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196
An InformationTheoretic Definition of Similarity
 In Proceedings of the 15th International Conference on Machine Learning
, 1998
"... Similarity is an important and widely used concept. Previous definitions of similarity are tied to a particular application or a form of knowledge representation. We present an informationtheoretic definition of similarity that is applicable as long as there is a probabilistic model. We demonstrate ..."
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Cited by 761 (0 self)
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Similarity is an important and widely used concept. Previous definitions of similarity are tied to a particular application or a form of knowledge representation. We present an informationtheoretic definition of similarity that is applicable as long as there is a probabilistic model. We demonstrate how our definition can be used to measure the similarity in a number of different domains.
Markov Logic Networks
 Machine Learning
, 2006
"... Abstract. We propose a simple approach to combining firstorder logic and probabilistic graphical models in a single representation. A Markov logic network (MLN) is a firstorder knowledge base with a weight attached to each formula (or clause). Together with a set of constants representing objects ..."
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Cited by 569 (34 self)
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Abstract. We propose a simple approach to combining firstorder logic and probabilistic graphical models in a single representation. A Markov logic network (MLN) is a firstorder knowledge base with a weight attached to each formula (or clause). Together with a set of constants representing objects in the domain, it specifies a ground Markov network containing one feature for each possible grounding of a firstorder formula in the KB, with the corresponding weight. Inference in MLNs is performed by MCMC over the minimal subset of the ground network required for answering the query. Weights are efficiently learned from relational databases by iteratively optimizing a pseudolikelihood measure. Optionally, additional clauses are learned using inductive logic programming techniques. Experiments with a realworld database and knowledge base in a university domain illustrate the promise of this approach.
An Analysis of FirstOrder Logics of Probability
 Artificial Intelligence
, 1990
"... : We consider two approaches to giving semantics to firstorder logics of probability. The first approach puts a probability on the domain, and is appropriate for giving semantics to formulas involving statistical information such as "The probability that a randomly chosen bird flies is greater than ..."
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Cited by 272 (18 self)
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: We consider two approaches to giving semantics to firstorder logics of probability. The first approach puts a probability on the domain, and is appropriate for giving semantics to formulas involving statistical information such as "The probability that a randomly chosen bird flies is greater than .9." The second approach puts a probability on possible worlds, and is appropriate for giving semantics to formulas describing degrees of belief, such as "The probability that Tweety (a particular bird) flies is greater than .9." We show that the two approaches can be easily combined, allowing us to reason in a straightforward way about statistical information and degrees of belief. We then consider axiomatizing these logics. In general, it can be shown that no complete axiomatization is possible. We provide axiom systems that are sound and complete in cases where a complete axiomatization is possible, showing that they do allow us to capture a great deal of interesting reasoning about prob...
On the Hardness of Approximate Reasoning
, 1996
"... Many AI problems, when formalized, reduce to evaluating the probability that a propositional expression is true. In this paper we show that this problem is computationally intractable even in surprisingly restricted cases and even if we settle for an approximation to this probability. We consider va ..."
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Cited by 219 (13 self)
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Many AI problems, when formalized, reduce to evaluating the probability that a propositional expression is true. In this paper we show that this problem is computationally intractable even in surprisingly restricted cases and even if we settle for an approximation to this probability. We consider various methods used in approximate reasoning such as computing degree of belief and Bayesian belief networks, as well as reasoning techniques such as constraint satisfaction and knowledge compilation, that use approximation to avoid computational difficulties, and reduce them to modelcounting problems over a propositional domain. We prove that counting satisfying assignments of propositional languages is intractable even for Horn and monotone formulae, and even when the size of clauses and number of occurrences of the variables are extremely limited. This should be contrasted with the case of deductive reasoning, where Horn theories and theories with binary clauses are distinguished by the e...
A Logic for Reasoning about Probabilities
 Information and Computation
, 1990
"... We consider a language for reasoning about probability which allows us to make statements such as “the probability of E, is less than f ” and “the probability of E, is at least twice the probability of E,, ” where E, and EZ are arbitrary events. We consider the case where all events are measurable ( ..."
