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On the Concept of a Notational Variant

In Alexandru Baltag, Jeremy Seligman & Tomoyuki Yamada (eds.), Logic, Rationality, and Interaction (LORI 2017, Sapporo, Japan). pp. 284-298 (2017)

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  1. What Can You Say? Measuring the Expressive Power of Languages.Alexander W. Kocurek - 2018 - Dissertation, University of California, Berkeley
    There are many different ways to talk about the world. Some ways of talking are more expressive than others—that is, they enable us to say more things about the world. But what exactly does this mean? When is one language able to express more about the world than another? In my dissertation, I systematically investigate different ways of answering this question and develop a formal theory of expressive power, translation, and notational variance. In doing so, I show how these investigations (...)
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  • On Logical and Scientific Strength.Luca Incurvati & Carlo Nicolai - manuscript
    The notion of strength has featured prominently in recent debates about abductivism in the epistemology of logic. Following Williamson and Russell, we distinguish between logical and scientific strength and discuss the limits of the characterizations they employ. We then suggest understanding logical strength in terms of interpretability strength and scientific strength as a special case of logical strength. We present applications of the resulting notions to comparisons between logics in the traditional sense and mathematical theories.
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  • On Equivalence Relations Between Interpreted Languages, with an Application to Modal and First-Order Language.Kai F. Wehmeier - forthcoming - Erkenntnis:1-21.
    I examine notions of equivalence between logics and develop two new ones that invoke not only the algebraic but also the string-theoretic structure of the underlying language. As an application, I show how to construe modal operator languages as what might be called typographical notational variants of bona fide first-order languages.
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