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The relationship between logic and information is an intimate one that goes both ways. Firstly, information has played a role in providing a basis for certain accounts of logic. At a basic level there is the interpretation that good logic arguments are just those arguments where the information in the conclusion is already contained in the premises of that argument. Furthermore, notions of information have been used to good effect in developing semantics for certain logics, particularly relevant logic. Secondly, logics of information have provided formal accounts of various information phenomena, such as logics of being informed.

Key works Jakko Hintikka has been one of the pioneers in investigating the relationship between logic and information, looking at measures of semantic information for contingent propositions and information measures for tautologies/deductive inferences. His Hintikka 1970 contains papers on the topic. Devlin 1991, Barwise & Seligman 1997 and Israel & Perry unknown represent an important collection of works that provide general accounts of information flow based on situation semantics/theory. Mares 1996 and Restall 1996 are attempts to provide an informational semantics for relevant logic.
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  1. 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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  2. Patrick Allo (2010). A Classical Prejudice? Knowledge, Technology and Policy 23 (1-2):25-40.
    In this paper, I reassess Floridi’s solution to the Bar-Hillel–Carnap paradox (the information yield of inconsistent propositions is maximal) by questioning the orthodox view that contradictions cannot be true. The main part of the paper is devoted to showing that the veridicality thesis (semantic information has to be true) is compatible with dialetheism (there are true contradictions) and that, unless we accept the additional non-falsity thesis (information cannot be false), there is no reason to presuppose that there is no such (...)
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  3. 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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  4. Patrick Allo (2007). Logical Pluralism and Semantic Information. Journal of Philosophical Logic 36 (6):659 - 694.
    Up to now theories of semantic information have implicitly relied on logical monism, or the view that there is one true logic. The latter position has been explicitly challenged by logical pluralists. Adopting an unbiased attitude in the philosophy of information, we take a suggestion from Beall and Restall at heart and exploit logical pluralism to recognise another kind of pluralism. The latter is called informational pluralism, a thesis whose implications for a theory of semantic information we explore.
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  5. Patrick Allo & Edwin Mares (2012). Informational Semantics as a Third Alternative? Erkenntnis 77 (2):167-185.
    Informational semantics were first developed as an interpretation of the model-theory of substructural (and especially relevant) logics. In this paper we argue that such a semantics is of independent value and that it should be considered as a genuine alternative explication of the notion of logical consequence alongside the traditional model-theoretical and the proof-theoretical accounts. Our starting point is the content-nonexpansion platitude which stipulates that an argument is valid iff the content of the conclusion does not exceed the combined content (...)
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  6. A. Baltag, H. P. van Ditmarsch & L. S. Moss (2008). Epistemic Logic and Information Update. In P. Adriaans & J. van Benthem (eds.), hilosophy of Information. MIT Press.
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  7. Yehoshua Bar-Hillel & Rudolf Carnap (1953). Semantic Information. British Journal for the Philosophy of Science 4 (14):147-157.
  8. Jon Barwise (1997). Information and Impossibilities. Notre Dame Journal of Formal Logic 38 (4):488-515.
    In this paper I explore informationalism, a pragmatic theory of modality that seems to solve some serious problems in the familiar possible worlds accounts of modality. I view the theory as an elaboration of Stalnaker's moderate modal realism, though it also derives from Dretske's semantic theory of information. Informationalism is presented in Section 2 after the prerequisite stage setting in Section 1. Some applications are sketched in Section 3. Finally, a mathematical model of the theory is developed in Section 4.How (...)
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  9. Jon Barwise (1993). Constraints, Channels and the Flow of Information. In Peter Aczel, David Israel, Yosuhiro Katagiri & Stanley Peters (eds.), Situation Theory and its Applications Vol. 3. Csli.
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  10. Jon Barwise & Jerry Seligman (1997). Information Flow: The Logic of Distributed Systems. Cambridge University Press.
    Presents a mathematically rigorous, philosophically sound foundation for a science of information.
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  11. Johan Van Benthem (2009). The Information in Intuitionistic Logic. Synthese 167 (2):251 - 270.
