About this topic
Summary Epistemic logics are logics that allow one to reason about knowledge in some way. The term ‘epistemic logic’ is often applied also to logics of related notions, such as logics of belief (more strictly, doxastic logics) and justification. Many epistemic logics are modal logics, whose language contains one or more knowledge operators and whose semantics is given in terms of relational Kripke models, containing epistemically possible worlds related to one another by epistemic accessibility relations. This modal approach to epistemic logic has been widely adopted in formal logic, philosophy, computer science, artificial intelligence, economics and game theory. The sub-sategory ‘Doxastic and Epistemic Logic’ also includes formal work on belief revision. This category also includes inductive logics and non-monotonic logics, both of which add to the stock of valid inferences, beyond those valid in classical logic. (These logics are super-classical, containing inferences which are not deductively valid and hence, in some sense, less than certain. In such logics, there is no guarantee that truth will be preserved from premises to conclusions. Non-monotonic logics have the feature that an inference from premises X to conclusion A may be valid, and yet the inference to may fail if we add an addition premise B to X, so that XA but not X, B ⊢ A.
Key works Modern epistemic logic began with Hintikka 1962, who developed Kripke-style semantics for epistemic notions and discussed appropriate axioms for knowledge and belief. Hintikka proposes a solution to the logical omniscience problem, whereby agents are treated as automatically knowing all consequences of what they know, in Hintikka 1975. Hintikka's approach is developed and applied to problems in computer science in Fagin et al 2003. The leading theory of belief revision, the ‘AGM’ theory, was first presented in Alchourrón et al 1985. Key early works in inductive logic are Keynes 1921 and Carnap’s 1945, 19521950. Key early works in non-monotonic logic are Moore 1985
Introductions Hintikka 1962 is a great introduction to epistemic and doxastic logics; Hendricks 2008 briefly surveys the area. Huber 2013 introduces and discusses AGM theories of belief revision. Hawthorne 2011 and Huber 2007 are good encyclopaedia entries on inductive logic; Hacking 2001 is a book-length introduction. Antonelli 2008 is a good, brief introduction to non-monotonic logic; an excellent book-length treatment is Makinson 2005
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  1. Unjustified untrue "beliefs": AI hallucinations and justification logics.Kristina Šekrst - forthcoming - In Kordula Świętorzecka, Filip Grgić & Anna Brozek (eds.), Logic, Knowledge, and Tradition. Essays in Honor of Srecko Kovac.
    In artificial intelligence (AI), responses generated by machine-learning models (most often large language models) may be unfactual information presented as a fact. For example, a chatbot might state that the Mona Lisa was painted in 1815. Such phenomenon is called AI hallucinations, seeking inspiration from human psychology, with a great difference of AI ones being connected to unjustified beliefs (that is, AI “beliefs”) rather than perceptual failures). -/- AI hallucinations may have their source in the data itself, that is, the (...)
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  2. A Formal Epistemological Defence of Direct Realism: Rebutting the Colour Delusion Argument.Wilfrid Wulf - forthcoming - Oxford Studies in Epistemology.
    I defend J. L. Austin's direct realism against the colour delusion argument by employing epistemic logic to demonstrate that perceiving colours does not necessitate an intermediary such as sense-data, thus preserving the directness of perception.
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  3. Epistemic Infinite Regress and the Limits of Metaphysical Knowledge.Wilfrid Wulf - forthcoming - Oxford Studies in Epistemology.
    I will explore the paradoxical nature of epistemic access. By critiquing the traditional conception of mental states that are labelled as ’knowledge’, I demonstrate the susceptibility of these states to an infinite regress, thus, challenging their existence and validity. I scrutinise the assumption that an epistemic agent can have complete epistemic access to all facts about a given object while simultaneously being ignorant of certain truths that impact the very knowledge claims about the object. I further analyse the implications of (...)
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  4. Hyperintensionality in Epistemic Democracy and Welfare Economics.David Elohim - manuscript
  5. Probabilistic epistemic logic based on neighborhood semantics.Meiyun Guo & Yixin Pan - 2024 - Synthese 203 (5):1-24.
    In the literature, different frameworks of probabilistic epistemic logic have been proposed. Most of these frameworks define knowledge or belief by relational structure. In this paper, we explore the relationship between probability and belief, based on the Lockean thesis, and adopt neighborhood semantics that defines belief directly using probability. We provide a sound and weakly complete axiomatization for our framework. We also try to explain the lottery paradox by modelling it within our framework. Moreover, the paper presents findings concerning the (...)
