: Belief functions are mathematical objects defined to satisfy three axioms that look somewhat similar to the Kolmogorov axioms defining probability functions. We argue that there are (at least) two useful and quite different ways of understanding belief functions. The first is as a generalized probability function (which technically corresponds to the inner measure induced by a probability function). The second is as a way of representing evidence. Evidence, in turn, can be understood as a mapping from probability functions to probability functions. It makes sense to think of updating a belief if we think of it as a generalized probability. On the other hand, it makes sense to combine two beliefs (using, say, Dempster's rule of combination) only if we think of the belief functions as representing evidence. Many previous papers have pointed out problems with the belief function approach; the claim of this paper is that these problems can be explained as a consequence of confounding the...

: We define a new notion of conditional belief, which plays the same role for Dempster-Shafer belief functions as conditional probability does for probability functions. Our definition is different from the standard definition given by Dempster, and avoids many of the well-known problems of that definition. Just as the conditional probability P r(\DeltajB) is a probability function which is the result of conditioning on B being true, so too our conditional belief function Bel(\DeltajB) is a belief function which is the result of conditioning on B being true. We define the conditional belief as the lower envelope (that is, the inf) of a family of conditional probability functions, and provide a closed-form expression for it. An alternate way of understanding our definition of conditional belief is provided by considering ideas from an earlier paper [FH91], where we connect belief functions with inner measures. In particular, we show here how to extend the definition of conditional pro...

: Judgments of similarity and soundness are important aspects of human analogical processing. This paper explores how these judgments can be modeled using SME, a simulation of Gentner's structure-mapping theory. We focus on structural evaluation, explicating several principles which psychologically plausible algorithms should follow. We introduce the Specificity Conjecture, which claims that naturalistic representations include a preponderance of appearance and low-order information. We demonstrate via computational experiments that this conjecture affects how structural evaluation should be performed, including the choice of normalization technique and how the systematicity preference is implemented. 1 Introduction Judging soundness and structural similarity are important aspects of human analogical processing. While other criteria (such as factual correctness and relevance to current goals) are also important, they cannot replace structural evaluation. For example, neither factual ...

The aim of this paper is to provide a tool which makes possible non-monotonic reasoning in a propositional knowledge system based on multivalued logic with certainty factors and fuzzy logic. The support system which results in the non-monotony will be a Truth Maintenance System (TMS). Particularly, we will use ATMS (TMS based on assumptions) defined by De Kleer. From this ATMS we will extend its use in case we have monotonic reasoning systems based on [0,1] valued logic and fuzzy logic. The latter case will be designed to reason with fuzzy truth values, although a parallel approach can be made by using directly linguistic labels. Keywords: Truth Maintenance System, Fuzzy Logic, Multivalued Logic, Knowledge Base System, Inconsistency. 1 Introduction Knowledge systems are used with ever greater efficacy in a great deal of scientific and social activities. Not long ago, was measured this efficacy according to the quality of knowledge representation and to the correct working of the reas...

We provide an overview of research on computational models of analogy-making. The survey ranges from a fairly basic introduction to the topic of computational analogy-making to reporting some quite recent advanced results concerning the study of these systems, their properties and particularities. When doing so, we mainly take a cognitive modeling and computer sciences inspired point of view, mostly discarding other possible criteria such as psychological or biological adequacy. We introduce different abstract types of computational models of analogy-making in terms of symbol-based models, connectionist models and hybrid models, before having a more detailed look at one or two characteristic examples for implemented systems of each category. Concludingly, after summarizing the characteristics of the studied systems in a crisp synopsis, we present some basic aspects of Heuristic-Driven Theory Projection, a mathematically sound framework for analogy-making currently under construction. Chapter 1