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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. Varol Akman & Mujdat Pakkan (1996). Nonstandard Set Theories and Information Management. Philosophical Explorations.
    The merits of set theory as a foundational tool in mathematics stimulate its use in various areas of artificial intelligence, in particular intelligent information systems. In this paper, a study of various nonstandard treatments of set theory from this perspective is offered. Applications of these alternative set theories to information or knowledge management are surveyed.
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  2. Patrick Allo (2012). Information and Logical Discrimination. In S. Barry Cooper (ed.), How the World Computes. pp. 17--28.
    Informational conceptions of logic are barely novel. We find them in the work of John Corcoran, in several papers on substructural and constructive logics by Heinrich Wansing, and in the interpretation of the Routley-Meyer semantics for relevant logics in terms of Barwises and Perrys theory of situations. Allo & Mares [2] present an informational account of logical consequence that is based on the content-nonexpantion platitude, but that also relies on a double inversion of the standard direction of explanation (in- formation (...)
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  3. 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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  4. Patrick Allo (2010). A Classical Prejudice? Knowledge, Technology & 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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  5. 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 thing (...)
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  6. 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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  7. 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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  8. 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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  9. 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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  10. 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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  11. Yehoshua Bar-Hillel & Rudolf Carnap (1953). Semantic Information. British Journal for the Philosophy of Science 4 (14):147-157.
  12. 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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  13. 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 Publications.
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  14. Jon Barwise (1986). Information and Circumstance. Notre Dame Journal of Formal Logic 27 (July):324-338.
  15. 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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  16. Mario Benevides & L. Schechter (2009). Using Modal Logics to Express and Check Global Graph Properties. Logic Journal of the IGPL 17 (5):559-587.
    Graphs are among the most frequently used structures in Computer Science. Some of the properties that must be checked in many applications are connectivity, acyclicity and the Eulerian and Hamiltonian properties. In this work, we analyze how we can express these four properties with modal logics. This involves two issues: whether each of the modal languages under consideration has enough expressive power to describe these properties and how complex it is to use these logics to actually test whether a given (...)
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  17. Johan 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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  18. 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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  19. Joseph E. Brenner (2010). A Logic of Ethical Information. Knowledge, Technology and Policy 23 (1-2):109-133.
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  20. Miroslav Bursa, Lenka Lhotska, Vaclav Chudacek, Jiri Spilka, Petr Janku & Lukas Hruban (2015). Information Retrieval From Hospital Information System: Increasing Effectivity Using Swarm Intelligence. Journal of Applied Logic 13 (2):126-137.
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  21. 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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  22. John Corcoran (2012). A Farewell Letter To My Students. Philosophy Now 92:18-18.
    I am saying farewell after more than forty happy years of teaching logic at the University of Buffalo. But this is only a partial farewell. I will no longer be at UB to teach classroom courses or seminars. But nothing else will change. I will continue to be available for independent study. I will continue to write abstracts and articles with people who have taken courses or seminars with me. And I will continue to honor the LogicLifetimeGuarantee™, which is earned (...)
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  23. John Corcoran (2011). Contra-Argumento/Contraejemplo. In Luis Vega and Paula Olmos (ed.), Compendio de Lógica, Argumentación y Retórica. Editorial Trotta. pp. 137--141.
    A universal proposition is shown false by a known counterexample. A premise-conclusion argument is shown invalid by a known counterargument. The failure to distinguish counterexample from counterargument is like the failure to distinguish falsehood from invalidity.
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  24. John Corcoran (2011). Forma lógica/Formalización. In Luis Vega and Paula Olmos (ed.), Compendio de Lógica, Argumentación y Retórica. Editorial Trotta. pp. 257--258.
    The logical form of a discourse—such as a proposition, a set of propositions, an argument, or an argumentation—is obtained by abstracting from the subject-matter of its content terms or by regarding the content terms as mere place-holders or blanks in a form. In a logically perfect language the logical form of a proposition, a set of propositions, an argument, or an argumentation is determined by the grammatical form of the sentence, the set of sentences, the argument-text, or the argumentation-text expressing (...)
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  25. John Corcoran (2010). Review of Striker Translation of Aristotle's PRIOR ANALYTICS. [REVIEW] Notre Dame Philosophical Reviews:1-13.