    Issues about information spring up wherever one scratches the surface of logic. Here is a case that raises delicate issues of 'factual' versus 'procedural' information, or 'statics' versus 'dynamics'. What does intuitionistic logic, perhaps the earliest source of informational and procedural thinking in contemporary logic, really tell us about information? How does its view relate to its 'cousin' epistemic logic? We discuss connections between intuitionistic models and recent protocol models for dynamic-epistemic logic, as well as more general issues that emerge.
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  12. Francesco Berto (2012). Non-Normal Worlds and Representation. In Michal Peliš & Vít Punčochář (eds.), The Logica Yearbook. College Publications.
    World semantics for relevant logics include so-called non-normal or impossible worlds providing model-theoretic counterexamples to such irrelevant entailments as (A ∧ ¬A) → B, A → (B∨¬B), or A → (B → B). Some well-known views interpret non-normal worlds as information states. If so, they can plausibly model our ability of conceiving or representing logical impossibilities. The phenomenon is explored by combining a formal setting with philosophical discussion. I take Priest’s basic relevant logic N4 and extend it, on the syntactic (...)
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  13. Joseph E. Brenner (2010). A Logic of Ethical Information. Knowledge, Technology and Policy 23 (1-2):109-133.
    The work of Luciano Floridi lies at the interface of philosophy, information science and technology, and ethics, an intersection whose existence and significance he was one of the first to establish. His closely related concepts of a philosophy of information (PI), informational structural realism, information logic (IL), and information ethics (IE) provide a new ontological perspective from which moral concerns can be addressed, especially but not limited to those arising in connection with the new information and communication technologies. In this (...)
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  14. Ariel Caticha (2014). Towards an Informational Pragmatic Realism. Minds and Machines 24 (1):37-70.
    I discuss the design of the method of entropic inference as a general framework for reasoning under conditions of uncertainty. The main contribution of this discussion is to emphasize the pragmatic elements in the derivation. More specifically: (1) Probability theory is designed as the uniquely natural tool for representing states of incomplete information. (2) An epistemic notion of information is defined in terms of its relation to the Bayesian beliefs of ideally rational agents. (3) The method of updating from a (...)
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  15. Marcello D'Agostino & Luciano Floridi (2009). The Enduring Scandal of Deduction: Is Propositional Logic Really Uninformative? Synthese 167 (2):271 - 315.
    Deductive inference is usually regarded as being "tautological" or "analytical": the information conveyed by the conclusion is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable in polynomial time), although by means of growing (...)
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  16. Simon D'Alfonso (forthcoming). The Logic of Knowledge and the Flow of Information. Minds and Machines:1-19.
    In this paper I look at Fred Dretske’s account of information and knowledge as developed in Knowledge and The Flow of Information. In particular, I translate Dretske’s probabilistic definition of information to a modal logical framework and subsequently use this to explicate the conception of information and its flow which is central to his account, including the notions of channel conditions and relevant alternatives. Some key products of this task are an analysis of the issue of information closure and an (...)
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  17. Keith Devlin (1991). Logic and Information. Cambridge University Press.
    Classical logic, beginning with the work of Aristotle, has developed into a powerful and rigorous mathematical theory with many applications in mathematics and ...
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  18. Luciano Floridi (forthcoming). The Logic of Being Informed. Logique Et Analyse.
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  19. Marcello Frixione & Antonio Lieto (2013). Dealing with Concepts: From Cognitive Psychology to Knowledge Representation. Frontiers of Psychological and Behevioural Science 2 (3):96-106.
    Concept representation is still an open problem in the field of ontology engineering and, more generally, of knowledge representation. In particular, the issue of representing “non classical” concepts, i.e. concepts that cannot be defined in terms of necessary and sufficient conditions, remains unresolved. In this paper we review empirical evidence from cognitive psychology, according to which concept representation is not a unitary phenomenon. On this basis, we sketch some proposals for concept representation, taking into account suggestions from psychological research. In (...)
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  20. Claudio Gnoli (2008). Facets: A Fruitful Notion in Many Domains. [REVIEW] Axiomathes 18 (2):127-130.
    Introduction to a special issue on facet analysis.
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  21. Joanna Golinska-Pilarek & Emilio Munoz-Velasco (2009). Dual Tableau for a Multimodal Logic for Order of Magnitude Qualitative Reasoning with Bidirectional Negligibility. International Journal of Computer Mathematics 86 (10-11):1707–1718.
