Results for 'non-monotonic inference'

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  1.  22
    Relevance Sensitive Non-Monotonic Inference on Belief Sequences.Samir Chopra, Konstantinos Georgatos & Rohit Parikh - 2001 - Journal of Applied Non-Classical Logics 11 (1-2):131-150.
    We present a method for relevance sensitive non-monotonic inference from belief sequences which incorporates insights pertaining to prioritized inference and relevance sensitive, inconsistency tolerant belief revision. Our model uses a finite, logically open sequence of propositional formulas as a representation for beliefs and defines a notion of inference from maxiconsistent subsets of formulas guided by two orderings: a temporal sequencing and an ordering based on relevance relations between the putative conclusion and formulas in the sequence. The (...)
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  2.  44
    Non-Monotonic Inference.Keith Frankish - 2005 - In Alex Barber (ed.), Encyclopedia of Language and Linguistics. Elsevier.
    In most logical systems, inferences cannot be invalidated simply by the addition of new premises. If an inference can be drawn from a set of premises S, then it can also be drawn from any larger set incorporrating S. The truth of the original premises guarantees the truth of the inferred conclusion, and the addition of extra premises cannot undermine it. This property is known as monotonicity. Nonmonotonic inference lacks this property. The conclusions drawn are provisional, and new (...)
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  3.  23
    Modelling Inference in Argumentation Through Labelled Deduction: Formalization and Logical Properties. [REVIEW]Carlos Iván Chesñevar & Guillermo Ricardo Simari - 2007 - Logica Universalis 1 (1):93-124.
    . Artificial Intelligence (AI) has long dealt with the issue of finding a suitable formalization for commonsense reasoning. Defeasible argumentation has proven to be a successful approach in many respects, proving to be a confluence point for many alternative logical frameworks. Different formalisms have been developed, most of them sharing the common notions of argument and warrant. In defeasible argumentation, an argument is a tentative (defeasible) proof for reaching a conclusion. An argument is warranted when it ultimately prevails over other (...)
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  4.  1
    Modelling Reasoning Processes in Natural Agents: A Partial-Worlds-Based Logical Framework for Elemental Non-Monotonic Inferences and Learning.Christel Grimaud - 2016 - Journal of Applied Non-Classical Logics 26 (4):251-285.
    In this paper we address the modelling of reasoning processes in natural agents. We focus on a very basic kind of non-monotonic inference for which we identify a simple and plausible underlying process, and we develop a family of logical models that allow to match this process. Partial worlds models, as we call them, are a variant of Kraus, Lehmann and Magidor’s cumulative models. We show that the inference relations they induce form a strict subclass of cumulative (...)
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  5.  43
    A Semantic Approach to Non-Monotonic Conditionals.James Hawthorne - 1988 - 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 (...)
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  6.  51
    Why Non-Monotonic Logic is Inadequate to Represent Balancing Arguments.Jan-R. Sieckmann - 2003 - Artificial Intelligence and Law 11 (2-3):211-219.
    This paper analyses the logical structure of the balancing of conflicting normative arguments, and asks whether non-monotonic logic is adequate to represent this type of legal or practical reasoning. Norm conflicts are often regarded as a field of application for non-monotonic logics. This paper argues, however, that the balancing of normative arguments consists of an act of judgement, not a logical inference, and that models of deductive as well as of defeasible reasoning do not give an adequate (...)
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  7.  18
    The Gärdenfors Impossibility Theorem in Non-Monotonic Contexts.David Makinson - 1990 - Studia Logica 49 (1):1 - 6.
    Gärdenfors' impossibility theorem draws attention to certain formal difficulties in defining a conditional connective from a notion of theory revision, via the Ramsey test. We show that these difficulties are not avoided by taking the background inference operation to be non-monotonic.
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  8.  60
    Non-Monotonic Logic.G. Aldo Antonelli - 2008 - 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 (...)
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  9.  29
    Non-Prioritized Ranked Belief Change.Samir Chopra, Aditya Ghose & Thomas Meyer - 2003 - Journal of Philosophical Logic 32 (4):417-443.
