Independence { the study of what is relevant to a given problem of reasoning { has received an increasing attention from the AI community. In this paper, we consider two basic forms of independence, namely, a syntactic one and a semantic one. We show features and drawbacks of them. In particular, while the syntactic form of independence is computationally easy to check, there are cases in which things that intuitively are not relevant are not recognized as such. We also consider the problem of forgetting, i.e., distilling from a knowledge base only the part that is relevant to the set of queries constructed from a subset of the alphabet. While such process is computationally hard, it allows for a simpli - cation of subsequent reasoning, and can thus be viewed as a form of compilation: once the relevant part of a knowledge base has been extracted, all reasoning tasks to be performed can be simpli ed.

We present a compiler for converting CNF formulas into deterministic, decomposable negation normal form (d-DNNF). This is a

We have recently proposed a tractable logical form, known as deterministic, decomposable negation normal form (d-DNNF). We have shown that d-DNNF supports a number of logical operations in polynomial time, including clausal entailment, model counting, model enumeration, model minimization, and probabilistic equivalence testing. In this paper, we discuss another major application of this logical form: the implementation of multi-linear functions (of exponential size) using arithmetic circuits (that are not necessarily exponential). Specifically, we show that each multi–linear function can be encoded using a propositional theory, and that each d-DNNF of the theory corresponds to an arithmetic circuit that implements the encoded multi–linear function. We discuss the application of these results to factoring belief networks, which can be viewed as multi–linear functions as has been shown recently. We discuss the merits of the proposed approach for factoring belief networks, and present experimental results showing how it can handle efficiently belief networks that are intractable to structure–based methods for probabilistic inference.

In this paper, we investigate the extent to which knowledge compilation can be used to improve inference from propositional weighted bases. We present a general notion of compilation of a weighted base that is parametrized by any equivalence--preserving compilation function.

Darwiche has recently proposed the representation of a belief network as a multivariate polynomial, allowing one to reduce probabilistic inference into a process of evaluating and dierentiating polynomials.

This article discusses several implementation aspects for Dempster-Shafer belief functions. The main objective is to propose an appropriate representation of mass functions and efficient data structures and algorithms for the two basic operations of combination and marginalization. © 2003 Wiley Periodicals, Inc. 1.

Although the equivalence of two Ordered Binary Decision Diagrams (OBDDs) can be decided in polynomial time, the equivalence of two Free Binary Decision Diagrams (FBDDs) is only known to be probabilistically decidable in polynomial time. FBDDs are a strict superset of OBDDs, and are more succinct than OBDDs, which explains the interest in testing their equivalence. We show that the probabilistic equivalence test for FBDDs holds for the class of deterministic, decomposable negation normal forms (d-DNNFs), which forms a strict superset of FBDDs and is more succinct than FBDDs. Our

In large open networks, handling trust and authenticity adequately is an important prerequisite for security. In a distributed approach, all network users are allowed to issue various types of credentials, e.g. certificates, recommendations, revocations, ratings, etc. This paper proposes such a distributed approach, in which the evaluation of trust and authenticity is based on so-called credential networks. The corresponding formal model includes many existing trust models as special cases. 1 1.

In this paper, we investigate the extent to which knowledge compilation can be used to circumvent the complexity of skeptical inference from a stratified belief base (SBB). We first analyze the compilability of skeptical inference from an SBB, under various requirements concerning both the selection policy under consideration, the possibility to make the stratification vary at the on-line query answering stage and the expected complexity of inference from the compiled form. Not surprisingly, the results are mainly negative. However, since they concern the worst case situation only, they do not prevent a compilation-based approach from being practically useful for some families of instances. While many approaches to compile an SBB can be designed, we are primarily interested in those which take advantage of existing knowledge compilation techniques for classical inference. Specifically, we present a general framework for compiling SBBs into so-called C-normal SBBs, where C is any tractable class for clausal entailment which is the target class of a compilation function. Another major advantage of the proposed approach lies in the flexibility of the C-normal belief bases obtained, which means that changing the stratification does not require to re-compile the SBB. For several families of compiled SBBs and several selection policies, the complexity of skeptical inference is identified. Some tractable restrictions are exhibited for each policy. Finally, some empirical results are presented.

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