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  1. Natasha Alechina, Mark Jago & Brian Logan (2008). Preference-Based Belief Revision for Rule-Based Agents. Synthese 165 (2):159-177.
    Agents which perform inferences on the basis of unreliable information need an ability to revise their beliefs if they discover an inconsistency. Such a belief revision algorithm ideally should be rational, should respect any preference ordering over the agent’s beliefs (removing less preferred beliefs where possible) and should be fast. However, while standard approaches to rational belief revision for classical reasoners allow preferences to be taken into account, they typically have quite high complexity. In this paper, we consider belief revision (...)
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  2. G. Aldo Antonelli, Non-Monotonic Logic. Stanford Encyclopedia of Philosophy.
    The term "non-monotonic logic" covers a family of formal frameworks devised to capture and represent defeasible inference , i.e., that kind of inference of everyday life in which reasoners draw conclusions tentatively, reserving the right to retract them in the light of further information. Such inferences are called "non-monotonic" because the set of conclusions warranted on the basis of a given knowledge base does not increase (in fact, it can shrink) with the size of the knowledge base itself. This is (...)
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  3. van Jfak Benthem (1986). Partiality and Non-Monmotonicity in Classical Logic. Logique Et Analyse 29:251-273.
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  4. David Billington & Andrew Rock (2001). Propositional Plausible Logic: Introduction and Implementation. Studia Logica 67 (2):243-269.
    Plausible Logic allows defeasible deduction with arbitrary propositions, and yet when sufficiently simplified it is very similar to the Defeasible Logics of Billington and Nute. This paper presents Plausible Logic, explains some of the ideas behind the definitions, applies Plausible Logic to an example, and proves a coherence result which indicates that Plausible Logic is well behaved. We also report the first complete implementation of propositional Plausible Logic. The implementation has a web interface which makes it available to researchers and (...)
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  5. Alexander Bochman (2001). A Logical Theory of Nonmonotonic Inference and Belief Change. Springer.
    This is the first book that integrates nonmonotonic reasoning and belief change into a single framework from an artificial intelligence logic point-of-view.
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  6. Gerhard Brewka, Jurgen Dix & Kurt Konolige (1997). Nonmonotonic Reasoning: An Overview. Center for the Study of Language and Inf.
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  7. K. Britz (1999). A Power Algebra for Theory Change. Journal of Logic, Language and Information 8 (4):429-443.
  8. Eugenio Bulygin (2003). Review of Jaap Hage's Law and Defeasibility. [REVIEW] Artificial Intelligence and Law 11 (2-3):245-250.
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  9. Peter Clark (1990). Nonmonotonic Reasoning , Argumentation and Machine Learning 1 Introduction. Argumentation:1-11.
    Machine learning and nonmonotonic reasoning are closely related, both concerned with making plausible as well as certain inferences based on available data. In this document a brief overview of different approaches to nonmonotonic reasoning is presented, and it is shown how the concept of argumentation systems arises. The relationship with machine learning work is also discussed. The document aims to highlight the links between nonmonotonic reasoning, argumentation and machine learning and as a result propose some potentially useful directions for new (...)
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  10. Charles B. Cross (2004). A Correction to “Nonmonotonic Inconsistency” [Artificial Intelligence 149 (2003) 161–178]. Artificial Intelligence 160 (1-2):191-192.
    This note corrects an error in the statement and proof of Propositions 9 and 10 of [C. Cross, Nonmonotonic inconsistency, Artificial Intelligence 149 (2) (2003) 161–178]. Both results turn out to depend on the postulate of Consistency Preservation.
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  11. Charles B. Cross (2003). Nonmonotonic Inconsistency. Artificial Intelligence 149 (2):161-178.
    Nonmonotonic consequence is the subject of a vast literature, but the idea of a nonmonotonic counterpart of logical inconsistency—the idea of a defeasible property representing internal conflict of an inductive or evidential nature—has been entirely neglected. After considering and dismissing two possible analyses relating nonmonotonic consequence and a nonmonotonic counterpart of logical inconsistency, this paper offers a set of postulates for nonmonotonic inconsistency, an analysis of nonmonotonic inconsistency in terms of nonmonotonic consequence, and a series of results showing that nonmonotonic (...)
