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 1995. 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 1929 and Carnap’s 1945, 19521962. 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. David Miller (1970). Review: Marguerite H. Foster, Michael L. Martin, Probability, Conformation, and Simplicity. Readings in the Philosophy of Inductive Logic. [REVIEW] Journal of Symbolic Logic 35 (3):451-454.
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  2. Krystyna Misiuna (2011). O pewnej logice informacji. Filozofia Nauki 1.
    The main aim of the present article is an outline of an intuitively adequate system of logic of the operator "being informed". Such a system should be different from the familiar systems of epistemic and doxastic logic. The principle of veracity occurring in epistemic logics does not describe adequately the information operator, since the information may be true as well as false. On the other hand, the principle of consistency of beliefs, occurring in doxastic logics, cannot be applied to information, (...)
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  3. Erik J. Olsson & David Westlund (2006). On the Role of the Research Agenda in Epistemic Change. Erkenntnis 65 (2):165 - 183.
    The standard way of representing an epistemic state in formal philosophy is in terms of a set of sentences, corresponding to the agent’s beliefs, and an ordering of those sentences, reflecting how well entrenched they are in the agent’s epistemic state. We argue that this wide-spread representational view – a view that we identify as a “Quinean dogma” – is incapable of making certain crucial distinctions. We propose, as a remedy, that any adequate representation of epistemic states must also include (...)
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  4. Wlodek Rabinowicz, Epistemic Logic: Questions and Answers.
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  5. Ana Rosa Pérez Ransanz (2011). El papel de las emociones en la producción de conocimiento. Estudios Filosóficos 60 (173):51-64.
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  6. Veikko Rantala (2006). Learning and Epistemic Logic. Acta Philosophica Fennica 78:139.
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  7. William J. Rapaport (1988). Review: Cynthia Dwork, Yoram Moses, Knowledge and Common Knowledge in a Byzantine Environment I: Crash Failures. [REVIEW] Journal of Symbolic Logic 53 (2):666-666.
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  8. Manuel Rebuschi (2006). IF and Epistemic Action Logic. In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics. Springer 261--281.
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  9. Nicholas Rescher (2005). Epistemic Logic: A Survey of the Logic of Knowledge. University of Pittsburgh Press.
    Epistemic logic is the branch of philosophical thought that seeks to formalize the discourse about knowledge. Its object is to articulate and clarify the general principles of reasoning about claims to and attributions of knowledge. This comprehensive survey of the topic offers the first systematic account of the subject as it has developed in the journal literature over recent decades. Rescher gives an overview of the discipline by setting out the general principles for reasoning about such matters as propositional knowledge (...)
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  10. Jan-Willem Romeijn (2012). Conditioning and Interpretation Shifts. Studia Logica 100 (3):583-606.
    This paper develops a probabilistic model of belief change under interpretation shifts, in the context of a problem case from dynamic epistemic logic. Van Benthem [4] has shown that a particular kind of belief change, typical for dynamic epistemic logic, cannot be modelled by standard Bayesian conditioning. I argue that the problems described by van Benthem come about because the belief change alters the semantics in which the change is supposed to be modelled: the new information induces a shift in (...)
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  11. Katsuhiko Sano & Satoshi Tojo (2013). Dynamic Epistemic Logic for Channel-Based Agent Communication. In Kamal Lodaya (ed.), Logic and its Applications. Springer 109--120.
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  12. Karl Schlechta (1997). Nonmonotonic Logics Basic Concepts, Results, and Techniques.
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  13. Renate A. Schmidt & Dmitry Tishkovsky (2008). On Combinations of Propositional Dynamic Logic and Doxastic Modal Logics. Journal of Logic, Language and Information 17 (1):109-129.
    We prove completeness and decidability results for a family of combinations of propositional dynamic logic and unimodal doxastic logics in which the modalities may interact. The kind of interactions we consider include three forms of commuting axioms, namely, axioms similar to the axiom of perfect recall and the axiom of no learning from temporal logic, and a Church–Rosser axiom. We investigate the influence of the substitution rule on the properties of these logics and propose a new semantics for the test (...)
