of these logics. Then, we prove a generalization of van Benthem modal characterization theorem for molecular logics. Our molecular connectives should be uniform and contain all conjunctions and disjunctions. We use modal logic, the Lambek calculus and modal intuitionistic logic as case study and compare in particular our work with Olkhovikov's work.","PeriodicalId":214417,"journal":{"name":"Non-Classical Logic. Theory and Applications","volume":"86 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123290518","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: 3
Decidability of Intuitionistic Sentential Logic with Identity via Sequent Calculus 用序演算研究具有恒等的直觉句子逻辑的可决性
Non-Classical Logic. Theory and Applications Pub Date : 2022-04-14 DOI: 10.4204/EPTCS.358.10
Agata Tomczyk, Dorota Leszczynska-Jasion
{"title":"Decidability of Intuitionistic Sentential Logic with Identity via Sequent Calculus","authors":"Agata Tomczyk, Dorota Leszczynska-Jasion","doi":"10.4204/EPTCS.358.10","DOIUrl":"https://doi.org/10.4204/EPTCS.358.10","url":null,"abstract":"The aim of our paper is twofold: firstly we present a sequent calculus for an intuitionistic non-Fregean logic ISCI, which is based on the calculus presented in the paper by Chlebowski and Leszczynska-Jasion, 'An Investigation into Intuitionistic Logic with Identity' (Bulletin of the Section of Logic 48(4), p. 259-283, 2019) and, secondly, we discuss the problem of decidability of ISCI via the obtained system. The original calculus from the mentioned paper did not provide the decidability result for ISCI. There are two problems to be solved in order to obtain this result: the so called loops characteristic for intuitionistic logic and the lack of the subformula property due to the form of the identity-dedicated rules. We discuss possible routes to overcome these problems: we consider a weaker version of the subformula property, guarded by the complexity of formulas which can be included within it; we also present a proof-search procedure such that when it fails, then there exists a countermodel (in Kripke semantics for ISCI).","PeriodicalId":214417,"journal":{"name":"Non-Classical Logic. Theory and Applications","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128292916","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
Combining First-Order Classical and Intuitionistic Logic 一阶经典逻辑与直觉逻辑的结合
Non-Classical Logic. Theory and Applications Pub Date : 2022-04-14 DOI: 10.4204/EPTCS.358.3
Masanobu Toyooka, Katsuhiko Sano
{"title":"Combining First-Order Classical and Intuitionistic Logic","authors":"Masanobu Toyooka, Katsuhiko Sano","doi":"10.4204/EPTCS.358.3","DOIUrl":"https://doi.org/10.4204/EPTCS.358.3","url":null,"abstract":"This paper studies a first-order expansion of a combination C+J of intuitionistic and classical propositional logic, which was studied by Humberstone (1979) and del Cerro and Herzig (1996), from a proof-theoretic viewpoint. While C+J has both classical and intuitionistic implications, our first-order expansion adds classical and intuitionistic universal quantifiers and one existential quantifier to C+J. This paper provides a multi-succedent sequent calculus G(FOC+J) for our combination of the first-order intuitionistic and classical logic. Our sequent calculus G(FOC+J) restricts contexts of the right rules for intuitionistic implication and intuitionistic universal quantifier to particular forms of formulas. The cut-elimination theorem is established to ensure the subformula property. As a corollary, G(FOC+J) is conservative over both first-order intuitionistic and classical logic. Strong completeness of G(FOC+J) is proved via a canonical model argument.","PeriodicalId":214417,"journal":{"name":"Non-Classical Logic. Theory and Applications","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115353111","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
Normalisation for Some Infectious Logics and Their Relatives 一些传染性逻辑及其相关逻辑的归一化
Non-Classical Logic. Theory and Applications Pub Date : 2022-04-14 DOI: 10.4204/EPTCS.358.2
Y. Petrukhin
{"title":"Normalisation for Some Infectious Logics and Their Relatives","authors":"Y. Petrukhin","doi":"10.4204/EPTCS.358.2","DOIUrl":"https://doi.org/10.4204/EPTCS.358.2","url":null,"abstract":"We consider certain infectious logics (Sfde, dSfde, K3w, and PWK) and several their non-infectious modifications, including two new logics, reformulate previously constructed natural deduction systems for them (or present such systems from scratch for the case of new logics) in way such that the proof of normalisation theorem becomes possible for these logics. We present such a proof and establish the negation subformula property for the logics in question.","PeriodicalId":214417,"journal":{"name":"Non-Classical Logic. Theory and Applications","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121146293","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
Puzzles of Existential Generalisation from Type-theoretic Perspective 类型论视角下存在概括的困惑
Non-Classical Logic. Theory and Applications Pub Date : 2022-04-14 DOI: 10.4204/EPTCS.358.6
J. Raclavský
{"title":"Puzzles of Existential Generalisation from Type-theoretic Perspective","authors":"J. Raclavský","doi":"10.4204/EPTCS.358.6","DOIUrl":"https://doi.org/10.4204/EPTCS.358.6","url":null,"abstract":"The present paper addresses several puzzles related to the Rule of Existential Generalization, (EG). In solution to these puzzles from the viewpoint of simple type theory, I distinguish (EG) from a modified Rule of Existential Quantifier Introduction which is derivable from (EG). Both these rules are often confused and both are considered as primitive but I show that (EG) itself is derivable from the proper Rule of Existential Quantifier Introduction. Moreover, the latter rule must be primitive in logical systems that treat both total and partial functions, for the universal and the existential quantifiers are not interdefinable in them. An appropriate natural deduction for such a system is deployed. The present logical system is simpler than the system recently proposed and applied by the present author. It utilises an adequate definition of substitution which is capable of handling not only a higher-order quantification, but also (hyper)intensional contexts.","PeriodicalId":214417,"journal":{"name":"Non-Classical Logic. Theory and Applications","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132835349","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