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  12. Charles B. Cross (1990). Belief Revision, Non-Monotonic Reasoning, and the Ramsey Test. In Kyburg Henry E., Loui Ronald P. & Carlson Greg N. (eds.), Knowledge Representation and Defeasible Reasoning. Kluwer 223--244.
    Peter Gärdenfors has proved (Philosophical Review, 1986) that the Ramsey rule and the methodologically conservative Preservation principle are incompatible given innocuous-looking background assumptions about belief revision. Gärdenfors gives up the Ramsey rule; I argue for preserving the Ramsey rule and interpret Gärdenfors's theorem as showing that no rational belief-reviser can avoid reasoning nonmonotonically. I argue against the Preservation principle and show that counterexamples to it always involve nonmonotonic reasoning. I then construct a new formal model of belief revision that does (...)
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  13. Todd R. Davies (1991). Knowledge Bases and Neural Network Synthesis. In Hozumi Tanaka (ed.), Artificial Intelligence in the Pacific Rim: Proceedings of the Pacific Rim International Conference on Artificial Intelligence. IOS Press, Inc. 717-722.
    We describe and try to motivate our project to build systems using both a knowledge based and a neural network approach. These two approaches are used at different stages in the solution of a problem, instead of using knowledge bases exclusively on some problems, and neural nets exclusively on others. The knowledge base (KB) is defined first in a declarative, symbolic language that is easy to use. It is then compiled into an efficient neural network (NN) representation, run, and the (...)
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  14. Jürgen Dix & David Makinson (1992). The Relationship Between KLM and MAK Models for Nonmonotonic Inference Operations. Journal of Logic, Language and Information 1 (2):131-140.
    The purpose of this note is to make quite clear the relationship between two variants of the general notion of a preferential model for nonmonotonic inference: the models of Kraus, Lehmann and Magidor (KLM models) and those of Makinson (MAK models).On the one hand, we introduce the notion of the core of a KLM model, which suffices to fully determine the associated nonmonotonic inference relation. On the other hand, we slightly amplify MAK models with a monotonic consequence operation as additional (...)
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  15. Tuan-Fang Fan, I. -Peng Lin & Churn-Jung Liau (1997). Nonmonotonic Reasoning Based on Incomplete Logic. Journal of Applied Non-Classical Logics 7 (4):375-395.
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  16. James Franklin (2013). Arguments Whose Strength Depends on Continuous Variation. Informal Logic 33 (1):33-56.
    Both the traditional Aristotelian and modern symbolic approaches to logic have seen logic in terms of discrete symbol processing. Yet there are several kinds of argument whose validity depends on some topological notion of continuous variation, which is not well captured by discrete symbols. Examples include extrapolation and slippery slope arguments, sorites, fuzzy logic, and those involving closeness of possible worlds. It is argued that the natural first attempts to analyze these notions and explain their relation to reasoning fail, so (...)
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  17. Michael Freund & Daniel Lehmann (1994). Nonmonotonic Reasoning: From Finitary Relations to Infinitary Inference Operations. Studia Logica 53 (2):161 - 201.
    A. Tarski [22] proposed the study of infinitary consequence operations as the central topic of mathematical logic. He considered monotonicity to be a property of all such operations. In this paper, we weaken the monotonicity requirement and consider more general operations, inference operations. These operations describe the nonmonotonic logics both humans and machines seem to be using when infering defeasible information from incomplete knowledge. We single out a number of interesting families of inference operations. This study of infinitary inference operations (...)
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  18. Konstantinos Georgatos (1997). Entrenchment Relations: A Uniform Approach to Nonmonotonic Inference. In D. Gabbay, R. Kruse, A. Nonnengart & H. J. Ohlbach (eds.), ESCQARU/FAPR 97. Springer 282--297.
    We show that Gabbay’s nonmonotonic consequence relations c an be reduced to a new family of relations, called entrenchment relations. Entrenchment relations provide a direct generalization of epistemic entrenchment and expectation ordering introduced by G ̈ardenfors and Makinson for the study of belief revision and expectation inference, respectively.
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  19. Konstantinos Georgatos (1996). Ordering-Based Representations of Rational Inference. In Jose Julio Alferes, Luis Moniz Pereira & Ewa Orlowska (eds.), JELIA 96. Springer 176-191.
    Rational inference relations were introduced by Lehmann and Magidor as the ideal systems for drawing conclusions from a conditional base. However, there has been no simple characterization of these relations, other than its original representation by preferential models. In this paper, we shall characterize them with a class of total preorders of formulas by improving and extending G ̈ardenfors and Makinson’s results f or expectation inference relations. A second representation is application-oriented and is obtained by considering a class of consequence (...)