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  6. A note on Williamson’s Gettier cases in epistemic logic.James Simpson - 2024 - Synthese 203 (3):1-12.
    In a recent series of papers, Timothy Williamson argues that one can reach Edmund Gettier’s conclusion that the justified-true-belief (JTB) theory of knowledge is insufficient for knowledge by constructing Gettier cases in the framework of epistemic logic. In this paper, I argue, however, that Williamson’s Gettier cases in the framework of epistemic logic crucially turn on an assumption that the JTB theorist can plausibly and justifiably reject. In particular, I argue that it is rational for the JTB theorist to reject (...)
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  7. Truthmaker Semantics for Epistemic Logic.Peter Hawke & Aybüke Özgün - 2023 - In Federico L. G. Faroldi & Frederik Van De Putte (eds.), Kit Fine on Truthmakers, Relevance, and Non-classical Logic. Springer Verlag. pp. 295-335.
    We explore some possibilities for developing epistemic logic using truthmaker semantics. We identify three possible targets of analysis for the epistemic logician. We then list some candidate epistemic principles and review the arguments that render some controversial. We then present the classic Hintikkan approach to epistemic logic and note—as per the ‘problem of logical omniscience’—that it validates all of the aforementioned principles, controversial or otherwise. We then lay out a truthmaker framework in the style of Kit Fine and present six (...)
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  8. An Epistemized Truthmaker Semantics for Epistemic Logic’: Response to Hawke’s and Özgün’s ‘Truthmaker Semantics for Epistemic Logic.Kit Fine - 2023 - In Federico L. G. Faroldi & Frederik Van De Putte (eds.), Kit Fine on Truthmakers, Relevance, and Non-classical Logic. Springer Verlag. pp. 337-348.
    In the light of Hawke’s and Özgün’s paper, I consider how and to what extent the sequent calculus and truthmaker semantics might be of help in formulating and solving problems within epistemic logic.
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  9. A probabilistic temporal epistemic logic: Decidability.Zoran Ognjanović, Angelina Ilić Stepić & Aleksandar Perović - forthcoming - Logic Journal of the IGPL.
    We study a propositional probabilistic temporal epistemic logic |$\textbf {PTEL}$| with both future and past temporal operators, with non-rigid set of agents and the operators for agents’ knowledge and for common knowledge and with probabilities defined on the sets of runs and on the sets of possible worlds. A semantics is given by a class |${\scriptsize{\rm Mod}}$| of Kripke-like models with possible worlds. We prove decidability of |$\textbf {PTEL}$| by showing that checking satisfiability of a formula in |${\scriptsize{\rm Mod}}$| is (...)
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  10. KK, Knowledge, Knowability.Weng Kin San - 2023 - Mind 132 (527):605-630.
    kk states that knowing entails knowing that one knows, and K¬K states that not knowing entails knowing that one does not know. In light of the arguments against kk and K¬K⁠, one might consider modally qualified variants of those principles. According to weak kk, knowing entails the possibility of knowing that one knows. And according to weakK¬K⁠, not knowing entails the possibility of knowing that one does not know. This paper shows that weak kk and weakK¬K are much stronger than (...)
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  11. The Value of Biased Information.Nilanjan Das - 2023 - British Journal for the Philosophy of Science 74 (1):25-55.
    In this article, I cast doubt on an apparent truism, namely, that if evidence is available for gathering and use at a negligible cost, then it’s always instrumentally rational for us to gather that evidence and use it for making decisions. Call this ‘value of information’ (VOI). I show that VOI conflicts with two other plausible theses. The first is the view that an agent’s evidence can entail non-trivial propositions about the external world. The second is the view that epistemic (...)
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  12. A hyperintensional approach to positive epistemic possibility.Niccolò Rossi & Aybüke Özgün - 2023 - Synthese 202 (44):1-29.
