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Knowledge and belief

Ithaca, N.Y.,: Cornell University Press (1962)

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  1. Category mistakes in m&e.Gilbert Harman - 2003 - Philosophical Perspectives 17 (1):165–180.
    Theories of causation may imply that your birth causes your death, which seems odd in the way that it is not odd to say that your birth precedes your death. Theories of knowledge may imply that the object of knowledge is the same as the object of belief, although we know but do not believe facts and we can know a proposition without knowing whether it is true.
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  • Against overconfidence: arguing for the accessibility of memorial justification.Jonathan Egeland - 2020 - Synthese 198 (9):1-21.
    In this article, I argue that access internalism should replace preservationism, which has been called “a received view” in the epistemology of memory, as the standard position about memorial justification. My strategy for doing so is two-pronged. First, I argue that the considerations which motivate preservationism also support access internalism. Preservationism is mainly motivated by its ability to answer the explanatory challenges posed by the problem of stored belief and the problem of forgotten evidence. However, as I will demonstrate, access (...)
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  • The paradox of the believer.Sven Ove Hansson - 1991 - Philosophia 21 (1-2):25-30.
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  • Reverse Public Announcement Operators on Expanded Models.Ryuichi Sebastian Haney - 2018 - Journal of Logic, Language and Information 27 (3):205-224.
    Past public announcement operators have been defined in Hoshi and Yap :259–281, 2009) and Yap, to describe an agent’s knowledge before an announcement occurs. These operators rely on branching-time structures that do not mirror the traditional, relativization-based semantics of public announcement logic, and favor a historical reading of past announcements. In this paper, we introduce reverse public announcement operators that are interpreted on expanded models. Our model expansion adds accessibility links from an epistemic model \ to a filtrated submodel of (...)
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  • New Essays on the Knowability Paradox – Edited by Joe Salerno.Hans Van Ditmarsch - 2010 - Theoria 76 (3):270-273.
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  • A history of theoria.Sven Ove Hansson - 2009 - Theoria 75 (1):2-27.
    Theoria , the international Swedish philosophy journal, was founded in 1935. Its contributors in the first 75 years include the major Swedish philosophers from this period and in addition a long list of international philosophers, including A. J. Ayer, C. D. Broad, Ernst Cassirer, Hector Neri Castañeda, Arthur C. Danto, Donald Davidson, Nelson Goodman, R. M. Hare, Carl G. Hempel, Jaakko Hintikka, Saul Kripke, Henry E. Kyburg, Keith Lehrer, Isaac Levi, David Lewis, Gerald MacCallum, Richard Montague, Otto Neurath, Arthur N. (...)
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  • On the unusual effectiveness of logic in computer science.Joseph Y. Halpern, Robert Harper, Neil Immerman, Phokion G. Kolaitis, Moshe Y. Vardi & Victor Vianu - 2001 - Bulletin of Symbolic Logic 7 (2):213-236.
    In 1960, E. P. Wigner, a joint winner of the 1963 Nobel Prize for Physics, published a paper titled On the Unreasonable Effectiveness of Mathematics in the Natural Sciences [61]. This paper can be construed as an examination and affirmation of Galileo's tenet that “The book of nature is written in the language of mathematics”. To this effect, Wigner presented a large number of examples that demonstrate the effectiveness of mathematics in accurately describing physical phenomena. Wigner viewed these examples as (...)
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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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  • On the event relativity of modal auxiliaries.Valentine Hacquard - 2010 - Natural Language Semantics 18 (1):79-114.
    Crosslinguistically, the same modal words can be used to express a wide range of interpretations. This crosslinguistic trend supports a Kratzerian analysis, where each modal has a core lexical entry and where the difference between an epistemic and a root interpretation is contextually determined. A long-standing problem for such a unified account is the equally robust crosslinguistic correlation between a modal’s interpretation and its syntactic behavior: epistemics scope high (in particular higher than tense and aspect) and roots low, a fact (...)
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  • On the interaction of aspect and modal auxiliaries.Valentine Hacquard - 2009 - Linguistics and Philosophy 32 (3):279-315.
