One of the fundamental problems in qualitative reasoning is to represent n-dimensional variable spaces. Generally states of a physical system are represented by hypersurfaces in an n-dimensional space, and it is difficult to represent such a situation by using direct product spaces of conventional one-dimensional qualitative values. This paper presents a qualitative representation and reasoning method for three-dimensional variable spaces. The notions of 'multivariant qualitative space' and 'qualitative region,' which are extensions of the quantity space and the qualitative value in one-dimensional space respectively, are used to describe physical situations. Multivariant qualitative spaces consist of qualitative regions and their topological relations, besides 'characteristic vectors' for each qualitative region. We describe a state of a physical system as a 'positional vector' whose value is defined as qualitative regions in a certain multivariant qualitative space, and each qualitative region corresponds to a possible state of the physical system. We can reason about behaviors of the physical system as transitions among qualitative regions, by using characteristic vectors and time derivations of positional vectors, based on the operations of qualitative vectors, i. e., scalar product and vector product. The method is applied to reasoning about the motion of a box sliding and rotating around an edge. The configuration space of possible motions of the box is represented by a multivariant qualitative space, and the reasoner predicts geometric transitions of the box. Since the method is constructed on symbolic inference and requires no numerical information, we can expect that it would be a basic technique for CAD systems of mechanical devices in conceptual design stages.

In this paper, we present a method which transforms predicate circumscription into a first-order sentence if its condition sentence is non-recursive with respect to predicates to be minimized. So far, fundamentally, the concept of the recursion in aribitrary first-order formulas has not been so clear. Therefore, at first, we consider and formalize this concept. Next, we define a computational condition that a formula is non-recursive with respect to predicates, and give an equivalent transformation method of non-recursive predicate circumscription into first-order sentences. A non-recursive formula A with respect to predicates p_1,…,p_n is defined only by the relations between positive and negative occurrences of p_1,…,p_n in A, without considering the number of the occurrences or the kinds of the quantification. Therefore, this transfomation method can deal with complex predicate circumscription such that its condition sentence is non-definite with respect to minimized predicates, or is quantified with both existential and universal quantifiers in any forms.

Parallel circumscription is an extension of predicate circumscription by adding parameters, which are predicates allowed to vary in the process in minimization. It is a very useful and important tool for commonsense reasoning. But, unfortunately, its direct computation is very difficult, because it is formulated as a higher-order formula. In this paper, we present an equivalent transformation method of parallel circumscription into first-order formulas. We have already presented a fundamental method for eliminating parameters of parallel circumscription and a method for transforming predicate circumscription into first-order formulas. Each of them is stronger than the well known Lifschitz's method. In this paper, based on these results, we give a sufficient condition for transforming parallel circumscription into first-order formulas, and present a transformation method which consists of the above two methods. This method can transform a complex parallel circumscription such that its condition sentence is quantified by both ∃ and ∀ quantifiers.

This paper proposes methods to derive the exogenously-driven causality of a physical system based on the intrinsic assumptions of evolutional causality and functional causality of each of the system's internal physical laws. The exogenously-driven causality of a physical system has previously been considered as being a feature of the entire system. The work reported here demonstrates that a major portion of the knowledge can be deriven from the intrinsic causal assumptions associated with each elementary physical law in the system description without requiring any information on external mechanisms. First, heuristics to extract the system-independent causal assumptions of each physical law are proposed. Second, a knowledge representation that describes the quantitative and causal assumptions of each physical law is established. This representation consists of 'assumptive structural equations'. Third, a method to derive candidate exogenous variables, causal structures, and mythical causality of the system is demonstrated based on the assumptive structural equations. Fourth, algebraic rules to derive various equations involving the knowledge of exogenously-driven causality of the system are shown. This methodology should be of use in simulation, design planning, and diagnosis of physical systems.

We have developed an experimental model as a prototype system concerning intelligent CAD (Computer Aided Design) and CAT (Computer Aided Testing) system for designing and testing electronic equipments with high reliability. As features of this model, we have a hybrid-type system consisting of a data processing machine (Sun-4) and an inference machine (PSI-II) for intelligent processing which are connected by communication lines (TCP/IP protocol). This allocation of tasks takes into account the development of faster online date processing and faster intelligent processing. This model has various intelligent processing functions regarding dialogue, retrieval, optimum searching and supporting FMEA (Failure Mode and Effects Analysis). Our development objectives and final goal in researching applications of artificial intelligence (i. e. an expert system) to CAD/CAT system are to find optimum points of harmony between man and machinery.