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  1. Granular knowledge and rational approximation in general rough sets – I.Indian Statistical Institute A. Mani Miu & India Kolkata - 2024 - Journal of Applied Non-Classical Logics 34 (2-3):294-329.
    Volume 34, Issue 2-3, June - September 2024.
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  2.  23
    Logics from rough sets.Mohua Banerjee, Mihir K. Chakraborty & Andrzej Szałas - 2024 - Journal of Applied Non-Classical Logics 34 (2):171-173.
    Rough Sets were introduced by Z. Pawlak in the year 1982 with the intention to address knowledge representation and data processing from the angle of computation and decision making. The main idea...
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  3.  7
    Modal reduction principles: a parametric shift to graphs.Willem Conradie, Krishna Manoorkar, Alessandra Palmigiano & Mattia Panettiere - 2024 - Journal of Applied Non-Classical Logics 34 (2):174-222.
    Graph-based frames have been introduced as a logical framework which internalises an inherent boundary to knowability (referred to as ‘informational entropy’), due, e.g. to perceptual, evidential or linguistic limits. They also support the interpretation of lattice-based (modal) logics as hyper-constructive logics of evidential reasoning. Conceptually, the present paper proposes graph-based frames as a formal framework suitable for generalising Pawlak's rough set theory to a setting in which inherent limits to knowability exist and need to be considered. Technically, the present paper (...)
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  4.  14
    Nelson algebras, residuated lattices and rough sets: A survey.Jouni Järvinen, Sándor Radeleczki & Umberto Rivieccio - 2024 - Journal of Applied Non-Classical Logics 34 (2):368-428.
    Over the past 50 years, Nelson algebras have been extensively studied by distinguished scholars as the algebraic counterpart of Nelson's constructive logic with strong negation. Despite these studies, a comprehensive survey of the topic is currently lacking, and the theory of Nelson algebras remains largely unknown to most logicians. This paper aims to fill this gap by focussing on the essential developments in the field over the past two decades. Additionally, we explore generalisations of Nelson algebras, such as N4-lattices which (...)
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  5. Nelson algebras, residuated lattices and rough sets: A survey.Lut School of Engineering Science Jouni Järvinen Sándor Radeleczki Umberto Rivieccio A. SOftware Engineering, Finlandb Institute Of Mathematics Lahti, Uned Hungaryc Departamento de Lógica E. Historia Y. Filosofía de la Ciencia & Spain Madrid - 2024 - Journal of Applied Non-Classical Logics 34 (2-3):368-428.
    Volume 34, Issue 2-3, June - September 2024.
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  6.  33
    A study of modal logic with semantics based on rough set theory.Md Aquil Khan, Ranjan & Amal Talukdar - 2024 - Journal of Applied Non-Classical Logics 34 (2):223-247.
    Volume 34, Issue 2-3, June - September 2024.
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  7.  17
    Some algebras and logics from quasiorder-generated covering-based approximation spaces.Arun Kumar & Mohua Banerjee - 2024 - Journal of Applied Non-Classical Logics 34 (2):248-268.
    In A. Kumar, & M. Banerjee [(2012). Definable and rough sets in covering-based approximation spaces. In T. Li. (eds.), Rough sets and knowledge technology (pp. 488–495). Springer-Verlag], A. Kumar, & M. Banerjee [(2015). Algebras of definable and rough sets in quasi order-based approximation spaces. Fundamenta Informaticae, 141(1), 37–55], authors proposed a pair of lower and upper approximation operators based on granules generated by quasiorders. This work is an extension of algebraic results presented therein. A characterisation has been presented for those (...)
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  8.  19
    Granular knowledge and rational approximation in general rough sets – I.A. Mani - 2024 - Journal of Applied Non-Classical Logics 34 (2):294-329.
    Rough sets are used in numerous knowledge representation contexts and are then empowered with varied ontologies. These may be intrinsically associated with ideas of rationality under certain conditions. In recent papers, specific granular generalisations of graded and variable precision rough sets are investigated by the present author from the perspective of rationality of approximations (and the associated semantics of rationality in approximate reasoning). The studies are extended to ideal-based approximations (sometimes referred to as subsethood-based approximations). It is additionally shown that (...)
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  9.  6
    Crypto-preorders, topological relations, information and logic.Piero Pagliani - 2024 - Journal of Applied Non-Classical Logics 34 (2):330-367.
    As is well known, any preorder R on a set U induces an Alexandrov topology on U. In some interesting cases related to data mining an Alexandrov topology can be transformed into different types of logico-algebraic models. In some cases, (pre)topological operators provided by Pointless Topology may define a topological space on U even if R is not a preorder. If this is the case, then we call R a crypto-preorder. The paper studies the conditions under which a relation R (...)
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  10.  13
    Modality-free pre-rough logic.Anirban Saha & Jayanta Sen - 2024 - Journal of Applied Non-Classical Logics 34 (2):429-451.