    This paper discusses the interaction of aspect and modality, and focuses on the puzzling implicative effect that arises when perfective aspect appears on certain modals: perfective somehow seems to force the proposition expressed by the complement of the modal to hold in the actual world, and not merely in some possible world. I show that this puzzling behavior, originally discussed in Bhatt (1999, Covert modality in non-finite contexts) for the ability modal, extends to all modal auxiliaries with a circumstantial modal (...)
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  • Syntactic awareness in logical dynamics.Davide Grossi & Fernando R. Velázquez-Quesada - 2015 - Synthese 192 (12):4071-4105.
    The paper develops an interface between syntax-based logical models of awareness and dynamic epistemic logic. The framework is shown to be able to accommodate a variety of notions of awareness and knowledge, as well as their dynamics. This, it is argued, offers a natural formal environment for the analysis of epistemic phenomena typical of multi-agent information exchange, such as how agents become aware of relevant details, how they perform inferences and how they share their information within a group. Technically, the (...)
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  • Logic and limits of knowledge and truth.Patrick Grim - 1988 - Noûs 22 (3):341-367.
    Though my ultimate concern is with issues in epistemology and metaphysics, let me phrase the central question I will pursue in terms evocative of philosophy of religion: What are the implications of our logic-in particular, of Cantor and G6del-for the possibility of omniscience?
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  • Iteration Principles in Epistemology I: Arguments For.Daniel Greco - 2015 - Philosophy Compass 10 (11):754-764.
    Epistemic iteration principles are principles according to which some or another epistemic operator automatically iterates---e.g., if it is known that P, then it is known that P, or there is evidence that P, then there is evidence that there is evidence that P. This article provides a survey of various arguments for and against epistemic iteration principles, with a focus on arguments relevant to a wide range of such principles.
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  • Iteration and Fragmentation.Daniel Greco - 2014 - Philosophy and Phenomenological Research 88 (1):656-673.
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  • The Hooded Man.Priest Graham - 2002 - Journal of Philosophical Logic 31 (5):445-467.
    The Hooded Man Paradox of Eubulides concerns the apparent failure of the substitutivity of identicals in epistemic (and other intentional) contexts. This paper formulates a number of different versions of the paradox and shows how these may be solved using semantics for quantified epistemic logic. In particular, two semantics are given which invalidate substitution, even when rigid designators are involved.
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  • What will they say?—Public Announcement Games.Hans van Ditmarsch & Thomas Ågotnes - 2011 - Synthese 179 (S1):57 - 85.
    Dynamic epistemic logic describes the possible information-changing actions available to individual agents, and their knowledge pre-and post conditions. For example, public announcement logic describes actions in the form of public, truthful announcements. However, little research so far has considered describing and analysing rational choice between such actions, i.e., predicting what rational self-interested agents actually will or should do. Since the outcome of information exchange ultimately depends on the actions chosen by all the agents in the system, and assuming that agents (...)
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  • True lies.Thomas Ågotnes, Hans van Ditmarsch & Yanjing Wang - 2018 - Synthese 195 (10):4581-4615.
    A true lie is a lie that becomes true when announced. In a logic of announcements, where the announcing agent is not modelled, a true lie is a formula that becomes true when announced. We investigate true lies and other types of interaction between announced formulas, their preconditions and their postconditions, in the setting of Gerbrandy’s logic of believed announcements, wherein agents may have or obtain incorrect beliefs. Our results are on the satisfiability and validity of instantiations of these semantically (...)
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  • Contextology.Simon Goldstein & Cameron Domenico Kirk-Giannini - 2022 - Philosophical Studies 179 (11):3187-3209.
    Contextology is the science of the dynamics of the conversational context. Contextology formulates laws governing how the shared information states of interlocutors evolve in response to assertion. More precisely, the contextologist attempts to construct a function which, when provided with just a conversation’s pre-update context and the content of an assertion, delivers that conversation’s post-update context. Most contextologists have assumed that the function governing the evolution of the context is simple: the post-update context is just the pre-update context intersected with (...)
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  • Saber que algo no existe: existencia y lógica epistémica.Emilio Gómez-Caminero Parejo - 2013 - Revista de Humanidades de Valparaíso 1:41-53.