  22. Joanna Golinska-Pilarek & Ewa Orlowska (2008). Logics of Similarity and Their Dual Tableaux. A Survey. In Giacomo Della Riccia, Didier Dubois & Hans-Joachim Lenz (eds.), Preferences and Similarities. Springer. 129--159.
  23. Jaakko Hintikka (1970). Information and Inference. D. Reidel.
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  24. Jaakko Hintikka (1970). Surface Information and Depth Information. In Jaakko Hintikka & O. Suppes (eds.), Information and Inference. Dordrecht, Reidel.
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  25. Wesley H. Holliday, Tomohiro Hoshi & Thomas F. Icard Iii (2013). Information Dynamics and Uniform Substitution. Synthese 190 (1):31-55.
    The picture of information acquisition as the elimination of possibilities has proven fruitful in many domains, serving as a foundation for formal models in philosophy, linguistics, computer science, and economics. While the picture appears simple, its formalization in dynamic epistemic logic reveals subtleties: given a valid principle of information dynamics in the language of dynamic epistemic logic, substituting complex epistemic sentences for its atomic sentences may result in an invalid principle. In this article, we explore such failures of uniform substitution. (...)
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  26. Wesley H. Holliday, Tomohiro Hoshi & Thomas F. Icard (2012). A Uniform Logic of Information Dynamics. In Thomas Bolander, Torben Braüner, Silvio Ghilardi & Lawrence Moss (eds.), Advances in Modal Logic 9. College Publications.
    Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitution. A distinction therefore arises between the logic and its substitution core, the set of formulas all of whose substitution instances are valid. The classic example of a non-uniform dynamic epistemic logic is Public Announcement Logic (PAL), and a well-known open problem is to axiomatize the substitution core of PAL. In this paper we solve this problem for PAL over the class of all relational models with infinitely (...)
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  27. Wesley H. Holliday & Thomas F. Icard (2010). Moorean Phenomena in Epistemic Logic. In Lev Beklemishev, Valentin Goranko & Valentin B. Shehtman (eds.), Advances in Modal Logic 8. College Publications.
    A well-known open problem in epistemic logic is to give a syntactic characterization of the successful formulas. Semantically, a formula is successful if and only if for any pointed model where it is true, it remains true after deleting all points where the formula was false. The classic example of a formula that is not successful in this sense is the “Moore sentence” p ∧ ¬BOXp, read as “p is true but you do not know p.” Not only is the (...)
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  28. Phyllis Illari (2012). The Philosophy of Information - a Simple Introduction. Society for the Philosophy of Information.
    This book serves as the main reference for an undergraduate course on Philosophy of Information. The book is written to be accessible to the typical undergraduate student of Philosophy and does not require propaedeutic courses in Logic, Epistemology or Ethics. Each chapter includes a rich collection of references for the student interested in furthering her understanding of the topics reviewed in the book. -/- The book covers all the main topics of the Philosophy of Information and it should be considered (...)
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  29. Mark Jago (2009). Logical Information and Epistemic Space. Synthese 167 (2):327 - 341.
    Gaining information can be modelled as a narrowing of epistemic space . Intuitively, becoming informed that such-and-such is the case rules out certain scenarios or would-be possibilities. Chalmers’s account of epistemic space treats it as a space of a priori possibility and so has trouble in dealing with the information which we intuitively feel can be gained from logical inference. I propose a more inclusive notion of epistemic space, based on Priest’s notion of open worlds yet which contains only those (...)
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  30. Isaac Levi (1967). Information and Inference. Synthese 17 (1):369 - 391.
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  31. Edwin D. Mares (2009). General Information in Relevant Logic. Synthese 167 (2):343 - 362.
    This paper sets out a philosophical interpretation of the model theory of Mares and Goldblatt (The Journal of Symbolic Logic 71, 2006). This interpretation distinguishes between truth conditions and information conditions. Whereas the usual Tarskian truth condition holds for universally quantified statements, their information condition is quite different. The information condition utilizes general propositions . The present paper gives a philosophical explanation of general propositions and argues that these are needed to give an adequate theory of general information.
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  32. Edwin D. Mares (1996). Relevant Logic and the Theory of Information. Synthese 109 (3):345 - 360.
    This paper provides an interpretation of the Routley-Meyer semantics for a weak negation-free relevant logic using Israel and Perry's theory of information. In particular, Routley and Meyer's ternary accessibility relation is given an interpretation in information-theoretic terms.
