This paper discusses a mathematical analysis for learning weights in a similarity function. Although there are many works on theoretical analyses of case-based reasoning systems [Aha 91, Albert 91, Janke 93, Langley 93], none has yet theoretically analyzed methods of producing a proper similarity function in accordance with a tendency of cases which many people have already proposed and empirically analyzed [Aha 89, Callan 91, Cardie 93, Stanfill 86]. In this paper, as the first step, we provide a PAC learning framework for weights with two kinds of distance information; one is qualitative distance information and the other is relative distance information. Qualitative distance information represents if case A is similar to case B or not and relative distance information represents if case A is more similar to case B than to case C. We give a mathematical analysis for learning weights from these information. In this setting, we show that we can efficiently learn a weight which has an error rate less than ε with a probability more than 1-δ such that the size of distance information is polynomially bounded in the dimension , n , and the inverses of ε and δ, and the running time is polynomially bounded in the size of distance information.

In this paper, we introduce a temporal logic called Interval Division Logic IDL based on the constructive temporal ontology. In IDL,time is regarded as a constructive object which is built from an interval by iterating the interval division in the process of temporal reasoning. Namely, every time an unknown (past, present or future) event is recognized, the current time structure is modified by dividing its corresponding interval into two intervals before and after that event, so that the time structure of IDL has a form of binary tree of which leaves constitute the current sequence of events. Although IDL itself is a sound and complete logical system which is as expressive as the Buich infinite tree automata, we extend IDL into a nonmonotonic version based on the model preference method in order to examine how the persistence problem is treated on this constructive ontology. Since the persistence itself is due to the retention of the belief rather than the inertia of real world, the interpretation for a sequence of events depends not only on the temporal order of the events but also on the epistemological order in which each event in the sequence is recognized. Therefore, we use the order of temporal inference rather than the temporal order for the model minimization. Temporal prediction and nondeterministic event problems are discussed in this framework.

Generally, all the values of each attribute do not always work well in induction of any domain. It often causes poor performance of decision trees to handle thus values as ones of adequate discriminating Power. This paper presents a method of building probabilistic decision trees from continuous-valued attributes, considering locality of their discriminating powers. We cluster out the set of the training data into subsets, focussing on correlations among value of attribute and probabilities of identifications with each class. A set of each distribution of probability density of data, which is presumed from each subset, generate such branches corresponding to the level of the discriminating power and dealing with the noises in the attribute values of data stochastically. Empirical results compared with C4.5 shows some advantages, in applying them to real-world domain, diagnosis problem of image-processed data of cancer cells.

Several studies have been carried out with the objective of introducing partial orders into probability distributions. However, there has been no study that introduces such a partial order into probability distributions as can be reasoned by a logic. This paper shows that discrete probability distributions can be reasoned by intuitionistic logic. The space of multi-linear functions, which is an extension of Boolean algebra, can be made into a Euclidean space. The space is Heyting algebra, which is the model of intuitionistic logic. Therefore, multi-linear functions can be reasoned by intuitionistic logic. Discrete probability distributions can be corresponded to multi-linear functions using the principle of indifference. So discrete probability distributions can be reasoned by intuitionistic logic.

Enabling Multiple-context type Truth Maintenance Systems such as ATMS and CMS to accept any logical (propositional) formula cannot avoid enumerating prime implicates from the set of logical formula. Since such an enumeration is an NP-complete problem, most systems accept some restricted logical formula to avoid its inefficiency. BDD(Binary Decision Diagram) is an efficient representation of Boolean formula and most its manipulations can be processed quite efficiently. In this paper, we present the BDD-based Multiple-context type Truth Maintenance System (BMTMS). BMTMS provides interfaces of three levels. Two levels are for conventional ATMS and its variants and one is to exploit full capabilities of BMTMS. QPE (Qualitative Physics Engine) is used to compare BMTMS and ATMS. BMTMS is quite efficient compared with CMS, because it processes most TMS operations without enumerating the prime implicates.

Default Logic is one of the most popular formalizations of nonmonotonic reasoning and a subclass of defaults called normal defaults has been used to formalize commonsense reasoning. Recent research such as Yale shooting problem, however, has revealed that the usage of arbitrary defaults is necessary for some commonsense reasoning. Although there are correct goal-directed procedures for normal default theories and some other restricted classes of default theories, no one has yet proposed any goal-directed proof procedure for a full class of arbitrary defaults even in a propositional case. In this paper, we present a correct goal-directed proof procedure for the extension membership problem of arbitrary consistent propositional default theories. This procedure is obtained by extending our previous procedure for general (abductive) logic program with integrity constraints so that clauses instead of atoms can be used in a head or a body of rules. Moreover, this procedure is complete if a default theory is finite. We also show that this procedure can be used for consistency checks of addition of rules.

This paper describes a computational cognitive model of display-based human-computer interaction based on Norman's action theory. The model consists of goals, stages of evaluation, and stages of execution; in the former, the processes of generating display representation and its elaboration are included, and in the latter, the processes of selecting candidate objects for a next action and selecting an action-object pair are assumed. Execution of these processes is modeled with a symbolic-connectionist theory of adaptive expertise, the construction-integration theory of text comprehension, proposed by Kintsch (1988). The theory is contrasted with a family of theories for routine expertise, which characterizes quick and accurate problem solving behavior for familiar types of problems. However, it has only modest capabilities in dealing with novel types of problems. This paper starts with a claim that the display-based HCI requires adaptive expertise, in which an example task in the HCI domain is used for illustration. A brief explanation of the model of display-based HCI follows. The model has a distinctive feature that it can produce erroneous actions as well as correct actions even if the model is provided with sufficient knowledge for selecting correct actions and without assuming built-in knowledge for committing errors. The paper describes that it is due to the cognitive architecture, the construction-integration theory, assumed to execute the action selection processes.