Results 1  10
of
35
Nonmonotonic Reasoning, Conditional Objects and Possibility Theory
 Artificial Intelligence
, 1997
"... . This short paper relates the conditional objectbased and possibility theorybased approaches for reasoning with conditional statements pervaded with exceptions, to other methods in nonmonotonic reasoning which have been independently proposed: namely, Lehmann's preferential and rational closu ..."
Abstract

Cited by 72 (20 self)
 Add to MetaCart
. This short paper relates the conditional objectbased and possibility theorybased approaches for reasoning with conditional statements pervaded with exceptions, to other methods in nonmonotonic reasoning which have been independently proposed: namely, Lehmann's preferential and rational closure entailments which obey normative postulates, the infinitesimal probability approach, and the conditional (modal) logicsbased approach. All these methods are shown to be equivalent with respect to their capabilities for reasoning with conditional knowledge although they are based on different modeling frameworks. It thus provides a unified understanding of nonmonotonic consequence relations. More particularly, conditional objects, a purely qualitative counterpart to conditional probabilities, offer a very simple semantics, based on a 3valued calculus, for the preferential entailment, while in the purely ordinal setting of possibility theory both the preferential and the rational closure entai...
Probabilistic Default Reasoning with Conditional Constraints
 ANN. MATH. ARTIF. INTELL
, 2000
"... We present an approach to reasoning from statistical and subjective knowledge, which is based on a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. More precisely, we introduce the notions of , lexicographic, ..."
Abstract

Cited by 35 (18 self)
 Add to MetaCart
We present an approach to reasoning from statistical and subjective knowledge, which is based on a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. More precisely, we introduce the notions of , lexicographic, and conditional entailment for conditional constraints, which are probabilistic generalizations of Pearl's entailment in system , Lehmann's lexicographic entailment, and Geffner's conditional entailment, respectively. We show that the new formalisms have nice properties. In particular, they show a similar behavior as referenceclass reasoning in a number of uncontroversial examples. The new formalisms, however, also avoid many drawbacks of referenceclass reasoning. More precisely, they can handle complex scenarios and even purely probabilistic subjective knowledge as input. Moreover, conclusions are drawn in a global way from all the available knowledge as a whole. We then show that the new formalisms also have nice general nonmonotonic properties. In detail, the new notions of , lexicographic, and conditional entailment have similar properties as their classical counterparts. In particular, they all satisfy the rationality postulates proposed by Kraus, Lehmann, and Magidor, and they have some general irrelevance and direct inference properties. Moreover, the new notions of  and lexicographic entailment satisfy the property of rational monotonicity. Furthermore, the new notions of , lexicographic, and conditional entailment are proper generalizations of both their classical counterparts and the classical notion of logical entailment for conditional constraints. Finally, we provide algorithms for reasoning under the new formalisms, and we analyze its computational com...
Weak nonmonotonic probabilistic logics
, 2004
"... Towards probabilistic formalisms for resolving local inconsistencies under modeltheoretic probabilistic entailment, we present probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment. We then analyze the nonmonotonic and semantic properties of the new ..."
Abstract

Cited by 24 (6 self)
 Add to MetaCart
Towards probabilistic formalisms for resolving local inconsistencies under modeltheoretic probabilistic entailment, we present probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment. We then analyze the nonmonotonic and semantic properties of the new notions of entailment. In particular, we show that they satisfy the rationality postulates of System P and the property of Rational Monotonicity. Moreover, we show that modeltheoretic probabilistic entailment is stronger than the new notion of lexicographic entailment, which in turn is stronger than the new notion of entailment in System Z. As an important feature of the new notions of entailment in System Z and lexicographic entailment, we show that they coincide with modeltheoretic probabilistic entailment whenever there are no local inconsistencies. We also show that the new notions of entailment in System Z and lexicographic entailment are proper generalizations of their classical counterparts. Finally, we present algorithms for reasoning under the new formalisms, and we give a precise picture of its computational complexity.
Default Reasoning from Conditional Knowledge Bases: Complexity and Tractable Cases
 Artif. Intell
, 2000
"... Conditional knowledge bases have been proposed as belief bases that include defeasible rules (also called defaults) of the form " ! ", which informally read as "generally, if then ." Such rules may have exceptions, which can be handled in different ways. A number of entailment ..."
Abstract