    Traditional accounts of belief change have been criticized for placing undue emphasis on the new belief provided as input. A recent proposal to address such issues is a framework for non-prioritized belief change based on default theories (Ghose and Goebel, 1998). A novel feature of this approach is the introduction of disbeliefs alongside beliefs which allows for a view of belief contraction as independently useful, instead of just being seen as an intermediate step in the process of belief revision. This (...)
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  10.  26
    Qualitative Probabilistic Inference Under Varied Entropy Levels.Paul D. Thorn & Gerhard Schurz - 2016 - Journal of Applied Logic 19 (2):87-101.
    In previous work, we studied four well known systems of qualitative probabilistic inference, and presented data from computer simulations in an attempt to illustrate the performance of the systems. These simulations evaluated the four systems in terms of their tendency to license inference to accurate and informative conclusions, given incomplete information about a randomly selected probability distribution. In our earlier work, the procedure used in generating the unknown probability distribution (representing the true stochastic state of the world) tended (...)
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  11.  40
    Odd Choices: On the Rationality of Some Alleged Anomalies of Decision and Inference.Hans Rott - 2011 - 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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  12.  60
    Adams Conditionals and Non-Monotonic Probabilities.Richard Bradley - 2006 - Journal of Logic, Language and Information 15 (1-2):65-81.
    Adams' famous thesis that the probabilities of conditionals are conditional probabilities is incompatible with standard probability theory. Indeed it is incompatible with any system of monotonic conditional probability satisfying the usual multiplication rule for conditional probabilities. This paper explores the possibility of accommodating Adams' thesis in systems of non-monotonic probability of varying strength. It shows that such systems impose many familiar lattice theoretic properties on their models as well as yielding interesting logics of conditionals, but that a standard complementation (...)
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  13.  93
    Non-Monotonic Probability Theory for N-State Quantum Systems.Fred Kronz - 2008 - Studies in History and Philosophy of Science Part B 39 (2):259-272.
    In previous work, a non-standard theory of probability was formulated and used to systematize interference effects involving the simplest type of quantum systems. The main result here is a self-contained, non-trivial generalization of that theory to capture interference effects involving a much broader range of quantum systems. The discussion also focuses on interpretive matters having to do with the actual/virtual distinction, non-locality, and conditional probabilities.
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  14.  83
    Précis of Bayesian Rationality: The Probabilistic Approach to Human Reasoning.Mike Oaksford & Nick Chater - 2009 - Behavioral and Brain Sciences 32 (1):69-84.
    According to Aristotle, humans are the rational animal. The borderline between rationality and irrationality is fundamental to many aspects of human life including the law, mental health, and language interpretation. But what is it to be rational? One answer, deeply embedded in the Western intellectual tradition since ancient Greece, is that rationality concerns reasoning according to the rules of logic – the formal theory that specifies the inferential connections that hold with certainty between propositions. Piaget viewed logical reasoning as defining (...)
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  15.  24
    Non-Monotonic Set Theory as a Pragmatic Foundation of Mathematics.Peter Verdée - 2013 - Foundations of Science 18 (4):655-680.
    In this paper I propose a new approach to the foundation of mathematics: non-monotonic set theory. I present two completely different methods to develop set theories based on adaptive logics. For both theories there is a finitistic non-triviality proof and both theories contain (a subtle version of) the comprehension axiom schema. The first theory contains only a maximal selection of instances of the comprehension schema that do not lead to inconsistencies. The second allows for all the instances, also the (...)
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  16.  29
    Non-Adjunctive Inference and Classical Modalities.Costa Horacio Arló - 2004 - Journal of Philosophical Logic 34 (5/6):581 - 605.
    The article focuses on representing different forms of non-adjunctive inference as sub-Kripkean systems of classical modal logic, where the inference from □A and □B to □A ∧ B fails. In particular we prove a completeness result showing that the modal system that Schotch and Jennings derive from a form of non-adjunctive inference in (Schotch and Jennings, 1980) is a classical system strictly stronger than EMN and weaker than K (following the notation for classical modalities presented in Chellas, (...)
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  17.  53
    Lakatos's Challenge? Auxiliary Hypotheses and Non-Monotonous Inference.Frank Zenker - 2006 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 37 (2):405 - 415.
