Results 1  10
of
14
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 (20 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...
Probabilistic Logic under Coherence: Complexity and Algorithms
 In Proceedings ISIPTA01
, 2001
"... We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore the relationship between coherencebased and classical modeltheoretic probabilistic logic. Interestingly, we show that the notions of gcoherence and of gcoherent entailment can be expre ..."
Abstract

Cited by 22 (11 self)
 Add to MetaCart
We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore the relationship between coherencebased and classical modeltheoretic probabilistic logic. Interestingly, we show that the notions of gcoherence and of gcoherent entailment can be expressed by combining notions in modeltheoretic probabilistic logic with concepts from default reasoning. Using these results, we analyze the computational complexity of probabilistic reasoning under coherence. Moreover, we present new algorithms for deciding gcoherence and for computing tight gcoherent intervals, which reduce these tasks to standard reasoning tasks in modeltheoretic probabilistic logic. Thus, efficient techniques for modeltheoretic probabilistic reasoning can immediately be applied for probabilistic reasoning under coherence, for example, column generation techniques. We then describe two other interesting techniques for efficient modeltheoretic probabilistic reasoning in the conjunctive case.
Weak nonmonotonic probabilistic logics
"... 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 21 (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.
Inference in conditional probability logic
 Kybernetika
, 2006
"... An important field of probability logic is the investigation of inference rules that propagate point probabilities or, more generally, interval probabilities from premises to conclusions. Conditional probability logic (CPL) interprets the common sense expressions of the form “if..., then... ” by con ..."
Abstract

Cited by 13 (10 self)
 Add to MetaCart
An important field of probability logic is the investigation of inference rules that propagate point probabilities or, more generally, interval probabilities from premises to conclusions. Conditional probability logic (CPL) interprets the common sense expressions of the form “if..., then... ” by conditional probabilities and not by the probability of the material implication. An inference rule is probabilistically informative if the coherent probability interval of its conclusion is not necessarily equal to the unit interval [0, 1]. Not all logically valid inference rules are probabilistically informative and vice versa. The relationship between logically valid and probabilistically informative inference rules is discussed and illustrated by examples such as the modus ponens or the affirming the consequent. We propose a method to evaluate the strength of CPL inference rules. Finally, an example of a proof is given that is purely based on CPL inference rules.
Towards a Mental Probability Logic
, 2007
"... We propose probability logic as an appropriate standard of reference for evaluating human inferences. Probability logical accounts of nonmonotonic reasoning with system p, and conditional syllogisms (modus ponens, etc.) are explored. Furthermore, we present categorical syllogisms with intermediate ..."
Abstract

Cited by 12 (8 self)
 Add to MetaCart
We propose probability logic as an appropriate standard of reference for evaluating human inferences. Probability logical accounts of nonmonotonic reasoning with system p, and conditional syllogisms (modus ponens, etc.) are explored. Furthermore, we present categorical syllogisms with intermediate quantifiers, like the “most... ” quantifier. While most of the paper is theoretical and intended to stimulate psychological studies, we summarize our empirical studies on human nonmonotonic reasoning.
Ordinal and probabilistic representations of acceptance
 J. Artificial Intelligence Research
, 2004
"... An accepted belief is a proposition considered likely enough by an agent, to be inferred from as if it were true. This paper bridges the gap between probabilistic and logical representations of accepted beliefs. To this end, natural properties of relations on propositions, describing relative streng ..."
Abstract

