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Weiru Liu - One of the best experts on this subject based on the ideXlab platform.

  • a belief revision framework for revising Epistemic States with partial Epistemic States
    International Journal of Approximate Reasoning, 2015
    Co-Authors: Weiru Liu, Salem Benferhat
    Abstract:

    Belief revision performs belief change on an agent's beliefs when new evidence (either of the form of a propositional formula or of the form of a total pre-order on a set of interpretations) is received. Jeffrey's rule is commonly used for revising probabilistic Epistemic States when new information is probabilistically uncertain. In this paper, we propose a general Epistemic revision framework where new evidence is of the form of a partial Epistemic State. Our framework extends Jeffrey's rule with uncertain inputs and covers well-known existing frameworks such as ordinal conditional function (OCF) or possibility theory. We then define a set of postulates that such revision operators shall satisfy and establish representation theorems to characterize those postulates. We show that these postulates reveal common characteristics of various existing revision strategies and are satisfied by OCF conditionalization, Jeffrey's rule of conditioning and possibility conditionalization. Furthermore, when reducing to the belief revision situation, our postulates can induce Darwiche and Pearl's postulates C1 and C2.

  • modeling belief change on Epistemic States
    The Florida AI Research Society, 2009
    Co-Authors: Weiru Liu
    Abstract:

    Belief revision always results in trusting new evidence, so it may admit an unreliable one and discard a more confident one. We therefore use belief change instead of belief revision to remedy this weakness. By introducing  Epistemic States, we take into account of the strength of evidence that influences the change of belief. In this paper, we present a set of postulates to characterize belief change by Epistemic States and establish representation  theorems to characterize those postulates. We show that from an Epistemic State, a corresponding ordinal conditional function by Spohn can be derived and the result of combining two Epistemic States is thus reduced to the result from combining two corresponding ordinal conditional functions proposed by Laverny and Lang. Furthermore, when reduced to the belief revision situation, we prove that our results induce all the Darwiche and Pearl's postulates.

  • a general model for Epistemic State revision using plausibility measures
    European Conference on Artificial Intelligence, 2008
    Co-Authors: Weiru Liu
    Abstract:

    In this paper, we present a general revision model on Epistemic States based on plausibility measures proposed by Friedman and Halpern. We propose our revision strategy and give some desirable properties, e.g., the reversible and commutative properties. Moreover, we develop a notion called plausibility kinematics and show that our revision strategy follows plausibility kinematics. Furthermore, we prove that the revision following plausibility kinematics satisfies the principle of minimal change based on some distance measures. Finally, we discuss a revision operator defined for plausibility functions and its relationship with iterated belief revision proposed by Darwiche and Pearl. We show that the revision operator satisfies all the DP postulates when it is Max-Additive.

Wolfgang Spohn - One of the best experts on this subject based on the ideXlab platform.

  • a general non probabilistic theory of inductive reasoning
    arXiv: Artificial Intelligence, 2013
    Co-Authors: Wolfgang Spohn
    Abstract:

    Probability theory, Epistemically interpreted, provides an excellent, if not the best available account of inductive reasoning. This is so because there are general and definite rules for the change of subjective probabilities through information or experience; induction and belief change are one and same topic, after all. The most basic of these rules is simply to conditionalize with respect to the information received; and there are similar and more general rules. 1 Hence, a fundamental reason for the epistemological success of probability theory is that there at all exists a well-behaved concept of conditional probability. Still, people have, and have reasons for, various concerns over probability theory. One of these is my starting point: Intuitively, we have the notion of plain belief; we believe propositions2 to be true (or to be false or neither). Probability theory, however, offers no formal counterpart to this notion. Believing A is not the same as having probability 1 for A, because probability 1 is incorrigible3; but plain belief is clearly corrigible. And believing A is not the same as giving A a probability larger than some 1 - c, because believing A and believing B is usually taken to be equivalent to believing A & B.4 Thus, it seems that the formal representation of plain belief has to take a non-probabilistic route. Indeed, representing plain belief seems easy enough: simply represent an Epistemic State by the set of all propositions believed true in it or, since I make the common assumption that plain belief is deductively closed, by the conjunction of all propositions believed true in it. But this does not yet provide a theory of induction, i.e. an answer to the question how Epistemic States so represented are changed tbrough information or experience. There is a convincing partial answer: if the new information is compatible with the old Epistemic State, then the new Epistemic State is simply represented by the conjunction of the new information and the old beliefs. This answer is partial because it does not cover the quite common case where the new information is incompatible with the old beliefs. It is, however, important to complete the answer and to cover this case, too; otherwise, we would not represent plain belief as conigible. The crucial problem is that there is no good completion. When Epistemic States are represented simply by the conjunction of all propositions believed true in it, the answer cannot be completed; and though there is a lot of fruitful work, no other representation of Epistemic States has been proposed, as far as I know, which provides a complete solution to this problem. In this paper, I want to suggest such a solution. In [4], I have more fully argued that this is the only solution, if certain plausible desiderata are to be satisfied. Here, in section 2, I will be content with formally defining and intuitively explaining my proposal. I will compare my proposal with probability theory in section 3. It will turn out that the theory I am proposing is structurally homomorphic to probability theory in important respects and that it is thus equally easily implementable, but moreover computationally simpler. Section 4 contains a very brief comparison with various kinds of logics, in particular conditional logic, with Shackle's functions of potential surprise and related theories, and with the Dempster - Shafer theory of belief functions.

