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  1. Knowledge Means ‘All’, Belief Means ‘Most’.Dimitris Askounis, Costas D. Koutras & Yorgos Zikos - 2016 - Journal of Applied Non-Classical Logics 26 (3):173-192.
    We introduce a bimodal epistemic logic intended to capture knowledge as truth in all epistemically alternative states and belief as a generalised ‘majority’ quantifier, interpreted as truth in most of the epistemically alternative states. This doxastic interpretation is of interest in knowledge-representation applications and it also holds an independent philosophical and technical appeal. The logic comprises an epistemic modal operator, a doxastic modal operator of consistent and complete belief and ‘bridge’ axioms which relate knowledge to belief. To capture the notion (...)
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  • The Structure of Justification.Sven Rosenkranz - 2018 - Mind 127 (506):629-629.
    The paper explores a structural account of propositional justification in terms of the notion of being in a position to know and negation. Combined with a non-normal logic for being in a position to know, the account allows for the derivation of plausible principles of justification. The account is neutral on whether justification is grounded in internally individuated mental states, and likewise on whether it is grounded in facts that are already accessible by introspection or reflection alone. To this extent, (...)
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  • Knowledge, Belief, Normality, and Introspection.Dominik Klein, Olivier Roy & Norbert Gratzl - 2018 - Synthese 195 (10):4343-4372.
    We study two logics of knowledge and belief stemming from the work of Stalnaker, omitting positive introspection for knowledge. The two systems are equivalent with positive introspection, but not without. We show that while the logic of beliefs remains unaffected by omitting introspection for knowledge in one system, it brings significant changes to the other. The resulting logic of belief is non-normal, and its complete axiomatization uses an infinite hierarchy of coherence constraints. We conclude by returning to the philosophical interpretation (...)
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  • Synonymous Logics.Francis Jeffry Pelletier & Alasdair Urquhart - 2003 - Journal of Philosophical Logic 32 (3):259-285.
    This paper discusses the general problem of translation functions between logics, given in axiomatic form, and in particular, the problem of determining when two such logics are "synonymous" or "translationally equivalent." We discuss a proposed formal definition of translational equivalence, show why it is reasonable, and also discuss its relation to earlier definitions in the literature. We also give a simple criterion for showing that two modal logics are not translationally equivalent, and apply this to well-known examples. Some philosophical morals (...)
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  • Philosophie des modalités épistémiques (la logique assertorique revisitée).Fabien Schang - 2007 - Dissertation, Nancy Université
    The relevance of any logical analysis lies in its ability to solve paradoxes and trace conceptual troubles back; with this respect, the task of epistemic logic is to handle paradoxes in connection with the concept of knowledge. Epistemic logic is currently introduced as the logical analysis of crucial concepts within epistemology, namely: knowledge, belief, truth, and justification. An alternative approach will be advanced here in order to enlighten such a discourse, as centred upon the word assertion and displayed in terms (...)
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  • On Definability in Multimodal Logic.Joseph Y. Halpern, Dov Samet & Ella Segev - 2009 - Review of Symbolic Logic 2 (3):451-468.
    Three notions of definability in multimodal logic are considered. Two are analogous to the notions of explicit definability and implicit definability introduced by Beth in the context of first-order logic. However, while by Beth’s theorem the two types of definability are equivalent for first-order logic, such an equivalence does not hold for multimodal logics. A third notion of definability, reducibility, is introduced; it is shown that in multimodal logics, explicit definability is equivalent to the combination of implicit definability and reducibility. (...)
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  • Intricate Axioms as Interaction Axioms.Guillaume Aucher - 2015 - Studia Logica 103 (5):1035-1062.
    In epistemic logic, some axioms dealing with the notion of knowledge are rather convoluted and difficult to interpret intuitively, even though some of them, such as the axioms.2 and.3, are considered to be key axioms by some epistemic logicians. We show that they can be characterized in terms of understandable interaction axioms relating knowledge and belief or knowledge and conditional belief. In order to show it, we first sketch a theory dealing with the characterization of axioms in terms of interaction (...)
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  • Knowledge, Belief, Normality, and Introspection.Dominik Klein, Olivier Roy & Norbert Gratzl - 2017 - Synthese:1-30.
    We study two logics of knowledge and belief stemming from the work of Stalnaker, omitting positive introspection for knowledge. The two systems are equivalent with positive introspection, but not without. We show that while the logic of beliefs remains unaffected by omitting introspection for knowledge in one system, it brings significant changes to the other. The resulting logic of belief is non-normal, and its complete axiomatization uses an infinite hierarchy of coherence constraints. We conclude by returning to the philosophical interpretation (...)
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  • A Quick Guided Tour to the Modal Logic S4.2.Aggeliki Chalki, Costas D. Koutras & Yorgos Zikos - 2018 - Logic Journal of the IGPL 26 (4):429-451.
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  • Defining Knowledge in Terms of Belief: The Modal Logic Perspective.Joseph Y. Halpern, Dov Samet & Ella Segev - 2009 - Review of Symbolic Logic 2 (3):469-487.
    The question of whether knowledge is definable in terms of belief, which has played an important role in epistemology for the last 50 years, is studied here in the framework of epistemic and doxastic logics. Three notions of definability are considered: explicit definability, implicit definability, and reducibility, where explicit definability is equivalent to the combination of implicit definability and reducibility. It is shown that if knowledge satisfies any set of axioms contained in S5, then it cannot be explicitly defined in (...)
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  • Beschränkte und Unbeschränkte Reduktion von Konjunktionen von Modalitäten in S4.Wolfgang Lenzen - 1980 - Mathematical Logic Quarterly 26 (7‐9):131-143.
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  • Beschränkte und Unbeschränkte Reduktion von Konjunktionen von Modalitäten in S4.Wolfgang Lenzen - 1980 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 26 (7-9):131-143.
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  • Conditions of Rationality for the Concepts Belief, Knowledge, and Assumption.Paul Weingartner - 1982 - Dialectica 36 (2‐3):243-263.
    SummaryIn the first part of the paper necessary conditions for the rationality of the notions of belief, knowledge, and assumption are given: Among the different conditions it is stressed that one needs two different concepts of belief, one such that if someone knows something he also believes it, the other exclusive such that if someone knows something he need not to believe it and if he believes it he does not yet know it. Another important point is that deductive infallibility (...)
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