MEBN A Language for First-Order Bayesian Knowledge Bases (original) (raw)
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Multi-entity bayesian networks without multi-tears
Draft Version, 2005
An introduction is provided to Multi-Entity Bayesian Networks (MEBN), a logic system that integrates First Order Logic (FOL) with Bayesian probability theory. MEBN extends ordinary Bayesian networks to allow representation of graphical models with repeated sub-structures. Knowledge is encoded as a collection of Bayesian network fragments (MFrags) that can be instantiated and combined to form highly complex situation-specific Bayesian networks. A MEBN theory (MTheory) implicitly represents a joint probability distribution over possibly unbounded numbers of hypotheses, and uses Bayesian learning to refine a knowledge base as observations accrue. MEBN provides a logical foundation for the emerging collection of highly expressive probability-based languages. A running example illustrates the representation and reasoning power of the MEBN formalism.
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Possibilistic logic and Bayesian networks have provided advantageous methodologies and techniques for computerbased knowledge representation. This paper proposes a framework that combines these two disciplines to exploit their own advantages in uncertain and imprecise knowledge representation problems. The framework proposed is a possibilistic logic based one in which Bayesian nodes and their properties are represented by local necessity-valued knowledge base. Data in properties are interpreted as set of valuated formulas. In our contribution possibilistic Bayesian networks have a qualitative part and a quantitative part, represented by local knowledge bases. The general idea is to study how a fusion of these two formalisms would permit representing compact way to solve efficiently problems for knowledge representation. We show how to apply possibility and necessity measures to the problem of knowledge representation with large scale data.
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Possibilistic logic and Bayesian networks have provided advantageous methodologies and techniques for computerbased knowledge representation. This paper proposes a framework that combines these two disciplines to exploit their own advantages in uncertain and imprecise knowledge representation problems. The framework proposed is a possibilistic logic based one in which Bayesian nodes and their properties are represented by local necessity-valued knowledge base. Data in properties are interpreted as set of valuated formulas. In our contribution possibilistic Bayesian networks have a qualitative part and a quantitative part, represented by local knowledge bases. The general idea is to study how a fusion of these two formalisms would permit representing compact way to solve efficiently problems for knowledge representation. We show how to apply possibility and necessity measures to the problem of knowledge representation with large scale data.
2005
Uncertainty is a fundamental and irreducible aspect of our knowledge about the world. Until recently, classical first-order logic has reigned as the de facto standard logical foundation for artificial intelligence. The lack of a built-in, semantically grounded capability for reasoning under uncertainty renders classical first-order logic inadequate for many important classes of problems. General-purpose languages are beginning to emerge for which the fundamental logical basis is probability. Increasingly expressive probabilistic languages demand a theoretical foundation that fully integrates classical first-order logic and probability. In first-order Bayesian logic (FOBL), probability distributions are defined over interpretations of classical first-order axiom systems. Predicates and functions of a classical first-order theory correspond to a random variables in the corresponding first-order Bayesian theory. This is a natural correspondence, given that random variables are formalized in mathematical statistics as measurable functions on a probability space. A formal system called Multi-Entity Bayesian Networks (MEBN) is presented for composing distributions on interpretations by instantiating and combining parameterized fragments of directed graphical models. A construction is given of a MEBN theory that assigns a non-zero probability to any satisfiable sentence in classical first-order logic. By conditioning this distribution on consistent sets of sentences, FOBL can represent a probability distribution over interpretations of any finitely axiomatizable first-order theory, as well as over interpretations of infinite axiom sets when a limiting distribution exists. FOBL is inherently open, having the ability to incorporate new axioms into existing theories, and to modify probabilities in the light of evidence. Bayesian inference provides both a proof theory for combining prior knowledge with observations, and a learning theory for refining a representation as evidence accrues. The results of this paper provide a logical foundation for the rapidly evolving literature on first-order Bayesian knowledge representation, and point the way toward Bayesian languages suitable for generalpurpose knowledge representation and computing. Because FOBL contains classical first-order logic as a deterministic subset, it is a natural candidate as a universal representation for integrating domain ontologies expressed in languages based on classical first-order logic or subsets thereof.
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While in principle probabilistic logics might be applied to solve a range of problems, in practice they are rarely applied at present. This is perhaps because they seem disparate, complicated, and computationally intractable. However, we shall argue in this programmatic paper that several approaches to probabilistic logic fit into a simple unifying framework: logically complex evidence can be used to associate probability intervals or probabilities with sentences.
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Causal probabilistic networks have proved to be a useful knowledge representation tool for modelling domains where causal relations in a broad sense are a natural way of relating domain objects and where uncertainty is inherited in these relations. This paper outlines an implementation the HUGIN shell -for handling a domain model expressed by a causal probabilistic network. The only topological restriction imposed on the network is that, it must not contain any directed loops. The approach is illustrated step by step by solving a. genetic breeding problem. A graph representation of the domain model is interactively created by using instances of the basic network componentsnodes and arcs-as building blocks. This structure, together with the quantitative relations between nodes and their immediate causes expressed as conditional probabilities, are automatically transformed into a tree structure, a junction tree. Here a computationally efficient and conceptually simple algebra of Bayesian belief universes supports incorporation of new evidence, propagation of information, and calculation of revised beliefs in the states of the nodes in the network. Finally, as an exam ple of a real world application, MUN1N an expert system for electromyography is discussed.
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Probabilistic Logic Programming and Bayesian Networks
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We present a probabilistic logic programming framework that allows the representation of conditional probabilities. While conditional probabilities are the most commonly used method for representing uncertainty in probabilistic expert systems, they have been largely neglected by work in quantitative logic programming. We define a fixpoint theory, declarative semantics, and proof procedure for the new class of probabilistic logic programs. Compared to other approaches to quantitative logic programming, we provide a true probabilistic framework with potential applications in probabilistic expert systems and decision support systems. We also discuss the relationship between such programs and Bayesian networks, thus moving toward a unification of two major approaches to automated reasoning.
Simplifying Probability Elicitation and Uncertainty Modeling in Bayesian Networks
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