    The received view says that possibility is the dual of necessity: a proposition is (metaphysically, logically, epistemically etc.) possible iff it is not the case that its negation is (metaphysically, logically, epistemically etc., respectively) necessary. This reading is usually taken for granted by modal logicians and indeed seems plausible when dealing with logical or metaphysical possibility. But what about epistemic possibility? We argue that the dual definition of epistemic possibility in terms of epistemic necessity generates tension when reasoning about non-idealized (...)
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  13. Epistemology Normalized.Jeremy Goodman & Bernhard Salow - 2023 - Philosophical Review 132 (1):89-145.
    We offer a general framework for theorizing about the structure of knowledge and belief in terms of the comparative normality of situations compatible with one’s evidence. The guiding idea is that, if a possibility is sufficiently less normal than one’s actual situation, then one can know that that possibility does not obtain. This explains how people can have inductive knowledge that goes beyond what is strictly entailed by their evidence. We motivate the framework by showing how it illuminates knowledge about (...)
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  14. Dynamic Epistemic Logic for Budget-Constrained Agents.Vitaliy Dolgorukov & Maksim Gladyshev - 2023 - In Carlos Areces & Diana Costa (eds.), Dynamic Logic. New Trends and Applications: 4th International Workshop, DaLí 2022, Haifa, Israel, July 31–August 1, 2022, Revised Selected Papers. Springer Verlag. pp. 56-72.
    We present a static (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsf{EL}_{\textsf{bc}}$$\end{document}) and dynamic (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsf{DEL}_{\textsf{bc}}$$\end{document}) epistemic logic for budget-constrained agents, in which an agent can obtain some information in exchange for budget resources. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsf{EL}_{\textsf{bc}}$$\end{document} extends a standard multi-agent epistemic logic with expressions concerning agent’s budgets and formulas’ costs. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsf{DEL}_{\textsf{bc}}$$\end{document} extends \documentclass[12pt]{minimal} \usepackage{amsmath} (...)
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  15. Inquiring Attitudes and Erotetic Logic: Norms of Restriction and Expansion.Dennis Whitcomb & Jared Millson - forthcoming - Journal of the American Philosophical Association:1-23.
    A fascinating recent turn in epistemology focuses on inquiring attitudes like wondering and being curious. Many have argued that these attitudes are governed by norms similar to those that govern our doxastic attitudes. Yet, to date, this work has only considered norms that might *prohibit* having certain inquiring attitudes (``norms of restriction''), while ignoring those that might *require* having them (``norms of expansion''). We aim to address that omission by offering a framework that generates norms of expansion for inquiring attitudes. (...)
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  16. A Reasoning Method based on Spatio-Temporal.Seyed Ahmad Mirsanei - 2016 - International Journal of Computer and Information Technologies (Ijocit) 4 (1): 27-32..
    In this paper, we continued the preparatory works of Jingde Cheng in conjunction with spatio-temporal relevant logics, and proposed several epistemic spatio-temporal relevant logics as basic logics for Mobile Multi-Agent Systems (MMAS). To establish an inference system, important elements are: semantics and syntax appropriate to it include a language, axioms and inference rules. By proving the meta-logical properties such as soundness and consistency, completeness and decidability and etc., we have a method to test the reliability of the systems. Finally, we (...)
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  17. The uncoordinated teachers puzzle.Michael Cohen - forthcoming - Episteme:1-8.
    Williamson (2000) argues that the KK principle is inconsistent with knowledge of margin for error in cases of inexact perceptual observations. This paper argues, primarily by analogy to a different scenario, that Williamson’s argument is fallacious. Margin for error principles describe the agent’s knowledge as a result of an inexact perceptual event, not the agent’s knowledge state in general. Therefore, epistemic agents can use their knowledge of margin for error at most once after a perceptual event, but not more. This (...)
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  18. Inferences with Ignorance: Logics of Questions. Inferential Erotetic Logic & Erotetic Epistemic Logic.Michal Peliš - 2016 - Karolinum Press.
  19. Compatibility, compossibility, and epistemic modality.Wesley Holliday & Matthew Mandelkern - forthcoming - Proceedings of the 23rd Amsterdam Colloquium.
    We give a theory of epistemic modals in the framework of possibility semantics and axiomatize the corresponding logic, arguing that it aptly characterizes the ways in which reasoning with epistemic modals does, and does not, diverge from classical modal logic.
