Selecting Uncertainty Calculi and Granularity: An Experiment in Trading-Off Precision and Complexity

The management of uncertainty in expert systems has usually been left to ad hoc representations and rules of combinations lacking either a sound theory or clear semantics. The objective of this paper is to establish a theoretical basis for defining the syntax and semantics of a small subset of calculi of uncertainty operating on a given term set of linguistic statements of likelihood. Each calculus is defined by specifying a negation, a conjunction and a disjunction operator. Families of Triangular norms and conorms constitute the most general representations of conjunction and disjunction operators. These families provide us with a formalism for defining an infinite number of different calculi of uncertainty. The term set will define the uncertainty granularity, i.e. the finest level of distinction among different quantifications of uncertainty. This granularity will limit the ability to differentiate between two similar operators. Therefore, only a small finite subset of the infinite number of calculi will produce notably different results. This result is illustrated by two experiments where nine and eleven different calculi of uncertainty are used with three term sets containing five, nine, and thirteen elements, respectively. Finally, the use of context dependent rule set is proposed to select the most appropriate calculus for any given situation. Such a rule set will be relatively small since it must only describe the selection policies for a small number of calculi (resulting from the analyzed trade-off between complexity and precision).

Using T-Norm Based Uncertainty Calculi in a Naval Situation Assessment Application

RUM (Reasoning with Uncertainty Module), is an integrated software tool based on a KEE, a frame system implemented in an object oriented language. RUM's architecture is composed of three layers: representation, inference, and control. The representation layer is based on frame-like data structures that capture the uncertainty information used in the inference layer and the uncertainty meta-information used in the control layer. The inference layer provides a selection of five T-norm based uncertainty calculi with which to perform the intersection, detachment, union, and pooling of information. The control layer uses the meta-information to select the appropriate calculus for each context and to resolve eventual ignorance or conflict in the information. This layer also provides a context mechanism that allows the system to focus on the relevant portion of the knowledge base, and an uncertain-belief revision system that incrementally updates the certainty values of well-formed formulae (wffs) in an acyclic directed deduction graph. RUM has been tested and validated in a sequence of experiments in both naval and aerial situation assessment (SA), consisting of correlating reports and tracks, locating and classifying platforms, and identifying intents and threats. An example of naval situation assessment is illustrated. The testbed environment for developing these experiments has been provided by LOTTA, a symbolic simulator implemented in Flavors. This simulator maintains time-varying situations in a multi-player antagonistic game where players must make decisions in light of uncertain and incomplete data. RUM has been used to assist one of the LOTTA players to perform the SA task.

Uncertainty and Incompleteness

Two major difficulties in using default logics are their intractability and the problem of selecting among multiple extensions. We propose an approach to these problems based on integrating nommonotonic reasoning with plausible reasoning based on triangular norms. A previously proposed system for reasoning with uncertainty (RUM) performs uncertain monotonic inferences on an acyclic graph. We have extended RUM to allow nommonotonic inferences and cycles within nonmonotonic rules. By restricting the size and complexity of the nommonotonic cycles we can still perform efficient inferences. Uncertainty measures provide a basis for deciding among multiple defaults. Different algorithms and heuristics for finding the optimal defaults are discussed.

Now that I Have a Good Theory of Uncertainty, What Else Do I Need?

Rather than discussing the isolated merits of a nominative theory of uncertainty, this paper focuses on a class of problems, referred to as Dynamic Classification Problem (DCP), which requires the integration of many theories, including a prescriptive theory of uncertainty. We start by analyzing the Dynamic Classification Problem and by defining its induced requirements on a supporting (plausible) reasoning system. We provide a summary of the underlying theory (based on the semantics of many-valed logics) and illustrate the constraints imposed upon it to ensure the modularity and computational performance required by the applications. We describe the technologies used for knowledge engineering (such as object-based simulator to exercise requirements, and development tools to build the Knowledge Base and functionally validate it). We emphasize the difference between development environment and run-time system, describe the rule cross-compiler, and the real-time inference engine with meta-reasoning capabilities. Finally, we illustrate how our proposed technology satisfies the pop's requirements and analyze some of the lessons reamed from its applications to situation assessment problems for Pilot's Associate and Submarine Commander Associate.

Extending Term Subsumption systems for Uncertainty Management

A major difficulty in developing and maintaining very large knowledge bases originates from the variety of forms in which knowledge is made available to the KB builder. The objective of this research is to bring together two complementary knowledge representation schemes: term subsumption languages, which represent and reason about defining characteristics of concepts, and proximate reasoning models, which deal with uncertain knowledge and data in expert systems. Previous works in this area have primarily focused on probabilistic inheritance. In this paper, we address two other important issues regarding the integration of term subsumption-based systems and approximate reasoning models. First, we outline a general architecture that specifies the interactions between the deductive reasoner of a term subsumption system and an approximate reasoner. Second, we generalize the semantics of terminological language so that terminological knowledge can be used to make plausible inferences. The architecture, combined with the generalized semantics, forms the foundation of a synergistic tight integration of term subsumption systems and approximate reasoning models.

Integrating Case-Based and Rule-Based Reasoning: the Possibilistic Connection

Rule based reasoning (RBR) and case based reasoning (CBR) have emerged as two important and complementary reasoning methodologies in artificial intelligence (Al). For problem solving in complex, real world situations, it is useful to integrate RBR and CBR. This paper presents an approach to achieve a compact and seamless integration of RBR and CBR within the base architecture of rules. The paper focuses on the possibilistic nature of the approximate reasoning methodology common to both CBR and RBR. In CBR, the concept of similarity is casted as the complement of the distance between cases. In RBR the transitivity of similarity is the basis for the approximate deductions based on the generalized modus ponens. It is shown that the integration of CBR and RBR is possible without altering the inference engine of RBR. This integration is illustrated in the financial domain of mergers and acquisitions. These ideas have been implemented in a prototype system called MARS.