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  14. Krister Segerberg (1997). A Doxastic Walk with Darwiche and Pearl. Nordic Journal of Philosophical Logic 2 (1):63-66.
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  15. Krister Segerberg (1995). Dynamic Logic. In Audi Robert (ed.), The Cambridge Dictionary of Philosophy. Cambridge University Press
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  16. Sebastian Sequoiah-Grayson (2013). Epistemic Closure and Commutative, Nonassociative Residuated Structures. Synthese 190 (1):113-128.
    K-axiom-based epistemic closure for explicit knowledge is rejected for even the most trivial cases of deductive inferential reasoning on account of the fact that the closure axiom does not extend beyond a raw consequence relation. The recognition that deductive inference concerns interaction as much as it concerns consequence allows for perspectives from logics of multi-agent information flow to be refocused onto mono-agent deductive reasoning. Instead of modeling the information flow between different agents in a communicative or announcement setting, we model (...)
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  17. Ricardo Silvestre (2010). An Inductive Modal Approach for the Logic of Epistemic Inconsistency. Abstracta 6 (1):136-155.
    The purpose of this paper is twofold. First we want to extent a specific paranormal modal logic in such a way as obtain a paraconsistent and paracomplete multimodal logic able to formalize the notions of plausibility and certainty. With this logic at hand, and this is our second purpose, we shall use a modified version of Reiter‘s default logic to build a sort of inductive logic of plausibility and certainty able to represent some basic principles of epistemic inductive reasoning, such (...)
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  18. Ricardo Sousa Silvestre (2011). Induction and Confirmation Theory: An Approach Based on a Paraconsistent Nonmonotonic Logic. Princípios 17 (28):71-98.
    This paper is an effort to realize and explore the connections that exist between nonmonotonic logic and confirmation theory. We pick up one of the most wide-spread nonmonotonic formalisms – default logic – and analyze to what extent and under what adjustments it could work as a logic of induction in the philosophical sense. By making use of this analysis, we extend default logic so as to make it able to minimally perform the task of a logic of induction, having (...)
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  19. Roy Sorenson (1987). George N. Schlesinger, The Range of Epistemic Logic. [REVIEW] Philosophy in Review 7:81-83.
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  20. Roy A. Sorenson (1987). George N. Schlesinger, The Range of Epistemic Logic Reviewed By. Philosophy in Review 7 (2):81-83.
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  21. Zbigniew Stachniak (1995). Nonmonotonic Theories and Their Axiomatic Varieties. Journal of Logic, Language and Information 4 (4):317-334.
    The properties of monotonic inference systems and the properties of their theories are strongly linked. These links, however, are much weaker in nonmonotonic inference systems. In this paper we introduce the notion of anaxiomatic variety for a theory and show how this notion, instead of the notion of a theory, can be used for the syntactic and semantic analysis of nonmonotonic inferences.
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  22. Lynn Andrea Stein (1991). Resolving Ambiguity in Nonmonotonic Reasoning. Dissertation, Brown University
    We address problems of conflicting evidence--ambiguity--in nonmonotonic reasoning. In particular, we provide a unified framework for studying such ambiguity and for identifying principles that may aid in resolving it. This framework clarifies the issues that underlie particular ambiguity problems. It unifies existing approaches by providing a common description language. And it suggests new solutions by shifting the focus to underlying principles, rather than particular procedures. We analyze three specific examples of ambiguity--in inheritance, temporal reasoning, and counterfactual reasoning--in terms of this (...)
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  23. Satoru Suzuki (2009). Prolegomena to Dynamic Epistemic Preference Logic. In Hattori (ed.), New Frontiers in Artificial Intelligence. Springer 177--192.
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  24. İskender Taşdelen (unknown). Epistemology and Epistemic Logic. Yeditepe'de Felsefe (Philosophy at Yeditepe) 8.