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  20. Matthew Ginsberg (ed.) (1980). Readings in Nonmonotonic Reasoning. Morgan Kauffman.
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  21. Thomas F. Gordon (1995). The Pleadings Games: An Artificial Intelligence Model of Procedural Justice. Springer.
    The Pleadings Game is a major contribution to artificial intelligence and legal theory. The book draws on jurisprudence and moral philosophy to develop a formal model of argumentation called the pleadings game. From a technical perspective, the work can be viewed as an extension of recent argumentation-based approaches to non-monotonic logic: (1) the game is dialogical rather than mono-logical; (2) the validity and priority of defeasible rules is subject to debate; and (3) resource limitations are acknowledged by rules for fairly (...)
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  22. Jaap Hage (2003). Law and Defeasibility. Artificial Intelligence and Law 11 (2-3):221-243.
    The paper consists of three parts. In the first part five kinds of defeasibility are distinguished that is ontological, conceptual, epistemic, justification and logical defeasibility. In the second part it is argued that from these, justification defeat is the phenomenon that plays a role in legal reasoning. In the third part, the view is defended that non-monotonic logics are not necessary to model justification defeat, but that they are so to speak the natural way to model this phenomenon.
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  23. Jaap Hage (2000). Donald NUTE (Ed.), Defeasible Deontic Logic. Artificial Intelligence and Law 8 (1):75-91.
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  24. James Hawthorne (1998). On the Logic of Nonmonotonic Conditionals and Conditional Probabilities: Predicate Logic. [REVIEW] Journal of Philosophical Logic 27 (1):1-34.
    In a previous paper I described a range of nonmonotonic conditionals that behave like conditional probability functions at various levels of probabilistic support. These conditionals were defined as semantic relations on an object language for sentential logic. In this paper I extend the most prominent family of these conditionals to a language for predicate logic. My approach to quantifiers is closely related to Hartry Field's probabilistic semantics. Along the way I will show how Field's semantics differs from a substitutional interpretation (...)
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  25. James Hawthorne (1996). On the Logic of Nonmonotonic Conditionals and Conditional Probabilities. Journal of Philosophical Logic 25 (2):185-218.
    I will describe the logics of a range of conditionals that behave like conditional probabilities at various levels of probabilistic support. Families of these conditionals will be characterized in terms of the rules that their members obey. I will show that for each conditional, →, in a given family, there is a probabilistic support level r and a conditional probability function P such that, for all sentences C and B, 'C → B' holds just in case P[B | C] ≥ (...)
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  26. James Hawthorne (1988). A Semantic Approach to Non-Monotonic Conditionals. In J. F. Lemmer & L. N. Kanal (eds.), Uncertainty in Artificial Intelligence 2. Elsevier
    Any inferential system in which the addition of new premises can lead to the retraction of previous conclusions is a non-monotonic logic. Classical conditional probability provides the oldest and most widely respected example of non-monotonic inference. This paper presents a semantic theory for a unified approach to qualitative and quantitative non-monotonic logic. The qualitative logic is unlike most other non- monotonic logics developed for AI systems. It is closely related to classical (i.e., Bayesian) probability theory. The semantic theory for qualitative (...)
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  27. James Hawthorne & David Makinson (2007). The Quantitative/Qualitative Watershed for Rules of Uncertain Inference. Studia Logica 86 (2):247-297.
    We chart the ways in which closure properties of consequence relations for uncertain inference take on different forms according to whether the relations are generated in a quantitative or a qualitative manner. Among the main themes are: the identification of watershed conditions between probabilistically and qualitatively sound rules; failsafe and classicality transforms of qualitatively sound rules; non-Horn conditions satisfied by probabilistic consequence; representation and completeness problems; and threshold-sensitive conditions such as ‘preface’ and ‘lottery’ rules.
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  28. Kyburg Henry E., Loui Ronald P. & Carlson Greg N. (eds.) (1990). Knowledge Representation and Defeasible Reasoning. Kluwer.
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  29. John F. Horty (2001). Argument Construction and Reinstatement in Logics for Defeasible Reasoning. Artificial Intelligence and Law 9 (1):1-28.
