. A rapidly growing number of user and student modeling systems have employed numerical techniques for uncertainty management. The three major paradigms are those of Bayesian networks, the Dempster-Shafer theory of evidence, and fuzzy logic. In this overview, each of the first three main sections focuses on one of these paradigms. It first introduces the basic concepts by showing how they can be applied to a relatively simple user modeling problem. It then surveys systems that have applied techniques from the paradigm to user or student modeling, characterizing each system within a common framework. The final main section discusses several aspects of the usability of these techniques for user and student modeling, such as their knowledge engineering requirements, their need for computational resources, and the communicability of their results. Key words: numerical uncertainty management, Bayesian networks, Dempster-Shafer theory, fuzzy logic, user modeling, student modeling 1. Introdu...

This paper surveys methods for representing and reasoning with imperfect information. It opens with an attempt to classify the different types of imperfection that may pervade data, and a discussion of the sources of such imperfections. The classification is then used as a framework for considering work that explicitly concerns the representation of imperfect information, and related work on how imperfect information may be used as a basis for reasoning. The work that is surveyed is drawn from both the field of databases and the field of artificial intelligence. Both of these areas have long been concerned with the problems caused by imperfect information, and this paper stresses the relationships between the approaches developed in each.

The paper examines ways in which the meanings of geographical concepts are affected by the phenomenon of vagueness. A logical analysis based on the theory of supervaluation semantics is developed and employed to describe differences and logical dependencies between different senses of vague concepts. Particular attention is given to analysing the concept of `forest' which exhibits many kinds of vagueness.

From laser-scanned data to feature human model: a system based on

At AAAI'93, Elkan has claimed to have a result trivializing fuzzy logic. This trivialization is based on too strong a view of equivalence in fuzzy logic and relates to a fully compositional treatment of uncertainty. Such a treatment is shown to be impossible in this paper. We emphasize the distinction between i) degrees of partial truth which are allowed to be truth functional and which pertain to gradual (or fuzzy) propositions, and ii) degrees of uncertainty which cannot be compositional with respect to all the connectives when attached to classical propositions. This distinction is exemplified by the difference between fuzzy logic and possibilistic logic. We also investigate an almost compositional uncertainty calculus, but it is shown to lack expressiveness. 1. Introduction There is a very active research trend in Artificial Intelligence concerning the management of uncertainty in knowledge-based systems. This trend is still influenced by the MYCIN experiments (Buchanan & Shortli...

The paper investigates the characterisation of vague concepts within the framework of modal logic. This work builds on the supervaluation approach of Fine and exploits the idea of a precisification space. A simple language is presented with two modalities: a necessity operator and an operator `it is unequivocal that' which is used to articulate the logic of vagueness. Both these operators obey the schemas of the logic S5. I show how this language can be used to represent logical properties of vague predicates which have a variety of possible precise interpretations. I consider the use within KR systems of number of different entailment relations that can be specified for this language. Certain vague predicates (such as `tall') may be indefinite even when there is no ambiguity in meaning. These can be accounted for by means of a three-valued logic, incorporating a definiteness operator. I also show the relationship between observable quantities (such as height) and vague predicates (su...

Cox's Theorem provides a theoretical basis for using probability theory as a general logic of plausible inference. The theorem states that any system for plausible reasoning that satisfies certain qualitative requirements intended to ensure consistency with classical deductive logic and correspondence with commonsense reasoning is isomorphic to probability theory. However, the requirements used to obtain this result have been the subject of much debate. We review Cox's Theorem, discussing its requirements, the intuition and reasoning behind these, and the most important objections, and finish with an abbreviated proof of the theorem.

The formal concept of logical equivalence in fuzzy logic, while theoretically sound, seems impractical. The misinterpretation of this concept has led to some pessimistic conclusions. Motivated by practical interpretation of truth values for fuzzy propositions, we take the class (lattice) of all sub-intervals of the unit interval [0,1] as the truth value space for fuzzy logic, subsuming the traditional class of numerical truth values from [0,1]. The associated concept of logical equivalence is stronger than the traditional one. Technically, we are dealing with much smaller set of pairs of equivalent formulas, so that we are able to check equivalence algorithmically. The checking is done by showing that our strong equivalence notion coincides with the equivalence in logic programming.

Abstract not found

We present a semantics for certain Fuzzy Logics of vagueness by identifying the fuzzy truth value an agent gives to a proposition with the number of independent arguments that the agent can muster in favour of that proposition. Introduction In the literature the expression `Fuzzy Logic' is used in two separate ways (at least). One is where `truth values' are intended to stand for measures of belief (or condence, or certainty of some sort) and the expression `Fuzzy Logic' is taken as a synonym for the assumption that belief values are truth functional. That is, if w() denotes an agent's belief value (on the usual scale [0; 1]) for 2 SL, where SL is the set of sentences from a nite propositional language L built up using the connectives :; ^; _ (we shall consider implication later), then w satises w(:) = F: (w()); w( ^ ) = F^ (w(); w()); w( _ ) = F_ (w(); w()); (1) for some xed functions F: : [0; 1] ! [0; 1] and F^ ; F_ : [0; 1] 2 ! [0; 1]; where ; 2 SL. Two p...