Statisticians deal with numerical data, but they do not discover logical propositions in the numerical data. This paper presents a method to discover logical propositions in numerical data. The author presented a topological model for non-classical logics. The author also showed that the extended model is a Euclidean space and the orthonormal system is the logical functions corresponding to the atoms in Boolean algebra. The method presented in this paper is based on this topological model for logics. A function obtained by multiple regression analysis in which data are normalized to [O, 1] belongs to this Euclidean space. Therefore, the function represents a non-classical logical proposition and it can be approximated by a classical logical function representing a classical logical proposition. The algorithm is as follows. 1. The numerical data are normalized to [0, 1]. 2. Multiple regression analysis is performed. 3. The result is a logical function of nonclassical logics, and it is approximated by a classical logical function. 4. The classical logical proposition is reduced to the minimum one. We show that the classical propositions obtained by this method can not be always obtained by the other methods. Experimental results show that this algorithm works well in general. However, another algorithm is presented, because this algorithm does not work well sometimes. This method will be applied to the discovery of logical propositions in numerical data.

We consider the case of heuristic search where the location of the goal may change during the course of the search. For example, the goal may be a target that is actively avoiding the problem solver. We present a moving target search algorithm (MTS) to solve this problem. MTS is the first search algorithm concerned with problem solving in a dynamically changing environment. We prove that the algorithm is complete, i.e., if the average speed of the target is slower than that of the problem solver, then the problem solver is guaranteed to eventually reach the target. However, since we constructed the algorithm with the minimum operations necessary for guaranteeing its completeness, the algorithm as proposed is neither efficient nor intelligent. We then introduce innovative notions created in the area of resource-bounded planning into the formal search algorithm, MTS, to improve its efficiency. Notions that are introduced are (i) commitment to goals, and (ii) deliberation for selecting Plans. We will show how these notions effectively overcome the bottleneck of MTS performance. The improved algorithm behaves like a predator. In clear situations, the problem solver is always sensitive to the target's moves and reactively moves toward the target's current position, while in uncertain situations, the problem solver ignores the target's moves, commits to its current goal, and deliberates to find a promising direction to reach the goal. Evaluation results demonstrate that the improved MTS is 10 to 20 times more efficient than the original MTS in uncertain situations.

We have developed a knowledge representation scheme DOT based on the dot notation and the IS-A relations between objects, and demonstrated that DOT gives a simple mathematical foundation for expressing the inheritance relationship between objects in deductive and object-oriented databases. As an extended research on the DOT scheme, we define in this paper the dependency of knowledge as a logical formula that expresses a specific IS-A relationship of DOT from which the knowledge is deduced in knowledge-bases. Then we propose a framework of knowledge based on the DOT in which negative knowledge is manipulated under the relationship to the notion of consistency constraint in database systems. Finally, employing developed dependency formulae, we propose an efficient update processing method which requires a small number of knowledge-base access and reduces the redundancy in closure calculation.

In order to make a dialog system cooperative, it needs to have a framework of describing beliefs of the partner (user) who converses with it. Because such descriptions contain beliefs of the system, itself, the entire belief description structure is nested. This paper proposes a framework in which we can describe both the participants' mental states and their dynamic changes during the dialog. Previous research on formalizing speech acts often define operators that correspond to each speech act. All these operators are defined in terms of preconditions and effects, and they are combined to make a sequence of speech acts. With these operators, however, it is not easy to show the course of overall dialog. This formalization is not powerful enough for making dialog cooperative, such as helping the partner to achieve his goal that is not specified during the dialog. In our framework, some constructs are employed to express the mental states. Some of the speech acts, such as informing and requesting, are regarded as manipulations on the constructs in our nested belief structure. These speech acts correspond to the addition of constructs from outer layers to inner layers in the nested belief structure. New construct "HOLE" is introduced to express the lack of belief. It enables us to handle both informing and requesting in the same manner, and to express the goal state of the dialog explicitly. The new construct also enables us to describe a strategy for making responses cooperative. With this framework, we can clearly express various phenomena of conveying propositions and intentions in terms of dynamic changes of belief descriptions.