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  25. Johan van Benthem (forthcoming). Epistemic Logic and Epistemology. The State of Their Affairs', to Appear in V. Hendricks, Ed., Special Issue Of. Philosophical Studies.
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  26. van Benthem, Johan, van Eijck, Jan & Kooi, Barteld, Logics of Communication and Change.
    Current dynamic epistemic logics for analyzing effects of informational events often become cumbersome and opaque when common knowledge is added for groups of agents. Still, postconditions involving common knowledge are essential to successful multi-agent communication. We propose new systems that extend the epistemic base language with a new notion of ‘relativized common knowledge’, in such a way that the resulting full dynamic logic of information flow allows for a compositional analysis of all epistemic postconditions via perspicuous ‘reduction axioms’. We also (...)
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  27. Johan van Benthem & Fernando R. Velázquez-Quesada (2010). The Dynamics of Awareness. Synthese 177 (1):5-27.
    Classical epistemic logic describes implicit knowledge of agents about facts and knowledge of other agents based on semantic information. The latter is produced by acts of observation or communication that are described well by dynamic epistemic logics. What these logics do not describe, however, is how significant information is also produced by acts of inference—and key axioms of the system merely postulate “deductive closure”. In this paper, we take the view that all information is produced by acts, and hence we (...)
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  28. H. van Ditmarsch, W. van der Hoek & B. Kooi (2005). Playing Cards with Hintikka: An Introduction to Dynamic Epistemic Logic. Australasian Journal of Philosophy 3:108-134.
    This contribution is a gentle introduction to so-called dynamic epistemic logics, that can describe how agents change their knowledge and beliefs. We start with a concise introduction to epistemic logic, through the example of one, two and finally three players holding cards; and, mainly for the purpose of motivating the dynamics, we also very summarily introduce the concepts of general and common knowledge. We then pay ample attention to the logic of public announcements, wherein agents change their knowledge as the (...)
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  29. Hans van Ditmarsch, Andreas Herzig & Tiago De Lima (2012). Public Announcements, Public Assignments and the Complexity of Their Logic. Journal of Applied Non-Classical Logics 22 (3):249-273.
    We study the extension of public announcement logic PAL by public assignments, which we call PALA. Just as in the case of PAL, the standard procedure for deciding PALA validity, i.e. the use of so-called reduction axioms to translate PALA formulae into formulae in epistemic logic EL, may lead to exponential growth. In this paper, we show that such a price is not mandatory, for we provide a polynomial translation of PALA into EL. This is based on abbreviations of subformulae (...)
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  30. Jan van Eijck, Modelling Epistemic Updates with Functional Programming.
    Epistemic logic is the logic of knowledge, and dynamic epistemic logic is the logic of effects of communicative actions on the knowledge states of a set of agents. Typical communicative actions are making public announcements, passing private messages, revealing secrets, telling lies. This paper takes its starting point from the version of dynamic epistemic logic of [3], and demonstrates a tool that can be used for showing what goes on during a series of epistemic updates: the dynamic epistemic modelling tool (...)
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  31. Jan van Eijck, Modelling the Epistemics of Communication with Functional Programming.
    Dynamic epistemic logic is the logic of the effects of epistemic actions like making public announcements, passing private messages, revealing secrets, telling lies. This paper takes its starting point from the version of dynamic epistemic logic of [2], and demonstrates a tool that can be used for showing what goes on during a series of epistemic updates: the dynamic epistemic modelling tool DEMO [7, 9]. DEMO allows modelling epistemic updates, graphical display of update results, graphical display of action models, formula (...)
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  32. Yanjing Wang & Qinxiang Cao (2013). On Axiomatizations of Public Announcement Logic. Synthese (S1):1-32.
    In the literature, different axiomatizations of Public Announcement Logic (PAL) have been proposed. Most of these axiomatizations share a “core set” of the so-called “reduction axioms”. In this paper, by designing non-standard Kripke semantics for the language of PAL, we show that the proof system based on this core set of axioms does not completely axiomatize PAL without additional axioms and rules. In fact, many of the intuitive axioms and rules we took for granted could not be derived from the (...)