Cited by 19 (11 self)
 Add to MetaCart
Conditional knowledge bases have been proposed as belief bases that include defeasible rules (also called defaults) of the form " ! ", which informally read as "generally, if then ." Such rules may have exceptions, which can be handled in different ways. A number of entailment semantics for conditional knowledge bases have been proposed in the literature. However, while the semantic properties and interrelationships of these formalisms are quite well understood, about their computational properties only partial results are known so far. In this paper, we fill these gaps and first draw a precise picture of the complexity of default reasoning from conditional knowledge bases: Given a conditional knowledge base KB and a default ! , does KB entail ! ? We classify the complexity of this problem for a number of wellknown approaches (including Goldszmidt et al.'s maximum entropy approach and Geffner's conditional entailment), where we consider the general propositional case as well as natural syntactic restrictions (in particular, to Horn and literalHorn conditional knowledge bases). As we show, the more sophisticated semantics for conditional knowledge bases are plagued with intractability in all these fragments. We thus explore cases in which these semantics are tractable, and find that most of them enjoy this property on feedbackfree Horn conditional knowledge bases, which constitute a new, meaningful class of conditional knowledge bases. Furthermore, we generalize previous tractability results from Horn to qHorn conditional knowledge bases, which allow for a limited use of disjunction. Our results complement and extend previous results, and contribute in refining the tractability/intractability frontier of default reasoning from conditional know...
Probabilistic Logic Programming under Inheritance with Overriding
 In Proceedings UAI01
, 2001
"... We present probabilistic logic programming under inheritance with overriding. This approach is based on new notions of entailment for reasoning with conditional constraints, which are obtained from the classical notion of logical entailment by adding inheritance with overriding. This is done by usin ..."
Abstract

Cited by 19 (11 self)
 Add to MetaCart
We present probabilistic logic programming under inheritance with overriding. This approach is based on new notions of entailment for reasoning with conditional constraints, which are obtained from the classical notion of logical entailment by adding inheritance with overriding. This is done by using recent approaches to probabilistic default reasoning with conditional constraints. We analyze the semantic properties of the new entailment relations. We also present algorithms for probabilistic logic programming under inheritance with overriding, and we analyze its complexity in the propositional case. 1
Combining probabilistic logic programming with the power of maximum entropy
 ARTIF. INTELL
, 2004
"... This paper is on the combination of two powerful approaches to uncertain reasoning: logic programming in a probabilistic setting, on the one hand, and the informationtheoretical principle of maximum entropy, on the other hand. More precisely, we present two approaches to probabilistic logic progra ..."
Abstract

Cited by 12 (3 self)
 Add to MetaCart
This paper is on the combination of two powerful approaches to uncertain reasoning: logic programming in a probabilistic setting, on the one hand, and the informationtheoretical principle of maximum entropy, on the other hand. More precisely, we present two approaches to probabilistic logic programming under maximum entropy. The first one is based on the usual notion of entailment under maximum entropy, and is defined for the very general case of probabilistic logic programs over Boolean events. The second one is based on a new notion of entailment under maximum entropy, where the principle of maximum entropy is coupled with the closed world assumption (CWA) from classical logic programming. It is only defined for the more restricted case of probabilistic logic programs over conjunctive events. We then analyze the nonmonotonic behavior of both approaches along benchmark examples and along general properties for default reasoning from conditional knowledge bases. It turns out that both approaches have very nice nonmonotonic features. In particular, they realize some inheritance of probabilistic knowledge along subclass relationships, without suffering from the problem of inheritance blocking and from the drowning problem. They both also satisfy the property of rational monotonicity and several irrelevance properties. We finally present algorithms for both approaches, which are based on generalizations of techniques from probabilistic
Complexity Results for Default Reasoning from Conditional Knowledge Bases
 In Proceedings KR2000
, 1999
"... Conditional knowledge bases have been proposed as belief bases that include defeasible rules (also called defaults) of the form " ! ", which informally read as "generally, if then ." Such rules may have exceptions, which can be handled in different ways. A number of entailm ..."
Abstract