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  20. A three-valued doxastic logic based on Kleene’s and Bochvar’s ideas.Janusz Wesserling - 2019 - Studia Philosophiae Christianae 55 (4):89-113.
    W tym artykule zaproponuję konstrukcję trójwartościowej logiki przekonań, którą nazywam: LSB3_1. Podam również i udowodnię kompletność LSB3_1 w odniesieniu do danej semantyki. LSB3_1 opiera się na preformalnych założeniach i intuicjach, które przedstawiono w sekcji 1. Sekcja 2 zawiera składnię i podział instrukcji LSB3_1 na wewnętrzne i zewnętrzne. Rozdział 3 przedstawia semantykę LSB3_1, a także szereg tautologii i formuł nietautologicznych w LSB3_1 wraz z ich intuicyjną interpretacją. System aksjomatyczny dla LSB3_1 i jego porównanie z silną logiką Kleene'a są przedstawione w sekcji (...)
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  21. Logic of faith and deed. The idea and an outline of the theoretical conception.Urszula Wybraniec-Skardowska - 2019 - Studia Philosophiae Christianae 55 (2):125-149.
    This paper discusses the theoretical assumptions behind the conception of the logic of faith and deed and outlines its formal-axiomatic frame and its method of construction, which enable us to understand it as a kind of deductive science. The paper is divided into several sections, starting with the logical analysis of the ambiguous terms of ‚faith’ and ‚action’, and focusing in particular on the concepts of religious faith and deed as a type of conscious activity relating to a matter or (...)
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  22. A Probabilistic Temporal Epistemic Logic: Strong Completeness.Zoran Ognjanović, Angelina Ilić Stepić & Aleksandar Perović - forthcoming - Logic Journal of the IGPL.
    The paper offers a formalization of reasoning about distributed multi-agent systems. The presented propositional probabilistic temporal epistemic logic |$\textbf {PTEL}$| is developed in full detail: syntax, semantics, soundness and strong completeness theorems. As an example, we prove consistency of the blockchain protocol with respect to the given set of axioms expressed in the formal language of the logic. We explain how to extend |$\textbf {PTEL}$| to axiomatize the corresponding first-order logic.
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  23. Integrating Abduction and Inference to the Best Explanation.Michael J. Shaffer - 2022 - European Journal of Pragmatism and American Philosophy 14 (2):1-18.
    Tomis Kapitan’s work on Peirce’s conception of abduction was instrumental for our coming to see how Peircean abduction both relates to and is importantly different from inference to the best explanation (IBE). However, he ultimately concluded that Peirce’s conception of abduction was a muddle. Despite the deeply problematic nature of Peirce’s theory of abduction in these respects, Kapitan’s work on Peircean abduction offers insight into the nature of abductive inquiry that is importantly relevant to the task of making sense of (...)
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  24. God's omniscience : a formal analysis in normal and non-normal epistemic logics.Antonino Rotolo & Erica Calardo - 2013 - In Bartosz Brożek, Adam Olszewski & Mateusz Hohol (eds.), Logic in theology. Kraków: Copernicus Center Press.
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  25. Hintikka's impossible worlds revisited : "second generation" epistemic logic and its impact on the epistemology of counterpossibles.Shahid Rahman - 2013 - In Jaakko Hintikka (ed.), Open problems in epistemology =. Helsinki: The Philosophical Society of Finland.
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  26. Some applications of dynamic epistemic logics in formal epistemology.Alexandru Dragomir - 2015 - București: Pro Universitaria.
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  27. The Logical Structure of ‘Rago-knowledge’.Wonjae Ha - 2022 - 철학적 분석 48:91-123.
    It is natural to suppose the following three: factivity of knowledge, alda-know synonymy, and the univocity of alda. However, rago-knowledge attribution, expressed by “rago alda” sentences, seems to defeat to hold them at once. In this paper, I try to dissolve this predicament, analyzing “rago alda” sentence as a kind of hybrid language expression. And the theoretical advantages, which my analysis has over other possible, alternative approaches, are to be shown.
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  28. Mighty Belief Revision.Stephan Krämer - 2022 - Journal of Philosophical Logic 51 (5):1175-1213.
