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  1.  2
    Completeness, Categoricity and Imaginary Numbers: The Debate on Husserl.Víctor Aranda - 2020 - Bulletin of the Section of Logic 49 (2).
    Husserl's two notions of "definiteness" enabled him to clarify the problem of imaginary numbers. The exact meaning of these notions is a topic of much controversy. A "definite" axiom system has been interpreted as a syntactically complete theory, and also as a categorical one. I discuss whether and how far these readings manage to capture Husserl's goal of elucidating the problem of imaginary numbers, raising objections to both positions. Then, I suggest an interpretation of "absolute definiteness" as semantic completeness and (...)
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  2.  1
    Computer-Supported Analysis of Positive Properties, Ultrafilters and Modal Collapse in Variants of Gödel's Ontological Argument.Christoph Benzmüller & David Fuenmayor - 2020 - Bulletin of the Section of Logic 49 (2).
    Three variants of Kurt Gödel's ontological argument, proposed by Dana Scott, C. Anthony Anderson and Melvin Fitting, are encoded and rigorously assessed on the computer. In contrast to Scott's version of Gödel's argument the two variants contributed by Anderson and Fitting avoid modal collapse. Although they appear quite different on a cursory reading they are in fact closely related. This has been revealed in the computer-supported formal analysis presented in this article. Key to our formal analysis is the utilization of (...)
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  3.  3
    Formal Methods and Science in Philosophy: Introduction to the Special Issue.Patrick Blackburn, Srećko Kovač & Kordula Świętorzecka - 2020 - Bulletin of the Section of Logic 49 (2).
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  4.  2
    Cantor on Infinitesimals. Historical and Modern Perspective.Piotr Błaszczyk & Marlena Fila - 2020 - Bulletin of the Section of Logic 49 (2).
    In his 1887's Mitteilungen zur Lehre von Transfiniten, Cantor seeks to prove inconsistency of infinitesimals. We provide a detailed analysis of his argument from both historical and mathematical perspective. We show that while his historical analysis are questionable, the mathematical part of the argument is false.
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  5.  1
    Compounding Objects.Zvonimir Šikić - 2020 - Bulletin of the Section of Logic 49 (2).
    We prove a characterization theorem for filters, proper filters and ultrafilters which is a kind of converse of Łoś's theorem. It is more natural than the usual intuition of these terms as large sets of coordinates, which is actually unconvincing in the case of ultrafilters. As a bonus, we get a very simple proof of Łoś's theorem.
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  6.  2
    What Is the Sense in Logic and Philosophy of Language.Urszula Wybraniec-Skardowska - 2020 - Bulletin of the Section of Logic 49 (2).
    In the paper, various notions of the logical semiotic sense of linguistic expressions – namely, syntactic and semantic, intensional and extensional – are considered and formalised on the basis of a formal-logical conception of any language L characterised categorially in the spirit of certain Husserl's ideas of pure grammar, Leśniewski-Ajdukiewicz's theory of syntactic/semantic categories and, in accordance with Frege's ontological canons, Bocheński's and some of Suszko's ideas of language adequacy of expressions of L. The adequacy ensures their unambiguous syntactic and (...)
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  7.  3
    A Topological Approach to Tense LMn×M-Algebras.Aldo V. Figallo, Inés Pascual & Gustavo Pelaitay - 2020 - Bulletin of the Section of Logic 49 (1).
    In 2015, tense n × m-valued Lukasiewicz–Moisil algebras were introduced by A. V. Figallo and G. Pelaitay as an generalization of tense n-valued Łukasiewicz–Moisil algebras. In this paper we continue the study of tense LMn×m-algebras. More precisely, we determine a Priestley-style duality for these algebras. This duality enables us not only to describe the tense LMn×m-congruences on a tense LMn×m-algebra, but also to characterize the simple and subdirectly irreducible tense LMn×m-algebras.
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  8.  2
    Inf-Hesitant Fuzzy Ideals in BCK/BCI-Algebras.Young Bae Jun & Seok-Zun Song - 2020 - Bulletin of the Section of Logic 49 (1).
    Based on the hesitant fuzzy set theory which is introduced by Torra in the paper [12], the notions of Inf-hesitant fuzzy subalgebras, Inf-hesitant fuzzy ideals and Inf-hesitant fuzzy p-ideals in BCK/BCI-algebras are introduced, and their relations and properties are investigated. Characterizations of an Inf-hesitant fuzzy subalgebras, an Inf-hesitant fuzzy ideals and an Inf-hesitant fuzzy p-ideal are considered. Using the notion of BCK-parts, an Inf-hesitant fuzzy ideal is constructed. Conditions for an Inf-hesitant fuzzy ideal to be an Inf-hesitant fuzzy p-ideal are (...)
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  9.  2
    May the Sea-Battle Tommorow Not Happen?Bożena Pięta - 2020 - Bulletin of the Section of Logic 49 (1).
    This note provides a review of the book 'On the Sea-Battle Tomorrow That May Not Happen' by Tomasz Jarmużek.
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  10.  2
    The Dynamic Epistemic Logic for Actual Knowledge.Arkadiusz Wójcik - 2020 - Bulletin of the Section of Logic 49 (1).
    The dynamic epistemic logic for actual knowledge models the phenomenon of actual knowledge change when new information is received. In contrast to the systems of dynamic epistemic logic which have been discussed in the past literature, our system is not burdened with the problem of logical omniscience, that is, an idealized assumption that the agent explicitly knows all classical tautologies and all logical consequences of his or her knowledge. We provide a sound and complete axiomatization for this logic.
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  11.  2
    Nilpotent Minimum Logic NM and Pretabularity.Eunsuk Yang - 2020 - Bulletin of the Section of Logic 49 (1).
    This paper deals with pretabularity of fuzzy logics. For this, we first introduce two systems NMnfp and NM½, which are expansions of the fuzzy system NM, and examine the relationships between NMnfp and the another known extended system NM—. Next, we show that NMnfp and NM½ are pretabular, whereas NM is not. We also discuss their algebraic completeness.
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