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  1. Modeling future indeterminacy in possibility semantics.Fabrizio Cariani - manuscript
    Possibility semantics offers an elegant framework for a semantic analysis of modal logic that does not recruit fully determinate entities such as possible worlds. The present papers considers the application of possibility semantics to the modeling of the indeterminacy of the future. Interesting theoretical problems arise in connection to the addition of object-language determinacy operator. We argue that adding a two-dimensional layer to possibility semantics can help solve these problems. The resulting system assigns to the two-dimensional determinacy operator a well-known (...)
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  2. The Logical Web.Matheus Silva - manuscript
    Different logic systems are motivated by attempts to fix the counter-intuitive instances of classical argumentative forms, e.g., strengthening of the antecedent, contraposition and conditional negation. These counter-examples are regarded as evidence that classical logic should be rejected in favour of a new logic system in which these argumentative forms are considered invalid. It is argued that these logical revisions are ad hoc, because those controversial argumentative forms are implied by other argumentative forms we want to keep. It is impossible to (...)
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  3. Subjunctive Conditionals are Material.Matheus Silva - manuscript
    The material account proposes that indicative conditionals are material, but it is widely believed that this account cannot be applied to subjunctive conditionals. There are three reasons for this consensus: (1) the concern that most subjunctive conditionals would be vacuously true if they were material, which seems implausible; (2) the inconsistency with Adams pair, which suggests that indicative and subjunctive conditionals have different truth conditions; and (3) the belief that the possible world theories are a superior alternative to the material (...)
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  4. ALL THE MORE: A Merged List of 72 Qal Vachomer Arguments in the Tanakh.Avi Sion - 2024 - Geneva, Switzerland: Avi Sion (via Kindle).
    ALL THE MORE, by Avi Sion, Ph.D., comprises a merged list of 72 qal vachomer arguments in the Tanakh, i.e. of a fortiori arguments in the Hebrew Bible. This listing brings together lists proposed in past rabbinic literature and in more recent studies by the author. The literature research for it was carried out mainly by R. Yaakov Gabay, who looked into works in Hebrew by five rabbis who had proposed lists, namely: R. Shmuel Yaffe Ashkenazi (Yefeh Toar, 1597), R. (...)
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  5. Outline of a Theory of Reasons.Vincenzo Crupi & Andrea Iacona - 2023 - Philosophical Quarterly 73 (1):117-142.
    This paper investigates the logic of reasons. Its aim is to provide an analysis of the sentences of the form ‘p is a reason for q’ that yields a coherent account of their logical properties. The idea that we will develop is that ‘p is a reason for q’ is acceptable just in case a suitably defined relation of incompatibility obtains between p and ¬q. As we will suggest, a theory of reasons based on this idea can solve three challenging (...)
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  6. What is LK? Vol.1. Sequent (Textbook Series in Symbolic Logic).Yusuke Kaneko - 2023 - Amazon Kindle.
    LK is much more difficult than NK, and to make matters worse, Gentzen's intention is still unclear when it comes to that system (LK). -/- This book, Vol.1 of the series titled What is LK?, tackles this issue, focusing on the sequent, the most enigmatic notion we find in LK. The dependence-relation we find in NK shall play a crucial role in that investigation. -/- The style is typically textbook-like, so readers can learn the system of LK, using this series (...)
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  7. Classical Logic.Seykora Maria L. - 2023 - San Diego: Cognella, Inc..
    Peer Review Book Description - Maria Seykora -/- Classical Logic will attempt to give a comprehensive and rigorous introduction and more advanced overview of the area of logic widely known as “classical logic,” as distinguished from modern-day “non-classical logic,” for undergraduate students in general. It will cover the topics of Informal Logic (including logical fallacies, deduction, induction, and abductive reasoning) and Formal Logic. (Because it aims to cover these two topics, the title may change to Informal and Classical Logic for (...)
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  8. The Exoteric Square of Opposition.Jean-Yves Beziau & Ioannis Vandoulakis (eds.) - 2022 - Birkhauser.
    The theory of the square of opposition has been studied for over 2,000 years and has seen a resurgence in new theories and research since the second half of the twentieth century. This volume collects papers presented at the Sixth World Congress on the Square of Opposition, held in Crete in 2018, developing an interdisciplinary exploration of the theory. Chapter authors explore subjects such as Aristotle’s ontological square, logical oppositions in Avicenna’s hypothetical logic, and the power of the square of (...)
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  9. Bilateral Inversion Principles.Nils Kürbis - 2022 - Electronic Proceedings in Theoretical Computer Science 358:202–215.
    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 Kürbis 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 (...)
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  10. In Defence of Discrete Plural Logic (or How to Avoid Logical Overmedication When Dealing with Internally Singularized Pluralities).Gustavo Picazo - 2022 - Disputatio 14 (64):51-63.