    Gerhard Schurz [2001, Journal for General Philosophy of Science, 32, 65-107] has proposed to reconstruct auxiliary hypothesis addition, e.g., postulation of Neptune to immunize Newtonian mechanics, with concepts from non-monotonous inference to avoid the retention of false predictions that are among the consequence-set of the deductive model. However, the non-monotonous reconstruction retains the observational premise that is indeed rejected in the deductive model. Hence, his proposal fails to do justice to Lakatos' core-belt model, therefore fails to meet what Schurz (...)
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  18.  84
    Conditionals in Reasoning.John Cantwell - 2009 - Synthese 171 (1):47 - 75.
    The paper presents a non-monotonic inference relation on a language containing a conditional that satisfies the Ramsey Test. The logic is a weakening of classical logic and preserves many of the ‘paradoxes of implication’ associated with the material implication. It is argued, however, that once one makes the proper distinction between supposing that something is the case and accepting that it is the case, these ‘paradoxes’ cease to be counterintuitive. A representation theorem is provided where conditionals are given (...)
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  19.  5
    Non Monotonic Reasoning and Belief Revision: Syntactic, Semantic, Foundational and Coherence Approaches.Alvaro del Val - 1997 - Journal of Applied Non-Classical Logics 7 (1-2):213-240.
    ABSTRACT The major approaches to belief revision and non monotonic reasoning proposed in the literature differ along a number of dimensions, including whether they are ?syntax- based? or ?semantic-based?, ?foundational? or ?coherentist?, ?consistence-restoring? or ?inconsistency-tolerant?. Our contribution towards clarifying the connections between these various approaches is threefold: ?We show that the two main approaches to belief revision, the foundations and coherence theories, are mathematically equivalent, thus answering a question left open in [Gar90, Doy92], The distinction between syntax-based approaches to revision (...)
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  20.  12
    Modal Logic Based Theory for Non-Monotonic Reasoning.Pierre Siegel & Camilla Schwind - 1993 - Journal of Applied Non-Classical Logics 3 (1):73-92.
    ABSTRACT This paper defines a new modal logic based theory for non-monotonic reasoning. This logic expresses notions about hypotheses and known information. These notions are defined in the framework of the modal system τ. A translation of default logic in terms of hypothesis theory is given with which it is possible to fully characterize default logic by giving a necessary and sufficient criterion for the existence and the non-existence of extensions. Moreover several problems relating to non-monotonic reasoning are (...)
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  21. The Discovery/Justification Context Dichotomy Within Formal and Computational Models of Scientific Theories: A Weakening of the Distinction Based on the Perspective of Non-Monotonic Logics.Jorge A. Morales & Mauricio Molina Delgado - 2016 - Journal of Applied Non-Classical Logics 26 (4):315-335.
    The present paper analyses the topic of scientific discovery and the problem of the existence of a logical framework involved in such endeavour. We inquire how several non-monotonic logic frameworks and other formalisms can account for such a task. In the same vein, we analyse some key aspects of the historical and theoretical debate surrounding scientific discovery, in particular, the context of discovery and context of justification context distinction. We present an argument concerning the weakening of the discovery/justification context (...)
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  22.  75
    Conditional Probability and Defeasible Inference.Rohit Parikh - 2005 - Journal of Philosophical Logic 34 (1):97 - 119.
    We offer a probabilistic model of rational consequence relations (Lehmann and Magidor, 1990) by appealing to the extension of the classical Ramsey-Adams test proposed by Vann McGee in (McGee, 1994). Previous and influential models of nonmonotonic consequence relations have been produced in terms of the dynamics of expectations (Gärdenfors and Makinson, 1994; Gärdenfors, 1993).'Expectation' is a term of art in these models, which should not be confused with the notion of expected utility. The expectations of an agent are some form (...)
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  23.  66
    Non-Monotonic Probability Theory and Photon Polarization.Fred Kronz - 2007 - Journal of Philosophical Logic 36 (4):449-472.
    A non-monotonic theory of probability is put forward and shown to have applicability in the quantum domain. It is obtained simply by replacing Kolmogorov's positivity axiom, which places the lower bound for probabilities at zero, with an axiom that reduces that lower bound to minus one. Kolmogorov's theory of probability is monotonic, meaning that the probability of A is less then or equal to that of B whenever A entails B. The new theory violates monotonicity, as its name suggests; (...)
