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  1. Neighborhood Semantics for Logics of Unknown Truths and False Beliefs.David Gilbert & Giorgio Venturi - 2017 - Australasian Journal of Logic 14 (1).
    This article outlines a semantic approach to the logics of unknown truths, and the logic of false beliefs, using neighborhood structures, giving results on soundness, completeness, and expressivity. Relational semantics for the logics of unknown truths are also addressed, specically the conditions under which sound axiomatizations of these logics might be obtained from their normal counterparts, and the relationship between refexive insensitive logics and logics containing the provability operator as the primary modal operator.
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  • Note on the Intuitionistic Logic of False Belief.Tomasz Witczak - 2022 - Bulletin of the Section of Logic 51 (1):57-71.
    In this paper we analyse logic of false belief in the intuitionistic setting. This logic, studied in its classical version by Steinsvold, Fan, Gilbert and Venturi, describes the following situation: a formula $\varphi$ is not satisfied in a given world, but we still believe in it. Another interpretations are also possible: e.g. that we do not accept $\varphi$ but it is imposed on us by a kind of council or advisory board. From the mathematical point of view, the idea is (...)
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  • Logics of (In)Sane and (Un)Reliable Beliefs.Jie Fan - 2022 - Logic Journal of the IGPL 30 (1):78-100.
    Inspired by an interesting quotation from the literature, we propose four modalities, called ‘sane belief’, ‘insane belief’, ‘reliable belief’ and ‘unreliable belief’, and introduce logics with each operator as the modal primitive. We show that the four modalities constitute a square of opposition, which indicates some interesting relationships among them. We compare the relative expressivity of these logics and other related logics, including a logic of false beliefs from the literature. The four main logics are all less expressive than the (...)
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  • Reflexive-Insensitive Modal Logics.David R. Gilbert & Giorgio Venturi - 2016 - Review of Symbolic Logic 9 (1):167-180.
  • Unknown Truths and False Beliefs: Completeness and Expressivity Results for the Neighborhood Semantics.Jie Fan - 2022 - Studia Logica 110 (1):1-45.
    In this article, we study logics of unknown truths and false beliefs under neighborhood semantics. We compare the relative expressivity of the two logics. It turns out that they are incomparable over various classes of neighborhood models, and the combination of the two logics are equally expressive as standard modal logic over any class of neighborhood models. We propose morphisms for each logic, which can help us explore the frame definability problem, show a general soundness and completeness result, and generalize (...)
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  • A Non-Standard Kripke Semantics for the Minimal Deontic Logic.Edson Bezerra & Giorgio Venturi - forthcoming - Logic and Logical Philosophy:1.
    In this paper we study a new operator of strong modality ⊞, related to the non-contingency operator ∆. We then provide soundness and completeness theorems for the minimal logic of the ⊞-operator.
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  • Strong Noncontingency: On the Modal Logics of an Operator Expressively Weaker Than Necessity.Jie Fan - 2019 - Notre Dame Journal of Formal Logic 60 (3):407-435.
    Operators can be compared in at least two respects: expressive strength and deductive strength. Inspired by Hintikka’s treatment of question embedding verbs, the variations of noncontingency operator, and also the various combinations of modal operators and Boolean connectives, we propose a logic with strong noncontingency operator as the only primitive modality. The novel operator is deductively but not expressively stronger than both noncontingency operator and essence operator, and expressively but not deductively weaker than the necessity operator. The frame-definability power of (...)
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