    In recent decades, plural logic has established itself as a well-respected member of the extensions of first-order classical logic. In the present paper, I draw attention to the fact that among the examples that are commonly given in order to motivate the need for this new logical system, there are some in which the elements of the plurality in question are internally singularized (e.g. ‘Whitehead and Russell wrote Principia Mathematica’), while in others they are not (e.g. ‘Some philosophers wrote Principia (...)
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  11. Oliver and Smiley on the Collective–Distributive Opposition.Gustavo Picazo - 2022 - Logos and Episteme 13 (2):201-205.
    Two objections are raised against Oliver and Smiley’s analysis of the collective–distributive opposition in their 2016 book: They take it as a basic premise that the collective reading of ‘baked a cake’ corresponds to a predicate different from its distributive reading, and the same applies to all predicate expressions that admit both a collective and a distributive interpretation. At the same time, however, they argue that inflectional forms of the same lexeme reveal a univocity that should be preserved in a (...)
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  12. Ācārya Māņikyanandi’s Parīkşāmukha Sūtra – Essence of the Jaina Nyāya आचार्य माणिक्यनन्दि विरचित परीक्षामुख सूत्र.Vijay K. Jain (ed.) - 2021 - Dehradun, India: Vikalp Printers.
    The science-of-thought (Nyāya) has always been an integral part of the four constituents (anuyoga) – prathamānuyoga, karuņānuyoga, caraņānuyoga, and dravyānuyoga – of the Jaina Scripture. Through Parīkşāmukha Sūtra, Ācārya Māņikyanandi (circa 7th-8th century A.D.) churned the nectar of the science-of-thought (Nyāya) from the ocean of the words of the master-composers like Ācārya Samantabhadra and Bhaţţa Akalańka Deva. The valid-knowledge (pramāņa) ascertains the true nature of objects while the fallacious-knowledge (pramāņābhāsa) does the opposite. Parīkşāmukha Sūtra characterizes, as per the earlier authoritative (...)
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  13. History of Arabic Logic.Mehmet Karabela - 2021 - In Islamic Thought Through Protestant Eyes. New York: Routledge. pp. 224-235.
    Johannes Steuchius’ disputatio uses Arabic logic to present an historical account of the development of philosophical thought in Arabia before and after the emergence of Islam. Steuchius first proposes that philosophy drew its origins from the East. His evidence for this claim is that many of the Greek philosophers, considered the forefathers of European philosophy, began cultivating their philosophical thinking as a result of exposure to ancient Eastern philosophy. After the introduction of Greek philosophy, it is agreed that dialectic was (...)
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  14. Approximating trees as coloured linear orders and complete axiomatisations of some classes of trees.Ruaan Kellerman & Valentin Goranko - 2021 - Journal of Symbolic Logic 86 (3):1035-1065.
    We study the first-order theories of some natural and important classes of coloured trees, including the four classes of trees whose paths have the order type respectively of the natural numbers, the integers, the rationals, and the reals. We develop a technique for approximating a tree as a suitably coloured linear order. We then present the first-order theories of certain classes of coloured linear orders and use them, along with the approximating technique, to establish complete axiomatisations of the four classes (...)
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  15. Normalisation for Bilateral Classical Logic with some Philosophical Remarks.Nils Kürbis - 2021 - Journal of Applied Logics 2 (8):531-556.
    Bilateralists hold that the meanings of the connectives are determined by rules of inference for their use in deductive reasoning with asserted and denied formulas. This paper presents two bilateral connectives comparable to Prior's tonk, for which, unlike for tonk, there are reduction steps for the removal of maximal formulas arising from introducing and eliminating formulas with those connectives as main operators. Adding either of them to bilateral classical logic results in an incoherent system. One way around this problem is (...)
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  16. The search for symmetry in Hohfeldian modalities.Matteo Pascucci & Giovanni Sileno - 2021 - In Amrita Basu, Gem Stapleton, Sven Linker, Catherine Legg, Emmanuel Manalo & Petrucio Viana (eds.), Diagrammatic Representation and Inference. Proceedings of Diagrams 2021. Springer. pp. 87-102.
    In this work we provide an analysis of some issues arising with geometrical representations of a family of deontic and potestative relations that can be classified as Hohfeldian modalities, traditionally illustrated on two diagrams, the Hohfeldian squares. Our main target is the lack of symmetry to be found in various formal accounts by drawing analogies with the square of opposition for alethic modalities. We argue that one should rather rely on an analogy with the alethic hexagon of opposition and exploit (...)
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  17. Traits essentiels d'une formalisation adéquate.Gheorghe-Ilie Farte - 2020 - Argumentum. Journal of the Seminar of Discursive Logic, Argumentation Theory and Rhetoric 18 (1):163-174.