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  24.  43
    Many-Valued Non-Monotonic Modal Logics.Melvin Fitting - unknown
    Among non-monotonic systems of reasoning, non-monotonic modal logics, and autoepistemic logic in particular, have had considerable success. The presence of explicit modal operators allows flexibility in the embedding of other approaches. Also several theoretical results of interest have been established concerning these logics. In this paper we introduce non-monotonic modal logics based on many-valued logics, rather than on classical logic. This extends earlier work of ours on many-valued modal logics. Intended applications are to situations involving several reasoners, (...)
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  25.  5
    Monotonic and Non-Monotonic Embeddings of Anselm’s Proof.Archambault Jacob - 2017 - Logica Universalis 11 (1):121-138.
    A consequence relation \ is monotonic iff for premise sets \ and conclusion \, if \, \, then \; and non-monotonic if this fails in some instance. More plainly, a consequence relation is monotonic when whatever is entailed by a premise set remains entailed by any of its supersets. From the High Middle Ages through the Early Modern period, consequence in theology is assumed to be monotonic. Concomitantly, to the degree the argument formulated by Anselm at Proslogion 2–4 is (...)
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  26.  7
    Reasoning Biases, Non‐Monotonic Logics and Belief Revision.Catarina Dutilh Novaes & Herman Veluwenkamp - 2017 - Theoria 83 (1):29-52.
    A range of formal models of human reasoning have been proposed in a number of fields such as philosophy, logic, artificial intelligence, computer science, psychology, cognitive science, etc.: various logics, probabilistic systems, belief revision systems, neural networks, among others. Now, it seems reasonable to require that formal models of human reasoning be empirically adequate if they are to be viewed as models of the phenomena in question. How are formal models of human reasoning typically put to empirical test? One way (...)
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  27.  48
    Why Friedman's Non-Monotonic Reasoning Defies Hempel's Covering Law Model.M. C. W. Janssen & Y. -H. Tan - 1991 - Synthese 86 (2):255 - 284.
    In this paper we will show that Hempel's covering law model can't deal very well with explanations that are based on incomplete knowledge. In particular the symmetry thesis, which is an important aspect of the covering law model, turns out to be problematic for these explanations. We will discuss an example of an electric circuit, which clearly indicates that the symmetry of explanation and prediction does not always hold. It will be argued that an alternative logic for causal explanation is (...)
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  28.  4
    Reasoning Biases, Non‐Monotonic Logics and Belief Revision.Catarina Dutilh Novaes & Herman Veluwenkamp - 2016 - Theoria 82 (4).
    A range of formal models of human reasoning have been proposed in a number of fields such as philosophy, logic, artificial intelligence, computer science, psychology, cognitive science, etc.: various logics, probabilistic systems, belief revision systems, neural networks, among others. Now, it seems reasonable to require that formal models of human reasoning be empirically adequate if they are to be viewed as models of the phenomena in question. How are formal models of human reasoning typically put to empirical test? One way (...)
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  29.  7
    A Non-Monotonic Intensional Framework for Framing Effects.Silvia Lerner - 2014 - Journal of Economic Methodology 21 (1):37-53.
    Expected Utility Theory (EUT) has anomalies when interpreted descriptively and tested empirically. Experiments show that the way in which options are formulated is, in most cases, relevant for decision-making. This kind of anomaly is directly related, however, not with a proper axiom of EUT but rather with the logical principle of extensionality and its decision theoretic version: the principle of invariance. This paper focuses on the phenomenon of framing effects (FE) and the associated failures of invariance. FE arise when different (...)
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  30.  1
    Lakatos’s Challenge? Auxiliary Hypotheses and Non-Monotonous Inference.Frank Zenker - 2006 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 37 (2):405-415.
