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Henkin Quantifiers,[w:] Krynicki M., Mostowski M., Szczerba LW (red.)

In M. Krynicki, M. Mostowski & L. Szczerba (eds.), Quantifiers: Logics, Models and Computation. Kluwer Academic Publishers (1995)

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  1. “Mathematics is the Logic of the Infinite”: Zermelo’s Project of Infinitary Logic.Jerzy Pogonowski - 2021 - Studies in Logic, Grammar and Rhetoric 66 (3):673-708.
    In this paper I discuss Ernst Zermelo’s ideas concerning the possibility of developing a system of infinitary logic that, in his opinion, should be suitable for mathematical inferences. The presentation of Zermelo’s ideas is accompanied with some remarks concerning the development of infinitary logic. I also stress the fact that the second axiomatization of set theory provided by Zermelo in 1930 involved the use of extremal axioms of a very specific sort.1.
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  • Existential Graphs: What a Diagrammatic Logic of Cognition Might Look Like.Ahti-Veikko Pietarinen - 2011 - History and Philosophy of Logic 32 (3):265-281.
    This paper examines the contemporary philosophical and cognitive relevance of Charles Peirce's diagrammatic logic of existential graphs (EGs), the ?moving pictures of thought?. The first part brings to the fore some hitherto unknown details about the reception of EGs in the early 1900s that took place amidst the emergence of modern conceptions of symbolic logic. In the second part, philosophical aspects of EGs and their contributions to contemporary logical theory are pointed out, including the relationship between iconic logic and images, (...)
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  • Quantificational Modal Logic with Sequential Kripke Semantics.Stefano Borgo - 2005 - Journal of Applied Non-Classical Logics 15 (2):137-188.
    We introduce quantificational modal operators as dynamic modalities with Henkin quantifiers as indices. The adoption of matrices of indices gives an expressive formalism which is here motivated with examples from the area of multi-agent systems. We study the formal properties of the resulting logic which, formally speaking, does not satisfy the normality condition. However, the logic admits a semantics in terms of Kripke structures. As a consequence, standard techniques for normal modal logic become available. We apply these to prove completeness (...)
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