    This paper points out some problems with two recent logical systems – one due to Prakken and Sartor, the other due to Kowalski and Toni – designedfor the representation of defeasible arguments in general, but with a specialemphasis on legal reasoning.
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  30. John F. Horty (1994). Moral Dilemmas and Nonmonotonic Logic. Journal of Philosophical Logic 23 (1):35 - 65.
    From a philosophical standpoint, the work presented here is based on van Fraassen [26]. The bulk of that paper is organized around a series of arguments against the assumption, built into standard deontic logic, that moral dilemmas are impossible; and van Fraassen only briefly sketches his alternative approach. His paper ends with the conclusion that “the problem of possibly irresolvable moral conflict reveals serious flaws in the philosophical and semantic foundations of ‘orthodox’ deontic logic, but also suggests a rich set (...)
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  31. Hykel Hosni (2006). Makinson David. Bridges From Classical to Nonmonotonic Logic. Text in Computing, Vol. 5. King's College, London, 2005, Xvi+ 216 Pp. [REVIEW] Bulletin of Symbolic Logic 12 (3):499-502.
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  32. William M. Keith & David E. Beard (2008). Toulmin's Rhetorical Logic: What's the Warrant for Warrants? Philosophy and Rhetoric 41 (1):22-50.
  33. David Elden Leasure (1993). The Modal Logic Z Applied to Lifschitz's Benchmark Problems for Formal Nonmonotonic Reasoning. Dissertation, University of Kansas
    To give a standard against which to judge the limitations and possibilities of a theory of nonmonotonic reasoning, V. Lifschitz presented a paper at the 1988 Second International Workshop on Non-Monotonic Reasoning entitled "Benchmark Problems for Formal Nonmonotonic Reasoning." We show in this work the application of the modal logic Z to these benchmark problems. The modal logic Z provides a consistency-based approach to nonmonotonic reasoning. Z is a fragment of second order modal quantificational logic involving quantification over propositions but (...)
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  34. Joohyung Lee, Vladimir Lifschitz & Hudson Turner, Nonmonotonic Causal Theories.
    cuted actions. It has been applied to several challenge problems in the theory of commonsense knowledge. We study the relationship between this formalism and other work on nonmonotonic reasoning and knowl-.
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  35. David Makinson (2009). Levels of Belief in Nonmonotonic Reasoning. In Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of Belief. Springer 341--354.
  36. David Makinson (2005). Bridges From Classical to Nonmonotonic Logic. King's College Publications.
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  37. David Makinson (1994). General Patterns in Nonmonotonic Reasoning. In Handbook of Logic in Artificial Intelligence Nad Logic Programming, Vol. Iii. Clarendon Press
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  38. David C. Makinson, Propositional Relevance Through Letter-Sharing: Review and Contribution.
    The concept of relevance between classical propositional formulae, defined in terms of letter-sharing, has been around for a very long time. But it began to take on a fresh life in 1999 when it was reconsidered in the context of the logic of belief change. Two new ideas appeared in independent work of Odinaldo Rodrigues and Rohit Parikh. First, the relation of relevance was considered modulo the belief set under consideration, Second, the belief set was put in a canonical form, (...)
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  39. David Makinson & Peter Gärdenfors (1991). Relations Between the Logic of Theory Change and Nonmonotonic Logic. In André Fuhrmann & Michael Morreau (eds.), The Logic of Theory Change. Springer 183--205.
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  40. John McCarthy (1986). Applications of Circumscription to Formalizing Common Sense Knowledge. Artificial Intelligence 28:89–116.
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  41. John McCarthy (1980). Circumscription — A Form of Non-Monotonic Reasoning. Artificial Intelligence 13:27–39.
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  42. Masaharu Mizumoto (2011). A Theory of Knowledge and Belief Change - Formal and Experimental Perspectives. Hokkaido University Press.
    This work explores the conceptual and empirical issues of the concept of knowledge and its relation to the pattern of our belief change, from formal and experimental perspectives. Part I gives an analysis of knowledge (called Sustainability) that is formally represented and naturalistically plausible at the same time, which is claimed to be a synthesized view of knowledge, covering not only empirical knowledge, but also knowledge of future, practical knowledge, mathematical knowledge, knowledge of general facts. Part II tries to formalize (...)
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  43. Robert C. Moore (1985). Semantic Considerations on Nonmonotonic Logic. Artificial Intelligence 25:75-94.
