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  1. Implicit and Explicit Stances in Logic.Johan van Benthem - 2019 - Journal of Philosophical Logic 48 (3):571-601.
    We identify a pervasive contrast between implicit and explicit stances in logical analysis and system design. Implicit systems change received meanings of logical constants and sometimes also the notion of consequence, while explicit systems conservatively extend classical systems with new vocabulary. We illustrate the contrast for intuitionistic and epistemic logic, then take it further to information dynamics, default reasoning, and other areas, to show its wide scope. This gives a working understanding of the contrast, though we stop short of a (...)
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  • On Expressive Power of Basic Modal Intuitionistic Logic as a Fragment of Classical FOL.Grigory K. Olkhovikov - 2017 - Journal of Applied Logic 21:57-90.
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  • The Relevant Fragment of First Order Logic.Guillermo Badia - 2016 - Review of Symbolic Logic 9 (1):143-166.
    Under a proper translation, the languages of propositional (and quantified relevant logic) with an absurdity constant are characterized as the fragments of first order logic preserved under (world-object) relevant directed bisimulations. Furthermore, the properties of pointed models axiomatizable by sets of propositional relevant formulas have a purely algebraic characterization. Finally, a form of the interpolation property holds for the relevant fragment of first order logic.
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  • On Generalized Van Benthem-Type Characterizations.Grigory K. Olkhovikov - 2017 - Annals of Pure and Applied Logic 168 (9):1643-1691.
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  • Bi-Simulating in Bi-Intuitionistic Logic.Guillermo Badia - 2016 - Studia Logica 104 (5):1037-1050.
    Bi-intuitionistic logic is the result of adding the dual of intuitionistic implication to intuitionistic logic. In this note, we characterize the expressive power of this logic by showing that the first order formulas equivalent to translations of bi-intuitionistic propositional formulas are exactly those preserved under bi-intuitionistic directed bisimulations. The proof technique is originally due to Lindstrom and, in contrast to the most common proofs of this kind of result, it does not use the machinery of neither saturated models nor elementary (...)
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