    This review places this translation and commentary on Book A of Prior Analytics in historical, logical, and philosophical perspective. In particular, it details the author’s positions on current controversies. The author of this translation and commentary is a prolific and respected scholar, a leading figure in a large and still rapidly growing area of scholarship: Prior Analytics studies PAS. PAS treats many aspects of Aristotle’s Prior Analytics: historical context, previous writings that influenced it, preservation and transmission of its manuscripts, editions (...)
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  26. John Corcoran (2008). Schema. Stanford Encyclopedia of Philosophy.
    -/- A schema (plural: schemata, or schemas), also known as a scheme (plural: schemes), is a linguistic template or pattern together with a rule for using it to specify a potentially infinite multitude of phrases, sentences, or arguments, which are called instances of the schema. Schemas are used in logic to specify rules of inference, in mathematics to describe theories with infinitely many axioms, and in semantics to give adequacy conditions for definitions of truth. -/- 1. What is a Schema? (...)
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  27. John Corcoran (2006). George Boole. In Encyclopedia of Philosophy. 2nd edition. macmillan.
    2006. George Boole. Encyclopedia of Philosophy. 2nd edition. Detroit: Macmillan Reference USA. -/- George Boole (1815-1864), whose name lives among modern computer-related sciences in Boolean Algebra, Boolean Logic, Boolean Operations, and the like, is one of the most celebrated logicians of all time. Ironically, his actual writings often go unread and his actual contributions to logic are virtually unknown—despite the fact that he was one of the clearest writers in the field. Working with various students including Susan Wood and Sriram (...)
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  28. John Corcoran (1999). Information-Theoretic Logic and Transformation-Theoretic Logic,. In R. A. M. M. (ed.), Fragments in Science,. World Scientific Publishing Company,. pp. 25-35.
    Information-theoretic approaches to formal logic analyze the "common intuitive" concepts of implication, consequence, and validity in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; one given proposition is a consequence of a second if the latter contains all of the information contained by the former; an argument is valid if the conclusion contains no information beyond that of the premise-set. This (...)
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  29. John Corcoran & Idris Samawi Hamid (2016). Two-Method Errors: Having It Both Ways. Bulletin of Symbolic Logic 21:444-5.
    ►JOHN CORCORAN AND IDRIS SAMAWI HAMID, Two-method errors: having it both ways. Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA E-mail: corcoran@buffalo.edu Philosophy, Colorado State University, Fort Collins, CO 80523-1781 USA E-mail: ishamid@colostate.edu Where two methods produce similar results, mixing the two sometimes creates errors we call two-method errors, TMEs: in style, syntax, semantics, pragmatics, implicature, logic, or action. This lecture analyzes examples found in technical and in non-technical contexts. One can say “Abe knows whether Ben draws” in two other (...)
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  30. Marcello D'Agostino (forthcoming). An Informational View of Classical Logic. Theoretical Computer Science.
    We present an informational view of classical propositional logic that stems from a kind of informational semantics whereby the meaning of a logical operator is specified solely in terms of the information that is actually possessed by an agent. In this view the inferential power of logical agents is naturally bounded by their limited capability of manipulating “virtual information”, namely information that is not implicitly contained in the data. Although this informational semantics cannot be expressed by any finitely-valued matrix, it (...)
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  31. 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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  32. Marcello D'Agostinoemail (2013). Semantic Information and the Trivialization of Logic: Floridi on the Scandal of Deduction. Information 4 (1):33-59.
    In this paper we discuss Floridi’s views concerning semantic information in the light of a recent contribution (in collaboration with the present author) [1] that defies the traditional view of deductive reasoning as “analytic” or “tautological” and construes it as an informative, albeit non-empirical, activity. We argue that this conception paves the way for a more realistic notion of semantic information where the “ideal agents” that are assumed by the standard view can be indefinitely approximated by real ones equipped with (...)
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  33. Simon D'Alfonso (2014). The Logic of Knowledge and the Flow of Information. Minds and Machines 24 (3):307-325.
    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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  34. Todd R. Davies (1988). Determination, Uniformity, and Relevance: Normative Criteria for Generalization and Reasoning by Analogy. In David H. Helman (ed.), Analogical Reasoning. Kluwer Academic Publishers. pp. 227-250.
