Fuzzy reasoning morphological operators and their optical implementation

Fuzzy-reasoning theory is widely used in industrial control. Mathematical morphology is a powerful tool to perform image processing. We apply fuzzy-reasoning theory to morphology and suggest a scheme of fuzzy-reasoning morphology, including fuzzy-reasoning dilation and erosion functions. These functions retain more fine details than the corresponding conventional morphological operators with the same structuring element. An optical implementation has been developed with area-coding and thresholding methods. (C) 1997 Optical Society of America.

A logic for default reasoning

The need to make default assumptions is frequently encountered in reasoning about incompletely specified worlds. Inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations. It is this property which leads to the non-monotonicity of any logic of defaults. In this paper we propose a logic for default reasoning. We then specialize our treatment to a very large class of commonly occuring defaults. For this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover. Finally, we provide criteria under which the revision of derived beliefs must be effected.

constructing finite algebras with falcon

The generation of models and counterexamples is an important form of reasoning. In this paper, we give a formal account of a system, called FALCON, for constructing finite algebras from given equational axioms. The abstract algorithms, as well as some implementation details and sample applications, are presented. The generation of finite models is viewed as a constraint satisfaction problem, with ground instances of the axioms as constraints. One feature of the system is that it employs a very simple technique, called the least number heuristic, to eliminate isomorphic (partial) models, thus reducing the size of the search space. The correctness of the heuristic is proved. Some experimental data are given to show the performance and applications of the system.