Cited by 11 (4 self)
 Add to MetaCart
An accepted belief is a proposition considered likely enough by an agent, to be inferred from as if it were true. This paper bridges the gap between probabilistic and logical representations of accepted beliefs. To this end, natural properties of relations on propositions, describing relative strength of belief are augmented with some conditions ensuring that accepted beliefs form a deductively closed set. This requirement turns out to be very restrictive. In particular, it is shown that the sets of accepted belief of an agent can always be derived from a family of possibility rankings of states. An agent accepts a proposition in a given context if this proposition is considered more possible than its negation in this context, for all possibility rankings in the family. These results are closely connected to the nonmonotonic 'preferential' inference system of Kraus, Lehmann and Magidor and the socalled plausibility functions of Friedman and Halpern. The extent to which probability theory is compatible with acceptance relations is laid bare. A solution to the lottery paradox, which is considered as a major impediment to the use of nonmonotonic inference is proposed using a special kind of probabilities (called lexicographic, or bigstepped). The setting of acceptance relations also proposes another way of approaching the theory of belief change after the works of Gärdenfors and colleagues. Our view considers the acceptance relation as a primitive object from which belief sets are derived in various contexts. 1.
Nonmonotonicity and human probabilistic reasoning
 in: Proceedings of the 6th Workshop on Uncertainty Processing, Hejnice, September 24–27
"... Nonmonotonic logics allow—contrary to classical (monotone) logics— for withdrawing conclusions in the light of new evidence. Nonmonotonic reasoning is often claimed to mimic human common sense reasoning. Only a few studies, though, have investigated this claim empirically. system p is a central, bro ..."
Abstract

Cited by 11 (9 self)
 Add to MetaCart
Nonmonotonic logics allow—contrary to classical (monotone) logics— for withdrawing conclusions in the light of new evidence. Nonmonotonic reasoning is often claimed to mimic human common sense reasoning. Only a few studies, though, have investigated this claim empirically. system p is a central, broadly accepted nonmonotonic reasoning system that proposes basic rationality postulates. We previously investigated empirically a probabilistic interpretation of three selected rules of system p. We found a relatively good agreement of human reasoning and principles of nonmonotonic reasoning according to the coherence interpretation of system p. This study reports an experiment on the cautious monotonicity Rule and its “incautious ” counterpart that is not contained in system p, namely the monotonicity Rule. In accordance with our previous results, the data suggest that people reason nonmonotonically: the subjects in the cautious monotonicity condition infer significantly tighter intervals close to the coherence interpretation of system p compared with the subjects in the incautious monotonicity condition where rather wide (and hence noninformative) intervals are inferred. 1
Nonmonotonic Probabilistic Logics between ModelTheoretic Probabilistic Logic and Probabilistic Logic under Coherence
, 2002
"... Recently, it has been shown that probabilistic entailment under coherence is weaker than modeltheoretic probabilistic entailment. Moreover, probabilistic entailment under coherence is a generalization of default entailment in System P. In this paper, we continue this line of research by presenting ..."
Abstract

Cited by 7 (6 self)
 Add to MetaCart
Recently, it has been shown that probabilistic entailment under coherence is weaker than modeltheoretic probabilistic entailment. Moreover, probabilistic entailment under coherence is a generalization of default entailment in System P. In this paper, we continue this line of research by presenting probabilistic generalizations of more sophisticated notions of classical default entailment that lie between modeltheoretic probabilistic entailment and probabilistic entailment under coherence. That is, the new 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. The new formalisms are useful especially for handling probabilistic inconsistencies related to conditioning on zero events. They can also be applied for probabilistic belief revision. More generally, in the same spirit as a similar previous paper, this paper sheds light on exciting new formalisms for probabilistic reasoning beyond the wellknown standard ones.
Nonmonotonic probabilistic reasoning under variablestrength inheritance with overriding
 SYNTHESE
, 2005
"... We present new probabilistic generalizations of Pearl’s entailment in System ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
We present new probabilistic generalizations of Pearl’s entailment in System
Independence for Full Conditional Measures, Graphoids and Bayesian Networks
, 2007
"... This paper examines definitions of independence for events and variables in the context of full conditional measures; that is, when conditional probability is a primitive notion and conditioning is allowed on null events. Several independence concepts are evaluated with respect to graphoid propertie ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
This paper examines definitions of independence for events and variables in the context of full conditional measures; that is, when conditional probability is a primitive notion and conditioning is allowed on null events. Several independence concepts are evaluated with respect to graphoid properties; we show that properties of weak union, contraction and intersection may fail when null events are present. We propose a concept of “full” independence, characterize the form of a full conditional measure under full independence, and suggest how to build a theory of Bayesian networks that accommodates null events.