    In this paper we deal with a classical question of western philosophy: Is it possible to know that there are things which do not exist? We begin with a brief analysis of some fragments of Parmenides, and later we study whether these arguments are valid using three kinds of epistemic logic: a classical style epistemic logic, where axiom holds, a free epistemic logic, where this axiom does not hold, and finally, we study Lenzen's proposal of using two kinds of quantifiers: (...)
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  • Resolving questions, II.Jonathan Ginzburg - 1995 - Linguistics and Philosophy 18 (6):567 - 609.
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  • Resolving questions, I.Jonathan Ginzburg - 1995 - Linguistics and Philosophy 18 (5):459 - 527.
    The paper is in two parts. In Part I, a semantics for embedded and query uses of interrogatives is put forward, couched within a situation semantics framework. Unlike many previous analyses,questions are not reductively analysed in terms of their answers. This enables us to provide a notion of ananswer that resolves a question which varies across contexts relative to parameters such as goals and inferential capabilities. In Part II of the paper, extensive motivation is provided for an ontology that distinguishes (...)
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  • Bridging learning theory and dynamic epistemic logic.Nina Gierasimczuk - 2009 - Synthese 169 (2):371-384.
    This paper discusses the possibility of modelling inductive inference (Gold 1967) in dynamic epistemic logic (see e.g. van Ditmarsch et al. 2007). The general purpose is to propose a semantic basis for designing a modal logic for learning in the limit. First, we analyze a variety of epistemological notions involved in identification in the limit and match it with traditional epistemic and doxastic logic approaches. Then, we provide a comparison of learning by erasing (Lange et al. 1996) and iterated epistemic (...)
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  • The semantic roots of positive polarity: epistemic modal verbs and adverbs in English, Greek and Italian.Anastasia Giannakidou & Alda Mari - 2018 - Linguistics and Philosophy 41 (6):623-664.
    Epistemic modal verbs and adverbs of necessity are claimed to be positive polarity items. We study their behavior by examining modal spread, a phenomenon that appears redundant or even anomalous, since it involves two apparent modal operators being interpreted as a single modality. We propose an analysis in which the modal adverb is an argument of the MUST modal, providing a meta-evaluation \ which ranks the Ideal, stereotypical worlds in the modal base as better possibilities than the Non-Ideal worlds in (...)
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  • Comparing strengths of beliefs explicitly.S. Ghosh & D. de Jongh - 2013 - Logic Journal of the IGPL 21 (3):488-514.
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  • Presuppositions and anaphors in attitude contexts.Bart Geurts - 1998 - Linguistics and Philosophy 21 (6):545-601.
    This paper consists of two main parts and a coda. In the first part I present the ''binding theory'' of presupposition projection, which is the framework that I adopt in this paper (Section 1.1). I outline the main problems that arise in the interplay between presuppositions and anaphors on the one hand and attitude reports on the other (Section 1.2), and discuss Heim''s theory of presuppositions in attitude contexts (Section 1.3).In the second part of the paper I present my own (...)
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  • Definability in the class of all -frames – computability and complexity.D. T. Georgiev - 2017 - Journal of Applied Non-Classical Logics 27 (1-2):1-26.
    In the basic modal language and in the basic modal language with the added universal modality, first-order definability of all formulas over the class of all frames is shown. Also, it is shown that the problems of modal definability of first-order sentences over the class of all frames in the languages and are both PSPACE-complete.
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  • The brain attics: the strategic role of memory in single and multi-agent inquiry.Emmanuel J. Genot & Justine Jacot - 2020 - Synthese 197 (3):1203-1224.
    M. B. Hintikka and J. Hintikka claimed that their reconstruction of the ‘Sherlock Holmes sense of deduction’ can “serve as an explication for the link between intelligence and memory”. The claim is vindicated, first for the single-agent case, where the reconstruction captures strategies for accessing the content of a distributed and associative memory; then, for the multi-agent case, where the reconstruction captures strategies for accessing knowledge distributed in a community. Moreover, the reconstruction of the ‘Sherlock Holmes sense of deduction’ allows (...)
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  • Presupposition Projection and Conditionalization.Amaia Garcia-Odon - 2016 - Topoi 35 (1):145-156.