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Cited by 214 (19 self)
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We consider a language for reasoning about probability which allows us to make statements such as “the probability of E, is less than f ” and “the probability of E, is at least twice the probability of E,, ” where E, and EZ are arbitrary events. We consider the case where all events are measurable (i.e., represent measurable sets) and the more general case, which is also of interest in practice, where they may not be measurable. The measurable case is essentially a formalization of (the propositional fragment of) Nilsson’s probabilistic logic. As we show elsewhere, the general (nonmeasurable) case corresponds precisely to replacing probability measures by DempsterShafer belief functions. In both cases, we provide a complete axiomatization and show that the problem of deciding satistiability is NPcomplete, no worse than that of propositional logic. As a tool for proving our complete axiomatizations, we give a complete axiomatization for reasoning about Boolean combinations of linear inequalities, which is of independent interest. This proof and others make crucial use of results from the theory of linear programming. We then extend the language to allow reasoning about conditional probability and show that the resulting logic is decidable and completely axiomatizable, by making use of the theory of real closed fields. ( 1990 Academic Press. Inc 1.
Reasoning within Fuzzy Description Logics
 Journal of Artificial Intelligence Research
, 2001
"... Description Logics (DLs) are suitable, wellknown, logics for managing structured knowledge. They allow reasoning about individuals and well defined concepts, i.e. set of individuals with common properties. The experience in using DLs in applications has shown that in many cases we would like to ext ..."
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Cited by 151 (21 self)
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Description Logics (DLs) are suitable, wellknown, logics for managing structured knowledge. They allow reasoning about individuals and well defined concepts, i.e. set of individuals with common properties. The experience in using DLs in applications has shown that in many cases we would like to extend their capabilities. In particular, their use in the context of Multimedia Information Retrieval (MIR) leads to the convincement that such DLs should allow the treatment of the inherent imprecision in multimedia object content representation and retrieval. In this paper we will present a fuzzy extension of ALC, combining...
Probabilistic Logic Programming
, 1992
"... Of all scientific investigations into reasoning with uncertainty and chance, probability theory is perhaps the best understood paradigm. Nevertheless, all studies conducted thus far into the semantics of quantitative logic programming (cf. van Emden [51], Fitting [18, 19, 20], Blair and Subrahmanian ..."
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Cited by 131 (7 self)
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Of all scientific investigations into reasoning with uncertainty and chance, probability theory is perhaps the best understood paradigm. Nevertheless, all studies conducted thus far into the semantics of quantitative logic programming (cf. van Emden [51], Fitting [18, 19, 20], Blair and Subrahmanian [5, 6, 49, 50], Kifer et al [29, 30, 31]) have restricted themselves to nonprobabilistic semantical characterizations. In this paper, we take a few steps towards rectifying this situation. We define a logic programming language that is syntactically similar to the annotated logics of [5, 6], but in which the truth values are interpreted probabilistically. A probabilistic model theory and fixpoint theory is developed for such programs. This probabilistic model theory satisfies the requirements proposed by Fenstad [16] for a function to be called probabilistic. The logical treatment of probabilities is complicated by two facts: first, that the connectives cannot be interpreted truth function...
Model Checking vs. Theorem Proving: A Manifesto
, 1991
"... We argue that rather than representing an agent's knowledge as a collection of formulas, and then doing theorem proving to see if a given formula follows from an agent's knowledge base, it may be more useful to represent this knowledge by a semantic model, and then do model checking to see if the g ..."
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Cited by 117 (5 self)
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We argue that rather than representing an agent's knowledge as a collection of formulas, and then doing theorem proving to see if a given formula follows from an agent's knowledge base, it may be more useful to represent this knowledge by a semantic model, and then do model checking to see if the given formula is true in that model. We discuss how to construct a model that represents an agent's knowledge in a number of different contexts, and then consider how to approach the modelchecking problem.
PCLASSIC: A tractable probabilistic description logic
 In Proceedings of AAAI97
, 1997
"... Knowledge representation languages invariably reflect a tradeoff between expressivity and tractability. Evidence suggests that the compromise chosen by description logics is a particularly successful one. However, description logic (as for all variants of firstorder logic) is severely limited in i ..."
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Cited by 105 (4 self)
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Knowledge representation languages invariably reflect a tradeoff between expressivity and tractability. Evidence suggests that the compromise chosen by description logics is a particularly successful one. However, description logic (as for all variants of firstorder logic) is severely limited in its ability to express uncertainty. In this paper, we present PCLASSIC, a probabilistic version of the description logic CLASSIC. In addition to terminological knowledge, the language utilizes Bayesian networks to express uncertainty about the basic properties of an individual, the number of fillers for its roles, and the properties of these fillers. We provide a semantics for PCLASSIC and an effective inference procedure for probabilistic subsumption: computing the probability that a random individual in class C is also in class D. The effectiveness of the algorithm relies on independenceassumptions and on our ability to execute lifted inference: reasoning about similar individuals as a gr...