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124
Learning Stochastic Logic Programs
, 2000
"... Stochastic Logic Programs (SLPs) have been shown to be a generalisation of Hidden Markov Models (HMMs), stochastic contextfree grammars, and directed Bayes' nets. A stochastic logic program consists of a set of labelled clauses p:C where p is in the interval [0,1] and C is a firstorder r ..."
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Cited by 1181 (79 self)
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Stochastic Logic Programs (SLPs) have been shown to be a generalisation of Hidden Markov Models (HMMs), stochastic contextfree grammars, and directed Bayes' nets. A stochastic logic program consists of a set of labelled clauses p:C where p is in the interval [0,1] and C is a firstorder rangerestricted definite clause. This paper summarises the syntax, distributional semantics and proof techniques for SLPs and then discusses how a standard Inductive Logic Programming (ILP) system, Progol, has been modied to support learning of SLPs. The resulting system 1) nds an SLP with uniform probability labels on each definition and nearmaximal Bayes posterior probability and then 2) alters the probability labels to further increase the posterior probability. Stage 1) is implemented within CProgol4.5, which differs from previous versions of Progol by allowing userdefined evaluation functions written in Prolog. It is shown that maximising the Bayesian posterior function involves nding SLPs with short derivations of the examples. Search pruning with the Bayesian evaluation function is carried out in the same way as in previous versions of CProgol. The system is demonstrated with worked examples involving the learning of probability distributions over sequences as well as the learning of simple forms of uncertain knowledge.
Prior Probabilities
 IEEE Transactions on Systems Science and Cybernetics
, 1968
"... e case of location and scale parameters, rate constants, and in Bernoulli trials with unknown probability of success. In realistic problems, both the transformation group analysis and the principle of maximum entropy are needed to determine the prior. The distributions thus found are uniquely determ ..."
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Cited by 249 (4 self)
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e case of location and scale parameters, rate constants, and in Bernoulli trials with unknown probability of success. In realistic problems, both the transformation group analysis and the principle of maximum entropy are needed to determine the prior. The distributions thus found are uniquely determined by the prior information, independently of the choice of parameters. In a certain class of problems, therefore, the prior distributions may now be claimed to be fully as "objective" as the sampling distributions. I. Background of the problem Since the time of Laplace, applications of probability theory have been hampered by difficulties in the treatment of prior information. In realistic problems of decision or inference, we often have prior information which is highly relevant to the question being asked; to fail to take it into account is to commit the most obvious inconsistency of reasoning and may lead to absurd or dangerously misleading results. As an extreme examp
Betting on Theories
, 1993
"... Predictions about the future and unrestricted universal generalizations are never logically implied by our observational evidence, which is limited to particular facts in the present and past. Nevertheless, propositions of these and other kinds are often said to be confirmed by observational evidenc ..."
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Cited by 102 (4 self)
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Predictions about the future and unrestricted universal generalizations are never logically implied by our observational evidence, which is limited to particular facts in the present and past. Nevertheless, propositions of these and other kinds are often said to be confirmed by observational evidence. A natural place to begin the study of confirmation theory is to consider what it means to say that some evidence E confirms a hypothesis H. Incremental and absolute confirmation Let us say that E raises the probability of H if the probability of H given E is higher than the probability of H not given E. According to many confirmation theorists, “E confirms H ” means that E raises the probability of H. This conception of confirmation will be called incremental confirmation. Let us say that H is probable given E if the probability of H given E is above some threshold. (This threshold remains to be specified but is assumed to be at least one half.) According to some confirmation theorists, “E confirms H ” means that H is probable given E. This conception of confirmation will be called absolute confirmation. Confirmation theorists have sometimes failed to distinguish these two concepts. For example, Carl Hempel in his classic “Studies in the Logic of Confirmation ” endorsed the following principles: (1) A generalization of the form “All F are G ” is confirmed by the evidence that there is an individual that is both F and G. (2) A generalization of that form is also confirmed by the evidence that there is an individual that is neither F nor G. (3) The hypotheses confirmed by a piece of evidence are consistent with one another. (4) If E confirms H then E confirms every logical consequence of H. Principles (1) and (2) are not true of absolute confirmation. Observation of a single thing that is F and G cannot in general make it probable that all F are G; likewise for an individual that is neither
Reconciling simplicity and likelihood principles in perceptual organization
 Psychological Review
, 1996
"... Two principles of perceptual organization have been proposed. The likelihood principle, following H. L. E yon Helmholtz ( 1910 / 1962), proposes that perceptual organization is chosen to correspond to the most likely distal layout. The simplicity principle, following Gestalt psychology, suggests tha ..."