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  33. Peter Milne (2012). Probability as a Measure of Information Added. Journal of Logic, Language and Information 21 (2):163-188.
    Some propositions add more information to bodies of propositions than do others. We start with intuitive considerations on qualitative comparisons of information added . Central to these are considerations bearing on conjunctions and on negations. We find that we can discern two distinct, incompatible, notions of information added. From the comparative notions we pass to quantitative measurement of information added. In this we borrow heavily from the literature on quantitative representations of qualitative, comparative conditional probability. We look at two ways (...)
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  34. Krystyna Misiuna (2012). A Modal Logic of Information. Logic and Logical Philosophy 21 (1):33-51.
    We consider modal epistemic and doxastic logics as intuitively inadequate logics of information, and we outline a modal system of the operator being informed that which avoids inconsistency with our intuitive concept of information. The system has modal structure of the normal modal logic K4, and is sound and complete on the class of all transitive frames. We compare this logic with Floridi’s KTB information logic, and we consider a possibility of extending our system to a dynamic logic.
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  35. María G. Navarro (2011). Collective Challenges for the Realisation of a Collective Intelligence. Analytic Teaching and Philosophical Praxis 32 (1):40-47.
    Understanding Information and Communication Technologies through the networks in which people get con¬nected, communicate and co-operate has been a constant feature in the work of researchers who have not dissociated their view of the meaning of technologies from new social movements. This paper maintains that Information and Communication Technologies are not only networks that people join individually, but they also act as social technologies. Their improvement depends both on the diversity of their functions (social, political, cognitive, etc.) and the flexibility (...)
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  36. Paul Piwek (2011). Dialogue Structure and Logical Expressivism. Synthese 183 (S1):33-58.
    This paper aims to develop the implications of logical expressivism for a theory of dialogue coherence. I proceed in three steps. Firstly, certain structural properties of cooperative dialogue are identified. Secondly, I describe a variant of the multi-agent natural deduction calculus that I introduced in Piwek (J Logic Lang Inf 16(4):403–421, 2007 ) and demonstrate how it accounts for the aforementioned structures. Thirdly, I examine how the aforementioned system can be used to formalise an expressivist account of logical vocabulary that (...)
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  37. Paul Piwek (2007). Meaning and Dialogue Coherence: A Proof-Theoretic Investigation. Journal of Logic, Language and Information 16 (4):403-421.
    This paper presents a novel proof-theoretic account of dialogue coherence. It focuses on an abstract class of cooperative information-oriented dialogues and describes how their structure can be accounted for in terms of a multi-agent hybrid inference system that combines natural deduction with information transfer and observation. We show how certain dialogue structures arise out of the interplay between the inferential roles of logical connectives (i.e., sentence semantics), a rule for transferring information between agents, and a rule for information flow between (...)
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  38. G. Primiero (2008). Information and Knowledge. Springer.
    The constructive reformulation of the semantic theory suggests two basic principles to be assumed: first, the distinction between proper knowledge, expressed in judgemental form, and the assertion conditions for such knowledge; second, ...
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  39. Giuseppe Primiero (2009). An Epistemic Logic for Becoming Informed. Synthese 167 (2):363 - 389.
    Various conceptual approaches to the notion of information can currently be traced in the literature in logic and formal epistemology. A main issue of disagreement is the attribution of truthfulness to informational data, the so called Veridicality Thesis (Floridi 2005). The notion of Epistemic Constructive Information (Primiero 2007) is one of those rejecting VT. The present paper develops a formal framework for ECI. It extends on the basic approach of Artemov’s logic of proofs (Artemov 1994), representing an epistemic logic based (...)
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  40. Landon Rabern, Brian Rabern & Matthew Macauley (2013). Dangerous Reference Graphs and Semantic Paradoxes. Journal of Philosophical Logic 42 (5):727-765.
    The semantic paradoxes are often associated with self-reference or referential circularity. Yablo (Analysis 53(4):251–252, 1993), however, has shown that there are infinitary versions of the paradoxes that do not involve this form of circularity. It remains an open question what relations of reference between collections of sentences afford the structure necessary for paradoxicality. In this essay, we lay the groundwork for a general investigation into the nature of reference structures that support the semantic paradoxes and the semantic hypodoxes. We develop (...)