    This paper defines the form of prior knowledge that is required for sound inferences by analogy and single-instance generalizations, in both logical and probabilistic reasoning. In the logical case, the first order determination rule defined in Davies (1985) is shown to solve both the justification and non-redundancy problems for analogical inference. The statistical analogue of determination that is put forward is termed 'uniformity'. Based on the semantics of determination and uniformity, a third notion of "relevance" is defined, both logically and (...)
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  35. Rio de Janeiro & Ruy J. G. B. de Queiroz (2003). 9th Workshop on Logic, Language, Information and Computation. Bulletin of Symbolic Logic 9 (1):121-122.
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  36. J. G. B. de Queiroz (2004). 10th Workshop on Logic, Language, Information and Computation. Bulletin of Symbolic Logic 10 (2):295-296.
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  37. J. G. B. de Queiroz (1998). 4th Workshop on Logic, Language, Information and Computation. Bulletin of Symbolic Logic 4 (2):225-226.
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  38. Ruy J. G. B. de Queiroz (2005). 11th Workshop on Logic, Language, Information and Computation. Bulletin of Symbolic Logic 11 (1):120-121.
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  39. Ruy J. G. B. de Queiroz (2002). 8th Workshop on Logic, Language, Information and Computation. Bulletin of Symbolic Logic 8 (2):319-320.
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  40. Ruy J. G. B. de Queiroz (2001). 7th Workshop on Logic, Language, Information and Computation. Bulletin of Symbolic Logic 7 (2):293-294.
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  41. Ruy J. G. B. de Queiroz (1999). 5th Workshop on Logic, Language, Information and Computation. Bulletin of Symbolic Logic 5 (3):422-423.
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  42. 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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  43. Omar Doukari, Robert Jeansoulin & Eric Würbel (2008). Revision of Spatial Information by Containment. In Tu-Bao Ho & Zhi-Hua Zhou (eds.), Pricai 2008: Trends in Artificial Intelligence. Springer. pp. 939--944.
    In this paper, we define a revision approach based on a space decomposition using one property of the geographical that we name the containment property. This approach allows us to compute a correct and complete solution, which respects the principle of minimal change.
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  44. Marie Duží (2010). The Paradox of Inference and the Non-Triviality of Analytic Information. Journal of Philosophical Logic 39 (5):473 - 510.
    The classical theory of semantic information (ESI), as formulated by Bar-Hillel and Carnap in 1952, does not give a satisfactory account of the problem of what information, if any, analytically and/or logically true sentences have to offer. According to ESI, analytically true sentences lack informational content, and any two analytically equivalent sentences convey the same piece of information. This problem is connected with Cohen and Nagel's paradox of inference: Since the conclusion of a valid argument is contained in the premises, (...)
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  45. David Ellerman, On Classical and Quantum Logical Entropy.
    The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean logic is usually mis-specified as "propositional" logic). The notion of an element of a subset has as its dual the notion of a distinction of a partition (a pair of elements in different blocks). Boole developed finite logical probability as the normalized counting measure on elements of (...)
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  46. David Ellerman (2014). An Introduction to Partition Logic. Logic Journal of the IGPL 22 (1):94-125.
    Classical logic is usually interpreted as the logic of propositions. But from Boole's original development up to modern categorical logic, there has always been the alternative interpretation of classical logic as the logic of subsets of any given (nonempty) universe set. Partitions on a universe set are dual to subsets of a universe set in the sense of the reverse-the-arrows category-theoretic duality--which is reflected in the duality between quotient objects and subobjects throughout algebra. Hence the idea arises of a dual (...)
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  47. David Ellerman (2013). An Introduction to Logical Entropy and its Relation to Shannon Entropy. International Journal of Semantic Computing 7 (2):121-145.
    The logical basis for information theory is the newly developed logic of partitions that is dual to the usual Boolean logic of subsets. The key concept is a "distinction" of a partition, an ordered pair of elements in distinct blocks of the partition. The logical concept of entropy based on partition logic is the normalized counting measure of the set of distinctions of a partition on a finite set--just as the usual logical notion of probability based on the Boolean logic (...)
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  48. Xenopoulos Epaminondas (ed.) (1998). EPISTEMOLOGY OF LOGIC - Logic-Dialectic or Theory of the Knowledge. Athens, GREECE: KATERINA XENOPOULOU.
  49. Richard Evans (2009). Collective Intentionality VI, Berkeley.
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  50. Luciano Floridi (2006). 6. The Logic Of Being Informed. Logique Et Analyse 49.
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