    In this paper, we present a modality-free pre-rough algebra. Łukasiewicz Moisil algebra and Wajsberg algebra are equivalent under a transformation. A similar type of equivalence exists in our proposed definition and standard definition of pre-rough algebra. We obtain a few modality-free algebras weaker than pre-rough algebra. Furthermore, it is also established that modality-free versions for other analogous structures weaker than pre-rough algebra do not exist. Both Hilbert-type axiomatization and sequent calculi for all proposed algebras are presented.
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  11. Crypto-preorders, topological relations, information and logic.Piero Pagliani International Rough Set Society, Rome & Italy - 2024 - Journal of Applied Non-Classical Logics 34 (2-3):330-367.
    Volume 34, Issue 2-3, June - September 2024.
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  12.  15
    Decidability of topological quasi-Boolean algebras.Yiheng Wang, Zhe Lin & Minghui Ma - 2024 - Journal of Applied Non-Classical Logics 34 (2):269-293.
    A sequent calculus S for the variety tqBa of all topological quasi-Boolean algebras is established. Using a construction of syntactic finite algebraic model, the finite model property of S is shown, and thus the decidability of S is obtained. We also introduce two non-distributive variants of topological quasi-Boolean algebras. For the variety TDM5 of all topological De Morgan lattices with the axiom 5, we establish a sequent calculus S5 and prove that the cut elimination holds for it. Consequently the decidability (...)
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  13.  31
    Wansing's bi-intuitionistic logic: semantics, extension and unilateralisation.Juan C. Agudelo-Agudelo - 2024 - Journal of Applied Non-Classical Logics 34 (1):31-54.
    The well-known algebraic semantics and topological semantics for intuitionistic logic (Int) is here extended to Wansing's bi-intuitionistic logic (2Int). The logic 2Int is also characterised by a quasi-twist structure semantics, which leads to an alternative topological characterisation of 2Int. Later, notions of Fregean negation and of unilateralisation are proposed. The logic 2Int is extended with a ‘Fregean negation’ connective ∼, obtaining 2Int∼, and it is showed that the logic N4⋆ (an extension of Nelson's paraconsistent logic) results to be the unilateralisation (...)
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  14.  18
    Relational representation for subordination Tarski algebras.Sergio A. Celani - 2024 - Journal of Applied Non-Classical Logics 34 (1):75-96.
    In this work, we study the relational representation of the class of Tarski algebras endowed with a subordination, called subordination Tarski algebras. These structures were introduced in a previous paper as a generalisation of subordination Boolean algebras. We define the subordination Tarski spaces as topological spaces with a fixed basis endowed with a closed relation. We prove that there exist categorical dualities between categories whose objects are subordination Tarski algebras and categories whose objects are subordination Tarski spaces. These results extend (...)
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  15.  21
    The existential fragment of second-order propositional intuitionistic logic is undecidable.Ken-Etsu Fujita, Aleksy Schubert, Paweł Urzyczyn & Konrad Zdanowski - 2024 - Journal of Applied Non-Classical Logics 34 (1):55-74.
    The provability problem in intuitionistic propositional second-order logic with existential quantifier and implication (∃,→) is proved to be undecidable in presence of free type variables (constants). This contrasts with the result that inutitionistic propositional second-order logic with existential quantifier, conjunction and negation is decidable.
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  16.  37
    Temporal logic of surjective bounded morphisms between finite linear processes.David Gabelaia, Evgeny Kuznetsov, Radu Casian Mihailescu, Konstantine Razmadze & Levan Uridia - 2024 - Journal of Applied Non-Classical Logics 34 (1):1-30.
    In this paper, we study temporal logic for finite linear structures and surjective bounded morphisms between them. We give a characterisation of such structures by modal formulas and show that every pair of linear structures with a bounded morphism between them can be uniquely characterised by a temporal formula up to an isomorphism. As the main result, we prove Kripke completeness of the logic with respect to the class of finite linear structures with bounded morphisms between them.
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  17.  18
    Paraconsistent logic and query answering in inconsistent databases.C. A. Middelburg - 2024 - Journal of Applied Non-Classical Logics 34 (1):133-154.
    This paper concerns the paraconsistent logic LPQ⊃,F and an application of it in the area of relational database theory. The notions of a relational database, a query applicable to a relational database, and a consistent answer to a query with respect to a possibly inconsistent relational database are considered from the perspective of this logic. This perspective enables among other things the definition of a consistent answer to a query with respect to a possibly inconsistent database without resort to database (...)
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  18.  11
    Symmetric bi-derivations of UP(BCC)-algebras.Damla Yılmaz - 2024 - Journal of Applied Non-Classical Logics 34 (1):155-169.
    In this paper, we define the notions of (l,r)-symmetric bi-derivations and (r,l)-symmetric bi-derivations on UP-algebras and investigate some properties of them. For these derivations, we introduce the sets Kerd(U), Fixd(U) and FixD(U). Moreover, we examine with examples whether these sets are UP-subalgebra or UP-ideal.
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