    Belief revision theories standardly endorse a principle of intensionality to the effect that ideal doxastic agents do not discriminate between pieces of information that are equivalent within classical logic. I argue that this principle should be rejected. Its failure, on my view, does not require failures of logical omniscience on the part of the agent, but results from a view of the update as _mighty_: as encoding what the agent learns might be the case, as well as what must be. (...)
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  29. Inquisitive logic as an epistemic logic of knowing how.Haoyu Wang, Yanjing Wang & Yunsong Wang - 2022 - Annals of Pure and Applied Logic 173 (10):103145.
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  30. Weak relevant justification logics.Shawn Standefer - 2023 - Journal of Logic and Computation 33 (7):1665–1683.
    This paper will develop ideas from [44]. We will generalize their work in two directions. First, we provide axioms for justification logics over the base logic B and show that the logic permits a proof of the internalization theorem. Second, we provide alternative frames that more closely resemble the standard versions of the ternary relational frames, as well as a more general approach to the completeness proof. We prove that soundness and completeness hold for justification logics over a wide variety (...)
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  31. A Framework for Intuitionistic Grammar Logics.Tim Lyon - 2021 - In Pietro Baroni, Christoph Benzmüller & Yὶ N. Wang (eds.), Lecture Notes in Computer Science. 93413 Cham, Germany: pp. 495-503.
    We generalize intuitionistic tense logics to the multi-modal case by placing grammar logics on an intuitionistic footing. We provide axiomatizations for a class of base intuitionistic grammar logics as well as provide axiomatizations for extensions with combinations of seriality axioms and what we call "intuitionistic path axioms". We show that each axiomatization is sound and complete with completeness being shown via a typical canonical model construction.
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  32. Intellectual Modesty in Socratic Wisdom: Problems of Epistemic Logic and an Intuitionist Solution.Guido Löhrer - 2022 - History of Philosophy & Logical Analysis 25 (2):282-308.
    According to Plato’s Apology of Socrates, a humanly wise person is distinguished by her ability to correctly assess the epistemic status and value of her beliefs. She knows when she has knowledge or has mere belief or is ignorant. She makes no unjustified knowledge claims and considers her knowledge to be limited in scope and value. This means: A humanly wise person is intellectually modest. However, when interpreted classically, Socratic wisdom cannot be modest. For in classical epistemic logic, modelling second-order (...)
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  33. Justification and being in a position to know.Daniel Waxman - 2022 - Analysis 82 (2):289-298.
    According to an influential recent view, S is propositionally justified in believing p iff S is in no position to know that S is in no position to know p. I argue that this view faces compelling counterexamples.
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  34. Two accounts of assertion.Martin Smith - 2022 - Synthese 200 (3):1-18.
    In this paper I will compare two competing accounts of assertion: the knowledge account and the justified belief account. When it comes to the evidence that is typically used to assess accounts of assertion – including the evidence from lottery propositions, the evidence from Moore’s paradoxical propositions and the evidence from conversational patterns – I will argue that the justified belief account has at least as much explanatory power as its rival. I will argue, finally, that a close look at (...)
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  35. A Semantics for Hyperintensional Belief Revision Based on Information Bases.Sena Bozdag - 2022 - Studia Logica 110 (3):679-716.
    I propose a novel hyperintensional semantics for belief revision and a corresponding system of dynamic doxastic logic. The main goal of the framework is to reduce some of the idealisations that are common in the belief revision literature and in dynamic epistemic logic. The models of the new framework are primarily based on potentially incomplete or inconsistent collections of information, represented by situations in a situation space. I propose that by shifting the representational focus of doxastic models from belief sets (...)
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  36. Fragile Knowledge.Simon Goldstein - 2022 - Mind 131 (522):487-515.
    This paper explores the principle that knowledge is fragile, in that whenever S knows that S doesn’t know that S knows that p, S thereby fails to know p. Fragility is motivated by the infelicity of dubious assertions, utterances which assert p while acknowledging higher-order ignorance whether p. Fragility is interestingly weaker than KK, the principle that if S knows p, then S knows that S knows p. Existing theories of knowledge which deny KK by accepting a Margin for Error (...)
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  37. Is ~ K ~ KP a luminous condition?Martin Smith - 2022 - Asian Journal of Philosophy 1 (1):1-10.
