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  1. Formal System of Categorical Syllogistic Logic Based on the Syllogism AEE-4Long Wei - 2023 - Open Journal of Philosophy 13 (1):97-103.
    Adopting a different method from the previous scholars, this article deduces the remaining 23 valid syllogisms just taking the syllogism AEE-4 as the basic axiom. The basic idea of this study is as follows: firstly, make full use of the trichotomy structure of categorical propositions to formalize categorical syllogisms. Then, taking advantage of the deductive rules in classical propositional logic and the basic facts in the generalized quantifier theory, we deduce the remaining 23 valid categorical syllogisms by taking just one (...)
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  • Relational Syllogisms with Numerical Quantifiers and Beyond.Ka-fat Chow - 2021 - Journal of Logic, Language and Information 31 (1):1-34.
    In the first half of this paper, we present a fragment of relational syllogisms named RELSYLL consisting of quantified statements with a special set of numerical quantifiers, and introduce a number of concepts that are useful for the later sections, including indirect reduction, quantifier transformations and equivalence of syllogisms. After determining the valid and invalid syllogisms in RELSYLL, we then introduce two Derivation Methods which can be used to derive valid relational syllogisms based on known valid simple syllogisms. We also (...)
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