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Cited by 86 (17 self)
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Two principles of perceptual organization have been proposed. The likelihood principle, following H. L. E yon Helmholtz ( 1910 / 1962), proposes that perceptual organization is chosen to correspond to the most likely distal layout. The simplicity principle, following Gestalt psychology, suggests that perceptual organization is chosen to be as simple as possible. The debate between these two views has been a central topic in the study of perceptual organization. Drawing on mathematical results in A. N. Kolmogorov's ( 1965)complexity heory, the author argues that simplicity and likelihood are not in competition, but are identical. Various implications for the theory of perceptual organization and psychology more generally are outlined. How does the perceptual system derive a complex and structured description of the perceptual world from patterns of activity at the sensory receptors? Two apparently competing theories of perceptual organization have been influential. The first, initiated by Helmholtz ( 1910/1962), advocates the likelihood principle: Sensory input will be organized into the most probable distal object or event consistent with that input. The second, initiated by Wertheimer and developed by other Gestalt psychologists, advocates what Pomerantz and Kubovy (1986) called the simplicity principle: The perceptual system is viewed as finding the simplest, rather than the most likely, perceptual organization consistent with the sensory input '. There has been considerable theoretical nd empirical controversy concerning whether likelihood or simplicity is the governing principle of perceptual organization (e.g., Hatfield, &
Random Worlds and Maximum Entropy
 In Proc. 7th IEEE Symp. on Logic in Computer Science
, 1994
"... Given a knowledge base KB containing firstorder and statistical facts, we consider a principled method, called the randomworlds method, for computing a degree of belief that some formula ' holds given KB . If we are reasoning about a world or system consisting of N individuals, then we can co ..."
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Cited by 56 (13 self)
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Given a knowledge base KB containing firstorder and statistical facts, we consider a principled method, called the randomworlds method, for computing a degree of belief that some formula ' holds given KB . If we are reasoning about a world or system consisting of N individuals, then we can consider all possible worlds, or firstorder models, with domain f1; : : : ; Ng that satisfy KB , and compute the fraction of them in which ' is true. We define the degree of belief to be the asymptotic value of this fraction as N grows large. We show that when the vocabulary underlying ' and KB uses constants and unary predicates only, we can naturally associate an entropy with each world. As N grows larger, there are many more worlds with higher entropy. Therefore, we can use a maximumentropy computation to compute the degree of belief. This result is in a similar spirit to previous work in physics and artificial intelligence, but is far more general. Of equal interest to the result itself are...
Statistical Foundations for Default Reasoning
, 1993
"... We describe a new approach to default reasoning, based on a principle of indifference among possible worlds. We interpret default rules as extreme statistical statements, thus obtaining a knowledge base KB comprised of statistical and firstorder statements. We then assign equal probability to all w ..."
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Cited by 48 (8 self)
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We describe a new approach to default reasoning, based on a principle of indifference among possible worlds. We interpret default rules as extreme statistical statements, thus obtaining a knowledge base KB comprised of statistical and firstorder statements. We then assign equal probability to all worlds consistent with KB in order to assign a degree of belief to a statement '. The degree of belief can be used to decide whether to defeasibly conclude '. Various natural patterns of reasoning, such as a preference for more specific defaults, indifference to irrelevant information, and the ability to combine independent pieces of evidence, turn out to follow naturally from this technique. Furthermore, our approach is not restricted to default reasoning; it supports a spectrum of reasoning, from quantitative to qualitative. It is also related to other systems for default reasoning. In particular, we show that the work of [ Goldszmidt et al., 1990 ] , which applies maximum entropy ideas t...
A universal logic approach to adaptive logics. Logica universalis
, 2007
"... In this paper, adaptive logics are studied from the viewpoint of universal logic (in the sense of the study of common structures of logics). The common structure of a large set of adaptive logics is described. It is shown that this structure determines the proof theory as well as the semantics of t ..."
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Cited by 43 (11 self)
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In this paper, adaptive logics are studied from the viewpoint of universal logic (in the sense of the study of common structures of logics). The common structure of a large set of adaptive logics is described. It is shown that this structure determines the proof theory as well as the semantics of the adaptive logics, and moreover that most properties of the logics can be proved by relying solely on the structure, viz. without invoking any specific properties of the logics themselves. 1 Aim and Preliminaries In this paper the common features of a wide variety of logics is studied. The logics, viz. adaptive logics, are very different both in nature and in application context. Of the adaptive logics studied until now, some are close to CL (Classical Logic), others are many valued, still others modal, and there clearly are adaptive logics of a still very different nature. The application contexts too are very varied: handling inconsistency, inductive generalization, abduction, handling plausible inferences, interpreting a person’s changing position in an ongoing discussion, compatibility, etc. I shall show that all these logics have a common structure, which determines their proofs as well as their semantics, and moreover their metatheory. Specific adaptive logics will not even be mentioned, except as illustrative examples. Adaptive logics adapt themselves to specific premise sets. To be more precise, they interpret a premise set “as normally as possible ” with respect to some standard of normality. They explicate reasoning processes that display an internal and possibly an external dynamics. The external dynamics provides from the nonmonotonicity of the inference relation: if premises are added, some consequences may not be derivable any more—formally: there are Γ, ∆ and A such that Γ ` A and Γ ∪ ∆ 0 A. The internal dynamics plays at the level of ∗Research for this paper was supported by subventions from Ghent University and from the Fund for Scientific Research – Flanders. I am indebted to Peter Verdée for comments to a previous version. 1
A Natural Law of Succession
, 1995
"... Consider the following problem. You are given an alphabet of k distinct symbols and are told that the i th symbol occurred exactly ni times in the past. On the basis of this information alone, you must now estimate the conditional probability that the next symbol will be i. In this report, we presen ..."
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Cited by 40 (3 self)
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Consider the following problem. You are given an alphabet of k distinct symbols and are told that the i th symbol occurred exactly ni times in the past. On the basis of this information alone, you must now estimate the conditional probability that the next symbol will be i. In this report, we present a new solution to this fundamental problem in statistics and demonstrate that our solution outperforms standard approaches, both in theory and in practice.