    One of the most intriguing claims in Sven Rosenkranz’s Justification as Ignorance is that Timothy Williamson’s celebrated anti-luminosity argument can be resisted when it comes to the condition ~K~KP—the condition that one is in no position to know that one is in no position to know P. In this paper, I critically assess this claim.
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  38. Justification as ignorance and logical omniscience.Daniel Waxman - 2022 - Asian Journal of Philosophy 1 (1):1-8.
    I argue that there is a tension between two of the most distinctive theses of Sven Rosenkranz’s Justification as Ignorance: the central thesis concerning justification, according to which an agent has propositional justification to believe p iff they are in no position to know that they are in no position to know p and the desire to avoid logical omniscience by imposing only “realistic” idealizations on epistemic agents.
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  39. Relating Semantics for Epistemic Logic.Alessandro Giordani - 2021 - Logic and Logical Philosophy 30 (4):681-709.
    The aim of this paper is to explore the advantages deriving from the application of relating semantics in epistemic logic. As a first step, I will discuss two versions of relating semantics and how they can be differently exploited for studying modal and epistemic operators. Next, I consider several standard frameworks which are suitable for modelling knowledge and related notions, in both their implicit and their explicit form and present a simple strategy by virtue of which they can be associated (...)
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  40. Towards a Logic of Epistemic Theory of Measurement.Daniele Porello & Claudio Macolo - 2019 - In Gabor Bella & Paolo Bouquet (eds.), Modeling and Using Context - 11th International and Interdisciplinary Conference, {CONTEXT} 2019, Trento, Italy, November 20-22, 2019, Proceedings. Lecture Notes in Computer Science 11939. pp. 175-188.
    We propose a logic to reason about data collected by a num- ber of measurement systems. The semantic of this logic is grounded on the epistemic theory of measurement that gives a central role to measure- ment devices and calibration. In this perspective, the lack of evidences (in the available data) for the truth or falsehood of a proposition requires the introduction of a third truth-value (the undetermined). Moreover, the data collected by a given source are here represented by means (...)
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  41. Multi-Path vs. Single-Path Replies to Skepticism.Wen-Fang Wang - 2021 - Journal of Philosophical Logic 51 (2):383-412.
    In order to reply to the contemporary skeptic’s argument for the conclusion that we don’t have any empirical knowledge about the external world, several authors have proposed different fallibilist theories of knowledge that reject the epistemic closure principle. Holliday, 1–62 2015a), however, shows that almost all of them suffer from either the problem of containment or the problem of vacuous knowledge or both. Furthermore, Holliday suggests that the fallibilist should allow a proposition to have multiple sets of relevant alternatives, each (...)
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  42. Formalized Soundness and Completeness of Epistemic Logic.Asta Halkjær From - 2021 - In Alexandra Silva, Renata Wassermann & Ruy de Queiroz (eds.), Logic, Language, Information, and Computation: 27th International Workshop, Wollic 2021, Virtual Event, October 5–8, 2021, Proceedings. Springer Verlag. pp. 1-15.
    We strengthen the foundations of epistemic logic by formalizing the family of normal modal logics in the proof assistant Isabelle/HOL. We define an abstract canonical model and prove a truth lemma for any logic in the family. We then instantiate it with logics based on various epistemic principles to obtain completeness results for systems from K to S5. Our work gives a disciplined treatment of completeness-via-canonicity arguments and demonstrates their compositionality.
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  43. Wanted Dead or Alive: Epistemic Logic for Impure Simplicial Complexes.Hans van Ditmarsch - 2021 - In Alexandra Silva, Renata Wassermann & Ruy de Queiroz (eds.), Logic, Language, Information, and Computation: 27th International Workshop, Wollic 2021, Virtual Event, October 5–8, 2021, Proceedings. Springer Verlag. pp. 31-46.
    We propose a logic of knowledge for impure simplicial complexes. Impure simplicial complexes represent distributed systems under uncertainty over which processes are still active and which processes have failed or crashed. Our work generalizes the logic of knowledge for pure simplicial complexes, where all processes are alive, by Goubault et al. Our logical semantics has a satisfaction relation defined simultaneously with a definability relation. The latter restricts which formulas are allowed to have a truth value: dead processes cannot know or (...)