    I explain what exactly constrains presupposition projection in compound sentences and argue that the presuppositions that do not project are conditionalized, giving rise to inferable conditional presuppositions. I combine elements of and which, together with an additional, independently motivated assumption, make it possible to construct an analysis that makes correct predictions. The core of my proposal is as follows: When a speaker felicitously utters a compound sentence whose constituent clauses require presuppositions, the hearer will infer that the speaker presupposes those (...)
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  • Commentary on Gerson.Alessandra Fussi - 1999 - Proceedings of the Boston Area Colloquium of Ancient Philosophy 15 (1):254-262.
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  • Thomason’s Paradox for Belief, and Two Consequence Relations.Bas C. van Fraassen - 2011 - Journal of Philosophical Logic 40 (1):15 - 32.
    Thomason (1979/2010)'s argument against competence psychologism in semantics envisages a representation of a subject's competence as follows: he understands his own language in the sense that he can identify the semantic content of each of its sentences, which requires that the relation between expression and content be recursive. Then if the scientist constructs a theory that is meant to represent the body of the subject's beliefs, construed as assent to the content of the pertinent sentences, and that theory satisfies certain (...)
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  • Evaluative Discourse and Affective States of Mind.Nils Franzén - 2020 - Mind 129 (516):1095-1126.
    It is widely held within contemporary metaethics that there is a lack of linguistic support for evaluative expressivism. On the contrary, it seems that the predictions that expressivists make about evaluative discourse are not borne out. An instance of this is the so-called problem of missing Moorean infelicity. Expressivists maintain that evaluative statements express non-cognitive states of mind in a similar manner to how ordinary descriptive language expresses beliefs. Conjoining an ordinary assertion that p with the denial of being in (...)
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  • Armchair Access and Imagination.Giada Fratantonio - 2018 - Dialectica 72 (4):525-547.
    In this paper, I focus on the Armchair Access Problem for E=K as presented by Nicholas Silins (2005), and I argue, contra Silins, that it does not represent a real threat to E=K. More precisely, I put forward two lines of response, both of which put pressure on the main assumption of the argument, namely, the Armchair Access thesis. The first line of response focuses on its scope, while the second line of response focuses on its nature. The second line (...)
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  • A rule of minimal rationality: The logical link between beliefs and values.Jeffrey Foss - 1976 - Inquiry: An Interdisciplinary Journal of Philosophy 19 (1-4):341 – 353.
    The object of this essay is to demonstrate a logical connection between beliefs and values. It is argued that such a connection can be established only if one keeps in mind the question: What is minimally required in order that it makes sense to speak of beliefs and values at all? Thus, the concept of minimal rationality is indispensable to the task at hand. A particular example of a logical connection between a belief and a value is examined, which leads (...)
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  • Hintikka, Free Logician.Matthieu Fontaine - 2019 - Logica Universalis 13 (2):179-201.
    The combination of quantifiers with a semantics for epistemic operators in a modal framework is one of the major contributions of Hintikka in intensional logic. Hintikka’s starting point is his diagnosis of the failure of existential generalization and the substitution of identicals in terms of referential multiplicity. In this paper, I introduce Hintikka as a free logician. Indeed, Hintikka’s first-order epistemic logic is grounded on a logic free of ontological presuppositions with respect to singular terms. It is also a logic (...)
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  • Information closure and the sceptical objection.Luciano Floridi - 2014 - Synthese 191 (6):1037-1050.
    In this article, I define and then defend the principle of information closure (pic) against a sceptical objection similar to the one discussed by Dretske in relation to the principle of epistemic closure. If I am successful, given that pic is equivalent to the axiom of distribution and that the latter is one of the conditions that discriminate between normal and non-normal modal logics, a main result of such a defence is that one potentially good reason to look for a (...)
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  • The logic of proofs, semantically.Melvin Fitting - 2005 - Annals of Pure and Applied Logic 132 (1):1-25.
    A new semantics is presented for the logic of proofs (LP), [1, 2], based on the intuition that it is a logic of explicit knowledge. This semantics is used to give new proofs of several basic results concerning LP. In particular, the realization of S4 into LP is established in a way that carefully examines and explicates the role of the + operator. Finally connections are made with the conventional approach, via soundness and completeness results.