    In order to decide whether a discursive product of human reason corresponds or not to the logical order, one must analyze it in terms of syntactic correctness, consistency, and validity. The first step in logical analysis is formalization, that is, the process by which logical forms of thoughts are represented in different formal languages or logical systems. Although each thought can be properly formalized in different ways, the formalization variants are not equally adequate. The adequacy of formalization seems to depend (...)
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  18. Form and Content: An Introduction to Formal Logic.Derek D. Turner - 2020 - Digital Commons @ Connecticut College.
    Derek Turner, Professor of Philosophy, has written an introductory logic textbook that students at Connecticut College, or anywhere, can access for free. The book differs from other standard logic textbooks in its reliance on fun, low-stakes examples involving dinosaurs, a dog and his friends, etc. This work is published in 2020 under a Creative Commons AttributionNonCommercial-NoDerivatives 4.0 International License. You may share this text in any format or medium. You may not use it for commercial purposes. If you share it, (...)
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  19. The Completeness: From Henkin's Proposition to Quantum Computer.Vasil Penchev - 2018 - Логико-Философские Штудии 16 (1-2):134-135.
    The paper addresses Leon Hen.kin's proposition as a " lighthouse", which can elucidate a vast territory of knowledge uniformly: logic, set theory, information theory, and quantum mechanics: Two strategies to infinity are equally relevant for it is as universal and t hus complete as open and thus incomplete. Henkin's, Godel's, Robert Jeroslow's, and Hartley Rogers' proposition are reformulated so that both completeness and incompleteness to be unified and thus reduced as a joint property of infinity and of all infinite sets. (...)
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  20. Finitist set theory in ontological modeling.Avril Styrman & Aapo Halko - 2018 - Applied ontology 13 (2):107-133.
    This article introduces finitist set theory (FST) and shows how it can be applied in modeling finite nested structures. Mereology is a straightforward foundation for transitive chains of part-whole relations between individuals but is incapable of modeling antitransitive chains. Traditional set theories are capable of modeling transitive and antitransitive chains of relations, but due to their function as foundations of mathematics they come with features that make them unnecessarily difficult in modeling finite structures. FST has been designed to function as (...)
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  21. Proving properties of matrices over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{Z}_{2}}$$\end{document}. [REVIEW]Michael Soltys - 2012 - Archive for Mathematical Logic 51 (5-6):535-551.
    We prove assorted properties of matrices over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{Z}_{2}}$$\end{document}, and outline the complexity of the concepts required to prove these properties. The goal of this line of research is to establish the proof complexity of matrix algebra. It also presents a different approach to linear algebra: one that is formal, consisting in algebraic manipulations according to the axioms of a ring, rather than the traditional semantic approach via linear transformations.
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  22. A Note on Plural Logic.Gustavo Fernández Díez - 2010 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 17 (2):150-162.
    A distinction is introduced between itemized and non-itemized plural predication. It is argued that a full-fledged system of plural logic is not necessary in order to account for the validity of inferences concerning itemized collective predication. Instead, it is shown how this type of inferences can be adequately dealt with in a first-order logic system, after small modifications on the standard treatment. The proposed system, unlike plural logic, has the advantage of preserving completeness. And as a result, inferences such as (...)
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  23. Tarského definice pojmu pravdy a její kritika.Jan Štěpánek - 2010 - Pro-Fil 11 (1):10-36.
    This paper aims to describe and examine Alfred Tarski's famous semantic conception of truth as well as some of the critiques presented against it. The first part of this paper is divided into five segments: criteria imposed upon every adequate definition of truth are discussed in the first segment; the second is dedicated to Tarski’s Convention T; distinction between object language and metalanguage, as well as Tarski’s attitude toward formalized and colloquial languages, is described in the third segment; fourth segment (...)
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  24. Quantifier Elimination For Queues.Christian Straßer - 2006 - In Jan Draisma & Hanspeter Kraft (eds.), Rhine Workshop on Computer Algebra. Proceedings of the Rwca 2006. Universitaet Basel. pp. 239--248.
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  25. On an application of categoricity.Alexander Paseau - 2005 - Proceedings of the Aristotelian Society 105 (1):395-399.
    James Walmsley in “Categoricity and Indefinite Extensibility” argues that a realist about some branch of mathematics X (e.g. arithmetic) apparently cannot use the categoricity of an axiomatisation of X to justify her belief that every sentence of the language of X has a truth-value. My discussion note first corrects Walmsley’s formulation of his claim. It then shows that his argument for it hinges on the implausible idea that grasping that there is some model of the axioms amounts to grasping that (...)
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  26. Forallx Adelaide.Antony Eagle, Tim Button & P. D. Magnus - manuscript
  27. Notes on Hegel’s ‘New Account of Conceptual Form’,” Critique online symposium on Sally Sedgwick’s Hegel’s Critique of Kant; From Dichotomy to Identity.Sebastian Rand - unknown