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  44. On Artemov and Protopopescu’s Intuitionistic Epistemic Logic Expanded with Distributed Knowledge.Youan Su, Ryo Murai & Katsuhiko Sano - 2021 - In Sujata Ghosh & Thomas Icard (eds.), Logic, Rationality, and Interaction: 8th International Workshop, Lori 2021, Xi’an, China, October 16–18, 2021, Proceedings. Springer Verlag. pp. 216-231.
    Artemov and Protopopescu introduced a Brouwer-Heyting-Kolmogorov interpretation of knowledge operator to define the intuitionistic epistemic logic IEL, where the axiom A⊃KA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A\supset KA$$\end{document} is accepted but the axiom KA⊃A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$KA\supset A$$\end{document} is refused. This paper studies the notion of distributed knowledge on an expansion of the multi agent variant of IEL. We provide a BHK interpretation of distributed knowledge operator to define the intuitionistic epistemic (...)
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  45. How Knowledge Triggers Obligation.Davide Grossi, Barteld Kooi, Xingchi Su & Rineke Verbrugge - 2021 - In Sujata Ghosh & Thomas Icard (eds.), Logic, Rationality, and Interaction: 8th International Workshop, Lori 2021, Xi’an, China, October 16–18, 2021, Proceedings. Springer Verlag. pp. 201-215.
    Obligations can be affected by knowledge. Several approaches exist to formalize knowledge-based obligations, but no formalism has been developed yet to capture the dynamic interaction between knowledge and obligations. We introduce the dynamic extension of an existing logic for knowledge-based obligations here. We motivate the logic by analyzing several scenarios and by showing how it can capture in an original manner several fundamental deontic notions such as absolute, prima facie and all-things-considered obligations. Finally, in the dynamic epistemic logic tradition, we (...)
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  46. Review of Justification as Ignorance by Sven Rosenkranz. [REVIEW]Martin Smith - forthcoming - Mind.
  47. An enhanced model for Rosenkranz’s logic of justification.Niccolò Rossi - 2022 - Asian Journal of Philosophy 1 (1):1-9.
    Rosenkranz (2021) devised two bimodal epistemic logics: an idealized one and a realistic one. The former is shown to be sound with respect to a class of neighborhood frames called i-frames. Rosenkranz designed a specific i-frame able to invalidate a series of undesired formulas, proving that these are not theorems of the idealized logic. Nonetheless, an unwanted formula and an unwanted rule of inference are not invalidated. Invalidating the former guarantees the distinction between the two modal operators characteristic of the (...)
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  48. Epistemic logic for metadata modelling from scientific papers on Covid-19.Simone Cuconato - 2021 - Science and Philosophy 9 (2):83-96.
    The field of epistemic logic developed into an interdisciplinary area focused on explicating epistemic issues in, for example, artificial intelligence, computer security, game theory, economics, multiagent systems and the social sciences. Inspired, in part, by issues in these different ‘application’ areas, in this paper I propose an epistemic logic T for metadata extracted from scientific papers on COVID-19. More in details, I introduce a structure S to syntactically and semantically modelling metadata extracted with systems for extracting structured metadata from scientific (...)
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  49. The Role of the Common in Cognitive Prosperity: Our Command of the Unspeakable and Unwriteable.John Woods - 2021 - Logica Universalis 15 (4):399-433.
    There are several features of law which rightly draw the interest of philosophers, especially those whose expertise lies in ethics and social and political philosophy. But the law also has features which haven’t stirred much in the way of philosophical investigation. I must say that I find this surprising. For the fact is that a well-run criminal trial is a master-class in logic and epistemology. Below I examine the logical and epistemological properties of greatest operational involvement in a criminal proceedings, (...)
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  50. Dynamic Epistemic Logic.Hans van Ditmarsch, Wiebe van der Hoek & Barteld Kooi - 2007 - Dordrecht, Netherland: Springer.
    Dynamic Epistemic Logic is the logic of knowledge change. This book provides various logics to support such formal specifications, including proof systems. Concrete examples and epistemic puzzles enliven the exposition. The book also offers exercises with answers. It is suitable for graduate courses in logic. Many examples, exercises, and thorough completeness proofs and expressivity results are included. A companion web page offers slides for lecturers and exams for further practice.
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