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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. 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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  4. K. Britz (1999). A Power Algebra for Theory Change. Journal of Logic, Language and Information 8 (4):429-443.
    Various representation results have been established for logics of belief revision, in terms of remainder sets, epistemic entrenchment, systems of spheres and so on. In this paper I present another representation for logics of belief revision, as an algebra of theories. I show that an algebra of theories, enriched with a set of rejection operations, provides a suitable algebraic framework to characterize the theory change operations of systems of belief revision. The theory change operations arise as power operations of the (...)
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  5. 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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  6. 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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  7. 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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  8. 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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  9. 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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  10. 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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  11. 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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  12. 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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  13. Jaap Hage (2000). Donald NUTE (Ed.), Defeasible Deontic Logic. Artificial Intelligence and Law 8 (1):75-91.
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  14. 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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  15. 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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  16. 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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  17. 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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  18. 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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  19. 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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  20. William M. Keith & David E. Beard (2008). Toulmin's Rhetorical Logic: What's the Warrant for Warrants? Philosophy and Rhetoric 41 (1):22-50.
  21. David Makinson (2005). Bridges From Classical to Nonmonotonic Logic. King's College Publications.
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  22. 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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  23. John McCarthy (1986). Applications of Circumscription to Formalizing Common Sense Knowledge. Artificial Intelligence 28:89–116.
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  24. John McCarthy (1980). Circumscription — A Form of Non-Monotonic Reasoning. Artificial Intelligence 13:27–39.
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  25. 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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  26. Robert C. Moore (1985). Semantic Considerations on Nonmonotonic Logic. Artificial Intelligence 25:75-94.
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  27. 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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  28. 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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  29. 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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  30. 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.
    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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  31. 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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  32. 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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  33. 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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  34. Hans Rott (1989). Conditionals and Theory Change: Revisions, Expansions, and Additions. [REVIEW] Synthese 81 (1):91-113.
    This paper dwells upon formal models of changes of beliefs, or theories, which are expressed in languages containing a binary conditional connective. After defining the basic concept of a (non-trivial) belief revision model. I present a simple proof of Gärdenfors''s (1986) triviality theorem. I claim that on a proper understanding of this theorem we must give up the thesis that consistent revisions (additions) are to be equated with logical expansions. If negated or might conditionals are interpreted on the basis of (...)
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  35. Gerhard Schurz & Paul D. Thorn (2012). REWARD VERSUS RISK IN UNCERTAIN INFERENCE: THEOREMS AND SIMULATIONS. Review of Symbolic Logic 5 (4):574-612.
    Systems of logico-probabilistic (LP) reasoning characterize inference from conditional assertions that express high conditional probabilities. In this paper we investigate four prominent LP systems, the systems O, P, Z, and QC. These systems differ in the number of inferences they licence (O ⊂ P ⊂ Z ⊂ QC). LP systems that license more inferences enjoy the possible reward of deriving more true and informative conclusions, but with this possible reward comes the risk of drawing more false or uninformative conclusions. In (...)
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  36. Jan-R. Sieckmann (2003). Why Non-Monotonic Logic is Inadequate to Represent Balancing Arguments. 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 account of its (...)
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  37. Arnold Silverberg (1996). Psychological Laws and Nonmonotonic Logic. Erkenntnis 44 (2):199-224.
    In this essay I enter into a recently published debate between Stephen Schiffer and Jerry Fodor concerning whether adequate sense can be made of the ceteris paribus conditions in special science laws, much of their focus being on the case of putative psychological laws. Schiffer argues that adequate sense cannot be made of ceteris paribus clauses, while Fodor attempts to overcome Schiffer's arguments, in defense of special science laws. More recently, Peter Mott has attempted to show that Fodor's response to (...)
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  38. Paul D. Thorn & Gerhard Schurz (2014). A Utility Based Evaluation of Logico-Probabilistic Systems. Studia Logica 102 (4):867-890.
    Systems of logico-probabilistic (LP) reasoning characterize inference from conditional assertions interpreted as expressing high conditional probabilities. In the present article, we investigate four prominent LP systems (namely, systems O, P, Z, and QC) by means of computer simulations. The results reported here extend our previous work in this area, and evaluate the four systems in terms of the expected utility of the dispositions to act that derive from the conclusions that the systems license. In addition to conforming to the dominant (...)
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  39. Paul D. Thorn & Gerhard Schurz (2013). Ampliative Inference Under Varied Entropy Levels. In Christoph Beierle & Gabriele Kern-Isberner (eds.), Proceedings of the 4th Workshop on Dynamics of Knowledge and Belief (DKB-2013). Fakultät für Mathematik und Informatik, FernUniversität in Hagen. 77-88.
  40. Bart Verheij (2003). Dialectical Argumentation with Argumentation Schemes: An Approach to Legal Logic. [REVIEW] Artificial Intelligence and Law 11 (2-3):167-195.
    This paper describes an approach to legal logic based on the formal analysis of argumentation schemes. Argumentation schemes a notion borrowed from the .eld of argumentation theory - are a kind of generalized rules of inference, in the sense that they express that given certain premises a particular conclusion can be drawn. However, argumentation schemes need not concern strict, abstract, necessarily valid patterns of reasoning, but can be defeasible, concrete and contingently valid, i.e., valid in certain contexts or under certain (...)
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  41. Heinrich Wansing (2006). David Makinson, Bridges From Classical to Nonmonotonic Logic, Texts in Computingvox. 5, King's College Publications, London, 2005. XVI + 216 Pp. Isbn 1-904987-00-. [REVIEW] Theoria 72 (4):336-340.
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  42. Jonathan Weisberg, Pollock's Theory of Defeasible Reasoning.
    An introduction to the motivations and mechanics of John Pollock's theory of defeasible reasoning, from a lecture at the Northern Institute of Philosophy in 2010.
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  43. Gregory Wheeler (2004). A Resource-Bounded Default Logic. In J. Delgrande & T. Schaub (eds.), Proceedings of NMR 2004. AAAI.
    This paper presents statistical default logic, an expansion of classical (i.e., Reiter) default logic that allows us to model common inference patterns found in standard inferential statistics, including hypothesis testing and the estimation of a populations mean, variance and proportions. The logic replaces classical defaults with ordered pairs consisting of a Reiter default in the first coordinate and a real number within the unit interval in the second coordinate. This real number represents an upper-bound limit on the probability of accepting (...)
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  44. Gregory Wheeler & Carlos Damasio (2004). An Implementation of Statistical Default Logic. In Jose Alferes & Joao Leite (eds.), Logics in Artificial Intelligence (JELIA 2004). Springer.
    Statistical Default Logic (SDL) is an expansion of classical (i.e., Reiter) default logic that allows us to model common inference patterns found in standard inferential statistics, e.g., hypothesis testing and the estimation of a population‘s mean, variance and proportions. This paper presents an embedding of an important subset of SDL theories, called literal statistical default theories, into stable model semantics. The embedding is designed to compute the signature set of literals that uniquely distinguishes each extension on a statistical default theory (...)
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  45. Graham White (2008). Causality, Modality, and Explanation. Notre Dame Journal of Formal Logic 49 (3):313-343.
    We start with Fodor's critique of cognitive science in "The mind doesn't work that way: The scope and limits of computational psychology": he argues that much mental activity cannot be handled by the current methods of cognitive science because it is nonmonotonic and, therefore, is global in nature, is not context-free, and is thus not capable of being formalized by a Turing-like mental architecture. We look at the use of nonmonotonic logic in the artificial intelligence community, particularly with the discussion (...)
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