Cited by 9 (3 self)
 Add to MetaCart
Conditional knowledge bases have been proposed as belief bases that include defeasible rules (also called defaults) of the form " ! ", which informally read as "generally, if then ." Such rules may have exceptions, which can be handled in different ways. A number of entailment semantics for conditional knowledge bases have been proposed in the literature. However, while the semantic properties and interrelationships of these formalisms are quite well understood, about their algorithmic properties only partial results are known so far. In this paper, we fill these gaps and draw a precise picture of the complexity of default reasoning from conditional knowledge bases: Given a conditional knowledge base KB and a default ! , does KB entail ! ? We classify the complexity of this problem for a number of wellknown approaches (including Goldszmidt et al.'s maximum entropy approach and Geffner's conditional entailment). We consider the general propositional case as we...
Nonmonotonic Probabilistic Logics between ModelTheoretic Probabilistic Logic and Probabilistic Logic under Coherence
, 2002
"... The notion of logical entailment in modeltheoretic probabilistic logic is based on the idea of performing a conditioning on probability distributions. This is why logical entailment does not handle well the case where the conditioning event always has the probability zero. Recently, it has been arg ..."
Abstract

Cited by 7 (6 self)
 Add to MetaCart
The notion of logical entailment in modeltheoretic probabilistic logic is based on the idea of performing a conditioning on probability distributions. This is why logical entailment does not handle well the case where the conditioning event always has the probability zero. Recently, it has been argued in the artificial intelligence literature that the notion of entailment under coherence, which has been extensively studied especially in the area of statistics, should be used instead for conditioning on zero events. In this paper, however, it turns out that, even though probabilistic entailment under coherence handles situations where we condition on zero events, it is generally too weak. Note that it has been recently shown in [10, 11] that probabilistic entailment under coherence is weaker than modeltheoretic probabilistic entailment. Moreover, probabilistic entailment under coherence is a generalization of default entailment in System . As a central contribution of this paper, we then present new formalisms for conditioning on zero events, which are stronger than probabilistic entailment under coherence. More precisely, we elaborate probabilistic generalizations of more sophisticated notions of default entailment from conditional knowledge bases that lie between modeltheoretic probabilistic entailment and probabilistic entailment under coherence. That is, the new probabilistic formalisms properly generalize their counterparts in classical default reasoning, they are weaker than modeltheoretic probabilistic entailment, and they are stronger than probabilistic entailment under coherence. We also analyze the nonmonotonic properties of the new probabilistic formalisms. Moreover, we provide algorithms for computing tight consequences under the new formalisms, and dra...
A coherencebased approach to default reasoning
 In Proceedings of the FAPR'97, volume LNAI 1244
, 1997
"... Abstract. In the last 15 years, several default reasoning systems have been proposed to deal with rules having exceptions. Each of these systems has been shown to be either cautious (where some intuitive conclusions do not follow from the default base), or adventurous (some debatable conclusions are ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
Abstract. In the last 15 years, several default reasoning systems have been proposed to deal with rules having exceptions. Each of these systems has been shown to be either cautious (where some intuitive conclusions do not follow from the default base), or adventurous (some debatable conclusions are inferred). However, the cautiousness and the adventurous aspect of these systems are often due to the incomplete way of describing our knowledge, and that plausible conclusions depend on the meaning (semantics) assigned to propositional symbols. This paper mainly contains two parts. The first part discusses, with simple default bases (where the used symbols have no a priori meaning), which assumptions are assumed when a given conclusion is considered as intuitive. The second part investigates a local approach to deal with default rules of the form &quot;generally, if ct then I~ &quot; having possibly some exceptions. The idea is that when a conflict appears (due to observing exceptional situations), we first localize the sets of pieces of information which are responsible for conflicts. Next, using a new definition of specificity, we attach priorities to default rules inside each conflict. Lastly, three proposals are made to solve conflicts and restore the consistency of the knowledge base. A comparative study with some existing systems is given. I.