Conditional constraints, implication based rules, and possibilistic rule bases: are they any good?

To answer the question imposed in the title right away: Yes, they are. Conditional constraints, implication based rules, and possibilistic rule bases are different notions representing the very same concept. And this concept is as useful and interesting as the well known and widely used Mamdani approach. So far, real success in applying fuzzy rule bases is restricted to fuzzy control and Mamdani inference. We claim that the lack of applications making use of possibilistic reasoning is mainly due to a lack of understanding how to deal with rules based on possibility distributions. Mamdani inference as used in fuzzy control and possibilistic reasoning are complementary mechanisms. They are complementary with respect to the way they deal with incomplete and inconsistent information. From that point of view, it is not surprising that using the very same rule base in both settings does not work. This means, that the standard way of specifying Mamdani knowledge bases does not help in the possibilistic case. Based on the assumption that rule based systems are helpful and manageable as long as rules represent local information we present a new way how to specify possibilistic rule bases. In order to prove the usefulness of this approach, we show that there are some major drawbacks and limitations of Mamdani inference, that are easily solved by correctly applying possibilistic reasoning. We do not claim, however, that possibilistic reasoning is the one and only mechanism to choose. Both mechanisms have their advantages and drawbacks and it heavily depends on the problem at hand whether one or the other mechanism should be chosen. In complex situations we expect a combined mechanism to be useful

Nonmonotonic Probabilistic Logics between Model-Theoretic Probabilistic Logic and Probabilistic Logic under Coherence

Recently, it has been shown that probabilistic entailment under coherence is weaker than model-theoretic 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 model-theoretic probabilistic entailment and probabilistic entailment under coherence. That is, the new formalisms properly generalize their counterparts in classical default reasoning, they are weaker than model-theoretic 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 well-known standard ones.Comment: 10 pages; in Proceedings of the 9th International Workshop on Non-Monotonic Reasoning (NMR-2002), Special Session on Uncertainty Frameworks in Nonmonotonic Reasoning, pages 265-274, Toulouse, France, April 200

Probabilistic Default Reasoning with Conditional Constraints

We propose a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. In detail, we generalize the notions of Pearl's entailment in system Z, Lehmann's lexicographic entailment, and Geffner's conditional entailment to conditional constraints. We give some examples that show that the new notions of z-, lexicographic, and conditional entailment have similar properties like their classical counterparts. Moreover, we show that the new notions of z-, lexicographic, and conditional entailment are proper generalizations of both their classical counterparts and the classical notion of logical entailment for conditional constraints.Comment: 8 pages; to appear in Proceedings of the Eighth International Workshop on Nonmonotonic Reasoning, Special Session on Uncertainty Frameworks in Nonmonotonic Reasoning, Breckenridge, Colorado, USA, 9-11 April 200

Modal logics are coalgebraic

Applications of modal logics are abundant in computer science, and a large number of structurally different modal logics have been successfully employed in a diverse spectrum of application contexts. Coalgebraic semantics, on the other hand, provides a uniform and encompassing view on the large variety of specific logics used in particular domains. The coalgebraic approach is generic and compositional: tools and techniques simultaneously apply to a large class of application areas and can moreover be combined in a modular way. In particular, this facilitates a pick-and-choose approach to domain specific formalisms, applicable across the entire scope of application areas, leading to generic software tools that are easier to design, to implement, and to maintain. This paper substantiates the authors' firm belief that the systematic exploitation of the coalgebraic nature of modal logic will not only have impact on the field of modal logic itself but also lead to significant progress in a number of areas within computer science, such as knowledge representation and concurrency/mobility

Combining link and content-based information in a Bayesian inference model for entity search

An architectural model of a Bayesian inference network to support entity search in semantic knowledge bases is presented. The model supports the explicit combination of primitive data type and object-level semantics under a single computational framework. A flexible query model is supported capable to reason with the availability of simple semantics in querie