Bilateral Inversion Principles 双边倒置原则
Non-Classical Logic. Theory and Applications Pub Date : 2022-04-14 DOI: 10.4204/EPTCS.358.15
Nils Kürbis
{"title":"Bilateral Inversion Principles","authors":"Nils Kürbis","doi":"10.4204/EPTCS.358.15","DOIUrl":"https://doi.org/10.4204/EPTCS.358.15","url":null,"abstract":"This paper formulates a bilateral account of harmony that is an alternative to one proposed by Francez. It builds on an account of harmony for unilateral logic proposed by K\"urbis and the observation that reading the rules for the connectives of bilateral logic bottom up gives the grounds and consequences of formulas with the opposite speech act. I formulate a process I call 'inversion' which allows the determination of assertive elimination rules from assertive introduction rules, and rejective elimination rules from rejective introduction rules, and conversely. It corresponds to Francez's notion of vertical harmony. I also formulate a process I call 'conversion', which allows the determination of rejective introduction rules from assertive elimination rules and conversely, and the determination of assertive introduction rules from rejective elimination rules and conversely. It corresponds to Francez's notion of horizontal harmony. The account has a number of features that distinguishes it from Francez's.","PeriodicalId":214417,"journal":{"name":"Non-Classical Logic. Theory and Applications","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126198615","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
Natural Deduction for Assertibility and Deniability 可断言性和可否认性的自然演绎
Non-Classical Logic. Theory and Applications Pub Date : 2022-04-14 DOI: 10.4204/EPTCS.358.4
V. Punčochář, Berta Grimau
{"title":"Natural Deduction for Assertibility and Deniability","authors":"V. Punčochář, Berta Grimau","doi":"10.4204/EPTCS.358.4","DOIUrl":"https://doi.org/10.4204/EPTCS.358.4","url":null,"abstract":"In this paper we split every basic propositional connective into two versions, one is called extensional and the other one intensional. The extensional connectives are semantically characterized by standard truth conditions that are relative to possible worlds. Assertibility and deniability of sentences built out of atomic sentences by extensional connectives are defined in terms of the notion of truth. The intensional connectives are characterized directly by assertibility and deniability conditions without the notion of truth. We pay special attention to the deniability condition for intensional implication. We characterize the logic of this mixed language by a system of natural deduction that sheds some light on the inferential behaviour of these two kinds of connectives and on the way they can interact.","PeriodicalId":214417,"journal":{"name":"Non-Classical Logic. Theory and Applications","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127619912","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
The Forms of Categorical Proposition 直言命题的形式
Non-Classical Logic. Theory and Applications Pub Date : 2022-04-14 DOI: 10.4204/EPTCS.358.17
F. Schang, G. Englebretsen, J.-Martín Castro-Manzano
{"title":"The Forms of Categorical Proposition","authors":"F. Schang, G. Englebretsen, J.-Martín Castro-Manzano","doi":"10.4204/EPTCS.358.17","DOIUrl":"https://doi.org/10.4204/EPTCS.358.17","url":null,"abstract":"An exhaustive survey of categorical propositions is proposed in the present paper, both with respect to their nature and the logical problems raised by them. Through a comparative analysis of Term Logic and First-Order Logic, it is shown that the famous problem of existential import may be solved in two ways: with a model-adaptive strategy, in which the square of opposition is validated by restricting the models; with a language-adaptive strategy, in which the logical form of categorical propositions is extended in order to validate the square in every model. The latter strategy is advocated in the name of logic, which means truth in every model. Finally, the present paper needs some automatic process in order to determine the nature of logical relations between any pair of the available 256 categorical propositions. This requires the implementation of a programming machine in the style of Prolog.","PeriodicalId":214417,"journal":{"name":"Non-Classical Logic. Theory and Applications","volume":"3 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133293007","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
Normalization by Evaluation for the Lambek Calculus Lambek微积分的归一化求值
Non-Classical Logic. Theory and Applications Pub Date : 2022-04-14 DOI: 10.4204/EPTCS.358.8
Niccolò Veltri
{"title":"Normalization by Evaluation for the Lambek Calculus","authors":"Niccolò Veltri","doi":"10.4204/EPTCS.358.8","DOIUrl":"https://doi.org/10.4204/EPTCS.358.8","url":null,"abstract":"The syntactic calculus of Lambek is a deductive system for the multiplicative fragment of intuitionistic non-commutative linear logic. As a fine-grained calculus of resources, it has many applications, mostly in formal computational investigations of natural languages. This paper introduces a calculus of beta-eta-long normal forms for derivations in the Lambek calculus with multiplicative unit and conjunction among its logical connectives. Reduction to normal form follows the normalization by evaluation (NbE) strategy: (i) evaluate a derivation in a Kripke model of Lambek calculus; (ii) extract normal forms from the obtained semantic values. The implementation of the NbE algorithm requires the presence of a strong monad in the Kripke interpretation of positive formulae, in analogy with the extension of intuitionistic propositional logic with falsity and disjunction. The NbE algorithm can also be instantiated with minor variations to calculi for related substructural logics, such as multiplicative and dual intuitionistic linear logic (MILL and DILL).","PeriodicalId":214417,"journal":{"name":"Non-Classical Logic. Theory and Applications","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130144670","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
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