We investigate several realizations of parallel abductive reasoning systems using the model generation theorem prover MGTP. The first two methods, the "MGTP+ATMS" and "MGTP+MGTP" methods, are co-operative problem-solving architectures, in which model generation and consistency checks communicate with each other. There, parallelism is exploited by checking consistencies in parallel. However, since these systems consist of two different components, the possibilities for parallelization are limited. In contrast, the remaining two methods do not separate the inference engine from consistency checks, but realize both functions in only one MGTP that is used as a "generate-and-test" mechanism, so that consistency checks are automatically performed in reasoning processes. In these methods, multiple models can be kept in distributed memories, thus a great amount of parallelism can be obtained. In particular, we conjecture that the "Skip" method, which introduces hypotheses only when they are necessary, will be the most promising for parallel abduction. We also attempt the upside-down meta-interpretation approach for abduction, in which top-down reasoning is simulated by a bottem-up reasoner. Some evaluation of these abductive systems that are applied to planning and design problems is also described in this paper.

We present a new approach to problem solving using Genetic Algorithms (GA). Earlier GA did not contain local search (i.e. hill climbing) mechanisms, which led to optimization difficulties, especially in higher dimensions. To overcome such difficulties, we introduce a "bug-based" search strategy and implement a system called BUGS. The ideas behind this are derived from biologically realistic foraing behaviors of bugs or animals. The effectiveness of this approach is confirmed using optimization experiments, and computer vision applications.

This paper introduces a new concept, a decision list over tree patterns (DLTP), which is a natural extension of a decision list, for dealing with tree structured objects. First, we show a theoretical result of the learnability of this class. We define the class, k-node-DLTP, which is a subclass of decision lists over tree patterns whose number of tuples is bounded by k+1. A hardness result on the learnability of this class is shown. Then we propose a practical learning algorithm based on an information theoretical evaluation function. This algorithm is an extension of Quinlan's ID3 algorithm. One of the most interesting application areas of this work is inference control. We can use decision lists over tree patterns for controlling the application of rules in SLD resolution process. We apply the proposed algorithm to learning strategies for applying rules and experimental results in several domains are presented. These experiments show the effectiveness of the proposed heuristic evaluation function for finding small size hypotheses. From the view point of Explanation Based Learning, our method can be regarded as a method for refining domain rules so as not to backtrack while solving training examples.

Handling incomplete knowledge, involving exception or contradiction, is an important function to expand the capability of current knowledge-base. Hypothetical reasoning handles such incomplete knowledge as hypothesis. It can be directly applicable to model based diagnosis problems, design problems, etc. Thus hypothetical reasoning system is an important framework toward advanced knowledge-based system both from theoretical and practical viewpoints. The most crucial problem of hypothetical reasoning is its slow inference speed due to its non-monotonic reasoning nature. One practical way to overcome this problem is to incorporate such heuristic knowledge that serves to navigate inference-path. But this causes knowledge acquisition bottleneck, because it is difficult to collect all the necessary heuristic knowledge to cover all the problem domain. Therefore, a fast hypothetical reasoning method systematically working under declarative knowledge is indispensable. One key mechanism of efficiency is to combine the advantages of forward reasoning and back-ward one, to reason just once the necessary nodes for proving a goal. This is very effective in hypothetical reasoning, because inefficient backtracking is frequently caused by inconsistency among hypotheses. Meanwhile, variable plays an important role to expand the scope of knowledge representation capability. If we represent knowledge in propositional logic representation without variables, the scale of knowledge-base becomes too large for many practical cases. Using the variables in predicate logic representation, we can express necessary knowledge in a compact form. Thus it is required for a fast hypothetical reasoning system working for predicate-logic knowledge. In this paper we present a fast hypothetical reasoning mechanism for predicate-logic knowledge (actually for function-free predicate Horn-clause knowledge). The QSQR method in deductive data-base technology is effectively applied in the view of dealing with the variables in predicate. The improvement inference speed is shown by some experiments including a practical diagnosis problem of logic circuit.