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  1. 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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  2. 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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  3. 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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  4. 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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  5. 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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  6. 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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  7. 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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  8. Proving Properties of Matrices Over {\ Mathbb {Z} _ {2}}.Michael Soltys - 2012 - Archive for Mathematical Logic 51 (5-6):535-551.
    We prove assorted properties of matrices over ${\mathbb{Z}_{2}}$ , 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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  9. 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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  10. 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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  11. 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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