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  • Reasoning About Games.Melvin Fitting - 2011 - Studia Logica 99 (1-3):143-169.
    is used to give a formalization of Artemov’s knowledge based reasoning approach to game theory, (KBR), [ 4 , 5 ]. Epistemic states of players are represented explicitly and reasoned about formally. We give a detailed analysis of the Centipede game using both proof theoretic and semantic machinery. This helps make the case that PDL + E can be a useful basis for the logical investigation of game theory.
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  • A quantified logic of evidence.Melvin Fitting - 2008 - Annals of Pure and Applied Logic 152 (1):67-83.
    A propositional logic of explicit proofs, LP, was introduced in [S. Artemov, Explicit provability and constructive semantics, The Bulletin for Symbolic Logic 7 1–36], completing a project begun long ago by Gödel, [K. Gödel, Vortrag bei Zilsel, translated as Lecture at Zilsel’s in: S. Feferman , Kurt Gödel Collected Works III, 1938, pp. 62–113]. In fact, LP can be looked at in a more general way, as a logic of explicit evidence, and there have been several papers along these lines. (...)
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  • Adding a temporal dimension to a logic system.Marcelo Finger & Dov M. Gabbay - 1992 - Journal of Logic, Language and Information 1 (3):203-233.
    We introduce a methodology whereby an arbitrary logic system L can be enriched with temporal features to create a new system T(L). The new system is constructed by combining L with a pure propositional temporal logic T (such as linear temporal logic with Since and Until) in a special way. We refer to this method as adding a temporal dimension to L or just temporalising L. We show that the logic system T(L) preserves several properties of the original temporal logic (...)
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  • Saul Kripke e o paradoxo do dogmatismo.João Rizzio Vicent Fett - 2017 - Analytica. Revista de Filosofia 21 (1):227-243.
    O slogan "Conhecimento gera dogmatismo" causa-nos imediata perplexidade. O dogmatismo é trivialmente tomado como uma postura irracional de manutenção de crenças. Saul Kripke, contra esta intuitiva perspectiva, ofereceu um argumento que supostamente prova que se você sabe que uma proposição P é verdadeira, então você está autorizado a ser dogmático quanto a se P. Neste ensaio, temos os seguintes objetivos. Em primeiro lugar, vamos criticar uma recente objeção ao argumento pró-dogmatismo de Kripke feita por Rodrigo Borges, segundo a qual, uma (...)
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  • Informe bibliográfico sobre la lógica (epistémica) de la conciencia.Claudia Fernández-Fernández - 2019 - Contrastes: Revista Internacional de Filosofía 24 (3).
    La lógica de la conciencia es una extensión de la lógica epistémica que solventa el problema de la omnisciencia lógica incorporando un operador de conciencia para separar el conocimiento explícito del implícito. Este informe recopila los principales textos tanto de los orígenes de esta lógica, así como de sus desarrollos en las últimas tres décadas. En concreto analiza los enfoques desde la lógica epistémica dinámica, desde su combinación con otras lógicas y los enfoques de teoría de juegos.
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  • AGM 25 Years: Twenty-Five Years of Research in Belief Change.Eduardo Fermé & Sven Ove Hansson - 2011 - Journal of Philosophical Logic 40 (2):295 - 331.
    The 1985 paper by Carlos Alchourrón (1931–1996), Peter Gärdenfors, and David Makinson (AGM), "On the Logic of Theory Change: Partial Meet Contraction and Revision Functions" was the starting-point of a large and rapidly growing literature that employs formal models in the investigation of changes in belief states and databases. In this review, the first twentyfive years of this development are summarized. The topics covered include equivalent characterizations of AGM operations, extended representations of the belief states, change operators not included in (...)
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  • AGM 25 Years: Twenty-Five Years of Research in Belief Change.Eduardo Fermé & Sven Ove Hansson - 2011 - Journal of Philosophical Logic 40 (2):295-331.