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  44. Aleksander Peczenik (1996). Jumps and Logic in the Law. Artificial Intelligence and Law 4 (3-4):297-329.
    The main stream of legal theory tends to incorporate unwritten principles into the law. Weighing of principles plays a great role in legal argumentation, inter alia in statutory interpretation. A weighing and balancing of principles and other prima facie reasons is a jump. The inference is not conclusive.To deal with defeasibility and weighing, a jurist needs both the belief-revision logic and the nonmonotonic logic. The systems of nonmonotonic logic included in the present volume provide logical tools enabling one to speak (...)
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  45. Niki Pfeifer & G. D. Kleiter (2006). Is Human Reasoning About Nonmonotonic Conditionals Probabilistically Coherent? In Proceedings of the 7 T H Workshop on Uncertainty Processing. 138--150.
    Nonmonotonic conditionals (A |∼ B) are formalizations of common sense expressions of the form “if A, normally B”. The nonmonotonic conditional is interpreted by a “high” coherent conditional probability, P(B|A) > .5. Two important properties are closely related to the nonmonotonic conditional: First, A |∼ B allows for exceptions. Second, the rules of the nonmonotonic system p guiding A |∼ B allow for withdrawing conclusions in the light of new premises. This study reports a series of three experiments on reasoning (...)
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  46. Niki Pfeifer & Gernot D. Kleiter (2005). Coherence and Nonmonotonicity in Human Reasoning. Synthese 146 (1-2):93 - 109.
    Nonmonotonic reasoning is often claimed to mimic human common sense reasoning. Only a few studies, though, have investigated this claim empirically. We report four experiments which investigate three rules of SYSTEMP, namely the AND, the LEFT LOGICAL EQUIVALENCE, and the OR rule. The actual inferences of the subjects are compared with the coherent normative upper and lower probability bounds derived from a non-infinitesimal probability semantics of SYSTEM P. We found a relatively good agreement of human reasoning and principles of nonmonotonic (...)
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  47. Gilbert Plumer & Kenneth Olson (2007). Reasoning From Conflicting Sources. In Hans V. Hansen, Christopher W. Tindale, J. Anthony Blair, Ralph H. Johnson & David M. Godden (eds.), Dissensus and the Search for Common Ground. Proceedings 2007 [CD-ROM]. Ontario Society for the Study of Argumentation 1-9.
    One might ask of two or more texts—what can be inferred from them, taken together? If the texts happen to contradict each other in some respect, then the unadorned answer of standard logic is EVERYTHING. But it seems to be a given that we often successfully reason with inconsistent information from multiple sources. The purpose of this paper is to attempt to develop an adequate approach to accounting for this given.
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  48. John Pollock, Oscar: An Agent Architecture Based on Defeasible Reasoning.
    Proceedings of the 2008 AAAI Spring Symposium on Architectures for Intelligent Theory-Based Agents. “OSCAR is a fully implemented architecture for a cognitive agent, based largely on the author’s work in philosophy concerning epistemology and practical cognition. The seminal idea is that a generally intelligent agent must be able to function in an environment in which it is ignorant of most matters of fact. The architecture incorporates a general-purpose defeasible reasoner, built on top of an efficient natural deduction reasoner for first-order (...)
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  49. Giuseppe Primiero (2012). A Contextual Type Theory with Judgemental Modalities for Reasoning From Open Assumptions. Logique and Analyse 220:579-600.
    Contextual type theories are largely explored in their applications to programming languages, but less investigated for knowledge representation purposes. The combination of a constructive language with a modal extension of contexts appears crucial to explore the attractive idea of a type-theoretical calculus of provability from refutable assumptions for non-monotonic reasoning. This paper introduces such a language: the modal operators are meant to internalize two different modes of correctness, respectively with necessity as the standard notion of constructive verification and possibility as (...)
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  50. Hans Rott (2011). Odd Choices: On the Rationality of Some Alleged Anomalies of Decision and Inference. Topoi 30 (1):59-69.
    This paper presents a number of apparent anomalies in rational choice scenarios, and their translation into the logic of everyday reasoning. Three classes of examples that have been discussed in the context of probabilistic choice since the 1960s (by Debreu, Tversky and others) are analyzed in a non-probabilistic setting. It is shown how they can at the same time be regarded as logical problems that concern the drawing of defeasible inferences from a given information base. I argue that initial appearances (...)
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