    Gerhard Schurz [2001, Journal for General Philosophy of Science, 32, 65-107] has proposed to reconstruct auxiliary hypothesis addition, e.g., postulation of Neptune to immunize Newtonian mechanics, with concepts from non-monotonous inference to avoid the retention of false predictions that are among the consequence-set of the deductive model. However, the non-monotonous reconstruction retains the observational premise that is indeed rejected in the deductive model. Hence, his proposal fails to do justice to Lakatos' core-belt model, therefore fails to meet what Schurz (...)
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  31. Why Friedman's Non-Monotonic Reasoning Defies Hempel's Covering Law Model.M. C. W. Janssen & Y. Tan - 1991 - Synthese 86 (2):255-284.
    In this paper we will show that Hempel's covering law model can't deal very well with explanations that are based on incomplete knowledge. In particular the symmetry thesis, which is an important aspect of the covering law model, turns out to be problematic for these explanations. We will discuss an example of an electric circuit, which clearly indicates that the symmetry of explanation and prediction does not always hold. It will be argued that an alternative logic for causal explanation is (...)
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  32. An Axiomatic Treatment of Non-Monotonic Arguments.Ryszard Wojcicki - 1988 - Bulletin of the Section of Logic 17 (2):56-61.
    An axiomatic theory of non-monotonic consequence relations patterned upon some finitistic ideas going back to Gentzen was suggested by Gabbay [1985]. 1 More recently, an infinitistic approach patterned upon Tarski’s theory of consequence operation was examined by Makinson [l98.]. We compare the two approaches and examine them vis-`a-vis some intuitive adequacy conditions. An enlarged version of this note will appear in Studia Logica , in particular the reader is referred to it for the proofs of the results stated here.
     
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  33.  3
    Paraconsistent Conjectural Deduction Based on Logical Entropy Measures I: C-Systems as Non-Standard Inference Framework.Paola Forcheri & Paolo Gentilini - 2005 - Journal of Applied Non-Classical Logics 15 (3):285-319.
  34.  10
    Non Monotonic Reasoning and Belief Revision: Syntactic, Semantic, Foundational and Coherence Approaches.Alvaro Del Val - 1997 - Journal of Applied Non-Classical Logics 7 (1-2):213-240.
  35. An Intuitionistic Basis for Non-Monotonic Reasoning.M. R. B. Clarke & Dov M. Gabbay - 1988 - In Philippe Smets (ed.), Non-Standard Logics for Automated Reasoning. Academic Press.
     
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  36.  10
    Default Reasoning as Situated Monotonic Inference.Lawrence Cavedon - 1998 - Minds and Machines 8 (4):509-531.
    Since its inception, situation theory has been concerned with the situated nature of meaning and cognition, a theme which has also recently gained some prominence in Artificial Intelligence. Channel theory is a recently developed framework which builds on concepts introduced in situation theory, in an attempt to provide a general theory of information flow. In particular, the channel theoretic framework offers an account of fallible regularities, regularities which provide enough structure to an agent's environment to support efficient cognitive processing but (...)
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  37.  9
    Algebraic Semantics for Modal and Superintuitionistic Non-Monotonic Logics.David Pearce & Levan Uridia - 2013 - Journal of Applied Non-Classical Logics 23 (1-2):147-158.
  38. The Preferential-Models Approach to Non-Monotonic Logics.Philippe Besnard & Pierre Siegel - 1988 - In Philippe Smets (ed.), Non-Standard Logics for Automated Reasoning. Academic Press. pp. 137--161.
     
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  39. Circumscription — A Form of Non-Monotonic Reasoning.John McCarthy - 1980 - Artificial Intelligence 13:27–39.
     
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  40.  12
    When Can Non-Commutative Statistical Inference Be Bayesian?Miklós Rédei - 1992 - International Studies in the Philosophy of Science 6 (2):129 – 132.
    Based on recalling two characteristic features of Bayesian statistical inference in commutative probability theory, a stability property of the inference is pointed out, and it is argued that that stability of the Bayesian statistical inference is an essential property which must be preserved under generalization of Bayesian inference to the non-commutative case. Mathematical no-go theorems are recalled then which show that, in general, the stability can not be preserved in non-commutative context. Two possible interpretations of the (...)
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  41.  7
    When Can Non‐Commutative Statistical Inference Be Bayesian?Miklós Rédei - 1992 - International Studies in the Philosophy of Science 6 (2):129-132.