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  33. Charles Michael Wiseman (1969). Epistemic Logic: An Examination of the Logics of von Wright, Chisholm, and Hintikka. Dissertation, Columbia University
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  34. Frank Wolter & Michael Wooldridge (2012). Temporal and Dynamic Logic. Journal of the Indian Council of Philosophical Research 1.
    We present an introductory survey of temporal and dynamic logics: logics for reasoning about how environments change over time, and how dynamic processes affect their environments.We begin by introducing the historical development of temporal and dynamic logic, starting with the seminal work of Prior. This leads to a discussion of the use of temporal and dynamic logic in computer science. We describe LTL, CTL, and PDL; three key formalisms used in computer science for reasoning about programs, and illustrate how these (...)
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  35. Audrey Yap (2014). Idealization, Epistemic Logic, and Epistemology. Synthese 191 (14):3351-3366.
    Many criticisms of epistemic logic have centered around its use of devices such as idealized knowers with logical omniscience and perfect self-knowledge. One possible response to such criticisms is to say that these idealizations are normative devices, and that epistemic logic tells us how agents ought to behave. This paper will take a different approach, treating epistemic logic as descriptive, and drawing the analogy between its formal models and idealized scientific models on that basis. Treating it as descriptive matches the (...)
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  36. Paul Ziff (1950). Review: W. H. Werkmeister, The Basis and Structure of Knowledge. [REVIEW] Journal of Symbolic Logic 15 (1):74-74.
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  37. Piotr Łukowski (2013). Is Human Reasoning Really Nonmonotonic? Logic and Logical Philosophy 22 (1):63-73.
    It seems that nonmonotonicity of our reasoning is an obvious truth. Almost every logician not even believes, but simply knows very well that a human being thinks in a nonmonotonic way. Moreover, a nonmonotonicity of thinking seems to be a phenomenon parallel to the existence of human beings. Examples allegedly illustrating this phenomenon are not even analyzed today. They are simply quoted. Nowadays, this is a standard approach to nonmonotonicity. However, even simple analysis of those “obvious” examples shows that they (...)
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Doxastic and Epistemic Logic
  1. Thomas Ågotnes & Hans van Ditmarsch (2011). What Will They Say?—Public Announcement Games. 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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  2. Thomas Ågotnes & Hans van Ditmarsch (2011). What Will They Say?—Public Announcement Games. Synthese 179 (1):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 (...)
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  3. Carlos E. Alchourrón (1972). The Intuitive Background of Normative Legal Discourse and its Formalization. Journal of Philosophical Logic 1 (3/4):447 - 463.
  4. Natasha Alechina, Brian Logan, Hoang Nga Nguyen & Abdur Rakib (2009). Verifying Time, Memory and Communication Bounds in Systems of Reasoning Agents. Synthese 169 (2):385 - 403.
    We present a framework for verifying systems composed of heterogeneous reasoning agents, in which each agent may have differing knowledge and inferential capabilities, and where the resources each agent is prepared to commit to a goal (time, memory and communication bandwidth) are bounded. The framework allows us to investigate, for example, whether a goal can be achieved if a particular agent, perhaps possessing key information or inferential capabilities, is unable (or unwilling) to contribute more than a given portion of its (...)
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  5. Patrick Allo (2016). Logic, Reasoning and Revision. Theoria 82 (1):3-31.
    The traditional connection between logic and reasoning has been under pressure ever since Gilbert Harman attacked the received view that logic yields norms for what we should believe. In this article I first place Harman's challenge in the broader context of the dialectic between logical revisionists like Bob Meyer and sceptics about the role of logic in reasoning like Harman. I then develop a formal model based on contemporary epistemic and doxastic logic in which the relation between logic and norms (...)
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  6. Patrick Allo (2013). Adaptive Logic as a Modal Logic. Studia Logica 101 (5):933-958.
