Solving problems on a knowledge model of operators and application

Abstract

Knowledge of operators is useful to build the intelligent problem solver for knowledge domains about computing. In this paper, we present a mathematical approach for building a knowledge model of operators, called Ops-model. The foundation of this model includes: concepts, operators, and inference rules. Each concept of this model is a class of objects with the behaviours for solving problems on themselves. General problems on this model are also studied, such as: reducing an expression, prove an equality of expressions. The algorithms for solving these problems are also designed. Ops-model has been applied to specify a part of knowledge domain about vector algebra in high school. It is used to construct a program for solving some problems on this knowledge domain. The solutions of this program are step-by-step, readable and suitable with the learners' level. It is useful for supporting students to learn this subject.

A Method of Ontology Integration for Designing Intelligent Problem Solvers

“…The model of problems has the form (O, F, E) → G [22], where O is the set of objects, F is the set of facts, E = {e 1 , e 2 , . .…”

Some Criteria of the Knowledge Representation Method for an Intelligent Problem Solver in STEM Education

“…Lemma 1 (see [27]). Let a knowledge domain K as Rela-Ops model and (O, E, F) be the hypothesis of the problem as kind 2 in Definition 3. ere exists a unique maximum set L (O, E, F) such that it contains all facts that can be deduced from (O, E, F).…”

“…Let a knowledge domain K as Rela-Ops model and (O, E, F) be the hypothesis of the problem as kind 2 in Definition 3. ere exists a unique maximum set L (O, E, F) such that it contains all facts that can be deduced from (O, E, F). Theorem 2 (see [27]). Let a knowledge domain K as Rela-Ops model and a problem P � (O, E, F E, F) is a set of facts can be deduced from the list S and hypothesis of problem P eorem 2 shows that forward chaining reasoning will deduce the goals of problems.…”

“…Problems in kind 1 and kind 2 were studied and solved in [6,9,27]. e effectiveness of the algorithms for solving problems in kind 1 has been proven in [6,9] and for solving problems in kind 2 has been proven in [9,27].…”

“…Solutions of them are step-by-step, and their reasoning is like the solving method of students. e detailed structure of the Rela-Ops model and its problems has been presented in [6,27]. e finiteness, the effectiveness, and the complexity of algorithms have also been proved in [6,9,27].…”