    Abstract Based on recalling two characteristic features of Bayesian statistical inference in commutative probability theory, a stability property of the inference is pointed out, and it is argued that that stability of the Bayesian statistical inference is an essential property which must be preserved under generalization of Bayesian inference to the non?commutative case. Mathematical no?go theorems are recalled then which show that, in general, the stability can not be preserved in non?commutative context. Two possible interpretations of (...)
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  42.  35
    Pragmatic Meaning and Non-Monotonic Reasoning: The Case of Exhaustive Interpretation.Schulz Katrin & Rooij Robert van - 2006 - Linguistics and Philosophy 29 (2):205 - 250.
    In this paper an approach to the exhaustive interpretation of answers is developed. It builds on a proposal brought forward by Groenendijk and Stokhof (1984). We will use the close connection between their approach and McCarthy's (1980, 1986) predicate circumscription and describe exhaustive interpretation as an instance of interpretation in minimal models, well-known from work on counterfactuals (see for instance Lewis (1973)). It is shown that by combining this approach with independent developments in semantics/pragmatics one can overcome certain limitations of (...)
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  43.  37
    Non-Monotonic Reasoning From an Evolution-Theoretic Perspective: Ontic, Logical and Cognitive Foundations.Gerhard Schurz - 2005 - Synthese 146 (1-2):37-51.
    In the first part I argue that normic laws are the phenomenological laws of evolutionary systems. If this is true, then intuitive human reasoning should be fit in reasoning from normic laws. In the second part I show that system P is a tool for reasoning with normic laws which satisfies two important evolutionary standards: it is probabilistically reliable, and it has rules of low complexity. In the third part I finally report results of an experimental study which demonstrate that (...)
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  44.  26
    Non-Bayesian Inference: Causal Structure Trumps Correlation.Bénédicte Bes, Steven Sloman, Christopher G. Lucas & Éric Raufaste - 2012 - Cognitive Science 36 (7):1178-1203.
    The study tests the hypothesis that conditional probability judgments can be influenced by causal links between the target event and the evidence even when the statistical relations among variables are held constant. Three experiments varied the causal structure relating three variables and found that (a) the target event was perceived as more probable when it was linked to evidence by a causal chain than when both variables shared a common cause; (b) predictive chains in which evidence is a cause of (...)
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  45.  30
    Cartographic Systems and Non-Linguistic Inference.Mariela Aguilera - 2016 - Philosophical Psychology 29 (3):349-364.
    It is often assumed that the capability to make inferences requires language. Against this assumption, I claim that inferential abilities do not necessarily require a language. On the contrary, certain cartographic systems could be used to explain some forms of inferences, and they are capable of warranting rational relations between contents they represent. By arguing that certain maps, as well as sentences, are adequate for inferential processes, I do not mean to neglect that there are important differences between maps and (...)
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  46.  35
    Non-Monotonic NPI-Licensing, Definite Descriptions, and Grammaticalized Implicatures.Daniel Rothschild - manuscript
    A downward-entailing context has the property that the replacement of the predicate in the context by a stronger predicate preserves truth. So, for instance, presuppositions aside, the context after “every” in (1) where the NPI “ever” appears is downward entailing.
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  47.  37
    Ancient Indian Logic as a Theory of Non-Monotonic Reasoning.Claus Oetke - 1996 - Journal of Indian Philosophy 24 (5):447-539.
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  48.  13
    Wellfoundedness Proofs by Means of Non-Monotonic Inductive Definitions I: Π₂⁰-Operators.Toshiyasu Arai - 2004 - Journal of Symbolic Logic 69 (3):830-850.
    In this paper, we prove the wellfoundedness of recursive notation systems for reflecting ordinals up to Π₃-reflection by relevant inductive definitions.
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  49.  6
    Wellfoundedness Proofs by Means of Non-Monotonic Inductive Definitions II: First Order Operators.Toshiyasu Arai - 2010 - Annals of Pure and Applied Logic 162 (2):107-143.
  50.  35
    Self-Reference and Incompleteness in a Non-Monotonic Setting.Timothy G. Mccarthy - 1994 - Journal of Philosophical Logic 23 (4):423 - 449.
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