    The 1985 paper by Carlos Alchourrón, Peter Gärdenfors, and David Makinson, “On the Logic of Theory Change: Partial Meet Contraction and Revision Functions” was the starting-point of a large and rapidly growing literature that employs formal models in the investigation of changes in belief states and databases. In this review, the first twenty-five years of this development are summarized. The topics covered include equivalent characterizations of AGM operations, extended representations of the belief states, change operators not included in the original (...)
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  • Awareness Logic: an Epistemological Defence Correlations between Awareness Logic and Epistemology.Claudia Fernández-Fernández - 2019 - Kairos 22 (1):72-85.
    with this paper, we intend to clarify some of the central notions that are commonly used in contemporary developments of Epistemic Logic, which lack a proper theoretical foundation. We want to follow the steps of some prominent epistemologists and epistemic logicians, who advocate for a correlation between their respective fields of study. We will proceed with a first small step that will consist in adapting one contemporary version of Epistemic Internalism to the framework of Awareness Logic, such that the key (...)
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  • An expressivist approach to folk psychological ascriptions.Víctor Fernández Castro - 2023 - Philosophical Explorations (1):86-105.
    In recent years, some authors have shown a renewed interest in interpretivist theories of folk psychological ascription [Hutto 2013. “Fictionalism About Folk Psychology.” The Monist 96 (4): 582–604.; Mölder 2010. Mind Ascribed: An Elaboration and Defence of Interpretivism. Amsterdam: John Benjamins; Sanchez-Curry 2020. “Interpretivism and Norms.” Philosophical Studies 177 (4): 905– 930.; Mölder 2021. “Interpretivism Without Judgement- Dependence.” Philosophia 49 (2): 611–615.; Slors 2015. "Interpretivism and the Meaning of Mental State Ascriptions." Studia Philosophica Estonica, 10 (2): 18–27.]. Part of the (...)
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  • A computational interpretation of conceptivism.Thomas Macaulay Ferguson - 2014 - Journal of Applied Non-Classical Logics 24 (4):333-367.
    The hallmark of the deductive systems known as ‘conceptivist’ or ‘containment’ logics is that for all theorems of the form , all atomic formulae appearing in also appear in . Significantly, as a consequence, the principle of Addition fails. While often billed as a formalisation of Kantian analytic judgements, once semantics were discovered for these systems, the approach was largely discounted as merely the imposition of a syntactic filter on unrelated systems. In this paper, we examine a number of prima (...)
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  • A Blind-Spot Argument Against Dispositionalist Accounts of Belief.Davide Fassio - 2014 - Acta Analytica 29 (1):71-81.
    Dispositionalist accounts of belief define beliefs in terms of specific sets of dispositions. In this article, I provide a blind-spot argument against these accounts. The core idea of the argument is that beliefs having the form [p and it is not manifestly believed that p] cannot be manifestly believed. This means that one cannot manifest such beliefs in one’s assertions, conscious thoughts, actions, behaviours, or any other type of activity. However, if beliefs are sets of dispositions, they must be manifestable (...)
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  • Unknown Truths and False Beliefs: Completeness and Expressivity Results for the Neighborhood Semantics.Jie Fan - 2021 - 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 working hypothesis for the logic of radical ignorance.Vincenzo Fano & Pierluigi Graziani - 2020 - Synthese 199 (1-2):601-616.
    The Dunning–Kruger effect focuses our attention on the notion of invisibility of ignorance, i.e., the ignorance of ignorance. Such a phenomenon is not only important for everyday life, but also, above all, for some philosophical disciplines, such as epistemology of sciences. When someone tries to understand formally the phenomenon of ignorance of ignorance, they usually end up with a nested epistemic operator highly resistant to proper regimentation. In this paper, we argue that to understand adequately the ignorance of ignorance phenomenon (...)
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  • Bimodal Logics with Contingency and Accident.Jie Fan - 2019 - Journal of Philosophical Logic 48 (2):425-445.
    Contingency and accident are two important notions in philosophy and philosophical logic. Their meanings are so close that they are mixed up sometimes, in both daily life and academic research. This indicates that it is necessary to study them in a unified framework. However, there has been no logical research on them together. In this paper, we propose a language of a bimodal logic with these two concepts, investigate its model-theoretical properties such as expressivity and frame definability. We axiomatize this (...)
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