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  41. Greg Restall, Logics, Situations and Channels.
    The notion of that information is relative to a context is important in many different ways. The idea that the context is small — that is, not necessarily a consistent and complete possible world — plays a role not only in situation theory, but it is also an enlightening perspective from which to view other areas, such as modal logics, relevant logics, categorial grammar and much more. In this article we will consider these areas, and focus then on one further (...)
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  42. Greg Restall (1996). Information Flow and Relevant Logics. In Jerry Seligman & Dag Westerståhl (eds.), Logic, Language and Computation. Csli Publications, Stanford. 1--463.
  43. J. Seligman (2009). Channels: From Logic to Probability. In G. Sommaruga (ed.), Channels: From Logic to Probability.
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  44. Sebastian Sequoiah-Grayson (2009). A Positive Information Logic for Inferential Information. Synthese 167 (2):409 - 431.
    Performing an inference involves irreducibly dynamic cognitive procedures. The article proposes that a non-associative information frame, corresponding to a residuated pogroupoid, underpins the information structure involved. The argument proceeds by expounding the informational turn in logic, before outlining the cognitive actions at work in deductive inference. The structural rules of Weakening, Contraction, Commutation, and Association are rejected on the grounds that they cause us to lose track of the information flow in inferential procedures. By taking the operation of information application (...)
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  45. Sebastian Sequoiah-grayson (2009). Dynamic Negation and Negative Information. Review of Symbolic Logic 2 (1):233-248.
    This essay proposes a procedural interpretation of negative information in terms of split negation as procedural prohibition. Information frames and models are introduced, with negation defined as the implication of bottom, 0. A method for extracting the procedures prohibited by complex formulas is outlined, and the relationship between types of prohibited procedures is identified. Definitions of negation types in terms of the implication of 0 on an informational interpretation have been criticized. This criticism turns on the definitions creating a purportedly (...)
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  46. Sebastian Sequoiah-Grayson (2008). The Scandal of Deduction. Journal of Philosophical Logic 37 (1):67 - 94.
    This article provides the first comprehensive reconstruction and analysis of Hintikka’s attempt to obtain a measure of the information yield of deductive inferences. The reconstruction is detailed by necessity due to the originality of Hintikka’s contribution. The analysis will turn out to be destructive. It dismisses Hintikka’s distinction between surface information and depth information as being of any utility towards obtaining a measure of the information yield of deductive inferences. Hintikka is right to identify the failure of canonical information theory (...)
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  47. Johan van Benthem (2011). Logical Dynamics of Information and Interaction. Cambridge University Press.
    Machine generated contents note: Preface; 1. Logical dynamics, agency, and intelligent interaction; 2. Epistemic logic and semantic information; 3. Dynamic logic of public observation; 4. Multi-agent dynamic-epistemic logic; 5. Dynamics of inference and awareness; 6. Questions and issue management; 7. Soft information, correction, and belief change; 8. An encounter with probability; 9. Preference statics and dynamics; 10. Decisions, actions, and games; 11. Processes over time; 12. Epistemic group structure and collective agency; 13. Logical dynamics in philosophy; 14. Computation as conversation; (...)
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  48. Johan van Benthem (2003). Logic and the Dynamics of Information. Minds and Machines 13 (4):503-519.
    We discuss how issues of information and computation interact with logic today, and what might be a natural extended agenda of investigation.
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  49. Johan van Benthem, Maricarmen Martinez, David Israel & John Perry, The Stories of Logic and Information.
    Information is a notion of wide use and great intuitive appeal, and hence, not surprisingly, different formal paradigms claim part of it, from Shannon channel theory to Kolmogorov complexity. Information is also a widely used term in logic, but a similar diversity repeats itself: there are several competing logical accounts of this notion, ranging from semantic to syntactic. In this chapter, we will discuss three major logical accounts of information.
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  50. Gregory Wheeler (forthcoming). Is There a Logic of Information? Journal of Theoretical and Applied Artificial Intelligence.
    Information-based epistemology maintains that ‘being informed’ is an independent cognitive state that cannot be reduced to knowledge or to belief, and the modal logic KTB has been proposed as a model. But what distinguishes the KTB analysis of ‘being informed’, the Brouwersche schema (B), is precisely its downfall, for no logic of information should include (B) and, more generally, no epistemic logic should include (B), either.
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