Olav B. Vassend - One of the best experts on this subject based on the ideXlab platform.

  • Goals and the Informativeness of Prior Probabilities
    Erkenntnis, 2018
    Co-Authors: Olav B. Vassend
    Abstract:

    I argue that information is a goal-relative concept for Bayesians. More precisely, I argue that how much information (or confirmation) is provided by a piece of evidence depends on whether the goal is to learn the truth or to rank actions by their expected utility, and that different confirmation measures should therefore be used in different contexts. I then show how information measures may reasonably be derived from confirmation measures, and I show how to derive goal-relative non-informative and informative priors given background information. Finally, I argue that my arguments have important implications for both objective and subjective Bayesianism. In particular, the Uniqueness Thesis is either false or must be modified. Moreover, objective Bayesians must concede that pragmatic factors systematically influence which priors are rational, and subjective Bayesians must concede that pragmatic factors sometimes partly determine which prior distribution most accurately represents an agent’s Epistemic State.

Christoph Beierle - One of the best experts on this subject based on the ideXlab platform.

  • a high level implementation of a system for automated reasoning with default rules system description
    International Joint Conference on Automated Reasoning, 2008
    Co-Authors: Christoph Beierle, Gabriele Kernisberner, Nicole Koch
    Abstract:

    An overview of a system modelling an intelligent agent being able to reason by using default rules is given. The semantics of the qualitative default rules is defined via ordinal conditional functions which model the Epistemic State of the agent, providing her with the basic equipment to perform different knowledge management and belief revision tasks. Using the concept of Abstract State Machines, the fully operational system was developed in AsmL, allowing for a high-level implementation that minimizes the gap between the mathematical specification of the underlying concepts and the executable code in the implemented system.

  • on the modelling of an agent s Epistemic State and its dynamic changes
    Electronic Communication of The European Association of Software Science and Technology, 2008
    Co-Authors: Christoph Beierle, Gabriele Kernisberner
    Abstract:

    Given a set of unquantified conditionals considered as default rules or a set of quantified conditionals such as probabilistic rules, an agent can build up its internal Epistemic State from such a knowledge base by inductive reasoning techniques. Besides certain (logical) knowledge, Epistemic States are supposed to allow the representation of preferences, beliefs, assumptions etc. of an intelligent agent. If the agent lives in a dynamic environment, it has to adapt its Epistemic State constantly to changes in the surrounding world in order to be able to react adequately to new demands. In this paper, we present a high-level specification of the Condor system that provides powerful methods and tools for managing knowledge represented by conditionals and the corresponding Epistemic States of an agent. Thereby, we are able to elaborate and formalize crucial interdependencies between different aspects of knowledge representation, knowledge discovery, and belief revision. Moreover, this specification, using Gurevich's Abstract State Machines, provides the basis for a stepwise refinement development process of the Condor system based on the ASM methodology.

Healey, Richard A. - One of the best experts on this subject based on the ideXlab platform.

  • Representation and the Quantum State
    2021
    Co-Authors: Healey, Richard A.
    Abstract:

    Alternative views of quantum States are often expressed using the language of representation. It is important to distinguish three questions here: What is a quantum State? How may a quantum State be represented? What, if anything, does a quantum State represent? I defend answers to these questions against alternatives. In brief, a quantum State is an objective relational property of a physical system that describes neither its intrinsic physical properties nor anyone’s Epistemic State. A quantum State is representational (in my preferred sense of that term) and many quantum States are real. Since its primary role is to assign Born probabilities to certain physical events involving the system, a quantum State may be represented in quantum theory by any mathematical object that facilitates this role. If it represents anything, a quantum State represents the objective probabilities it yields in this way

  • Laws as Epistemic Infrastructure not Metaphysical Superstructure
    2021
    Co-Authors: Healey, Richard A.
    Abstract:

    The status of laws of nature has been the locus of a lively debate in recent philosophy. Most participants have assumed laws play an important role in science and metaphysics while seeking their objective ground in the natural world, though some skeptics (Giere, van Fraassen, Cartwright) have questioned this assumption. So-called Humeans look to base laws on actual, particular facts such as those specified in David Lewis’s Humean mosaic. Their opponents (including Maudlin) argue that such a basis is neither necessary nor sufficient to support the independent existence of scientific laws. This essentially metaphysical debate has paid scant attention to the details of scientific practice. It has mostly focused on so-called fundamental laws, assumed to take a particular form (such as Maudlin’s FLOTEs). I propose a pragmatist alternative—not as another position in the debate but as an alternative to the debate itself. This pragmatist alternative offers a view that questions the representational conception of truth presupposed by participants to the debate as well as the metaphysical import of fundamental laws. Statements of law serve many different purposes in science: I’ll look at some. But their central role is in inference, primarily to improve the Epistemic State of a scientist with limited access to information. To play this role, a scientific law Statement need be neither necessary, unconditionally universal nor even true. It must merely be sufficiently reliable within its domain of application. The use of laws in astrophysics and metrology will help to illustrate these points