    Modal logics have in the past been used as a unifying framework for the minimality semantics used in defeasible inference, conditional logic, and belief revision. The main aim of the present paper is to add adaptive logics, a general framework for a wide range of defeasible reasoning forms developed by Diderik Batens and his co-workers, to the growing list of formalisms that can be studied with the tools and methods of contemporary modal logic. By characterising the class of abnormality models, (...)
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  7. Patrick Allo (2013). The Many Faces of Closure and Introspection. Journal of Philosophical Logic 42 (1):91-124.
    In this paper I present a more refined analysis of the principles of deductive closure and positive introspection. This analysis uses the expressive resources of logics for different types of group knowledge, and discriminates between aspects of closure and computation that are often conflated. The resulting model also yields a more fine-grained distinction between implicit and explicit knowledge, and places Hintikka’s original argument for positive introspection in a new perspective.
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  8. Patrick Allo (2011). The Logic of 'Being Informed' Revisited and Revised. Philosophical Studies 153 (3):417-434.
    The logic of ‘being informed’ gives a formal analysis of a cognitive state that does not coincide with either belief, or knowledge. To Floridi, who first proposed the formal analysis, the latter is supported by the fact that unlike knowledge or belief, being informed is a factive, but not a reflective state. This paper takes a closer look at the formal analysis itself, provides a pure and an applied semantics for the logic of being informed, and tries to find out (...)
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  9. Patrick Allo (2009). Reasoning About Data and Information. Synthese 167 (2):231-249.
    Cognitive states as well as cognitive commodities play central though distinct roles in our epistemological theories. By being attentive to how a difference in their roles affects our way of referring to them, we can undoubtedly accrue our understanding of the structure and functioning of our main epistemological theories. In this paper we propose an analysis of the dichotomy between states and commodities in terms of the method of abstraction, and more specifically by means of infomorphisms between different ways to (...)
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  10. Patrick Allo (2008). Formalising the 'No Information Without Data-Representation' Principle. In P. Brey, A. Briggle & K. Waelbers (eds.), Current Issues in Computing and Philosophy. IOS Press
    One of the basic principles of the general definition of information is its rejection of dataless information, which is reflected in its endorsement of an ontological neutrality. In general, this principles states that “there can be no information without physical implementation” (Floridi (2005)). Though this is standardly considered a commonsensical assumption, many questions arise with regard to its generalised application. In this paper a combined logic for data and information is elaborated, and specifically used to investigate the consequences of restricted (...)
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  11. Patrick Allo (2008). Vincent Hendricks, Mainstream and Formal Epistemology. [REVIEW] Erkenntnis 69 (3):427-432.
    As Vincent Hendricks remarks early on in this book, the formal and mainstream traditions of epistemic theorising have mostly evolved independently of each other. This initial impression is confirmed by a comparison of the main problems and methods practitioners in each tradition are concerned with. Mainstream epistemol- ogy engages in a dialectical game of proposing and challenging definitions of knowledge. Formal epistemologists proceed differently, as they design a wide variety of axiomatic and model-theoretic methods whose consequences they investigate independently of (...)
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  12. Patrick Allo (2006). Local Information and Adaptive Consequence. Logique Et Analyse 149:461-488.
    In this paper we provide a formal description of what it means to be in a local or partial information-state. Starting from the notion of locality in a relational structure, we define so-called adaptive gen- erated submodels. The latter are then shown to yield an adaptive logic wherein the derivability of Pφ is naturally interpreted as a core property of being in a state in which one holds the information that φ.
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  13. Giambattista Amati, Luigia Carlucci-Aiello & Fiora Pirri (1997). Intuitionistic Autoepistemic Logic. Studia Logica 59 (1):103-120.
    In this paper we address the problem of combining a logic with nonmonotonic modal logic. In particular we study the intuitionistic case. We start from a formal analysis of the notion of intuitionistic consistency via the sequent calculus. The epistemic operator M is interpreted as the consistency operator of intuitionistic logic by introducing intuitionistic stable sets. On the basis of a bimodal structure we also provide a semantics for intuitionistic stable sets.
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