Solving Logic Problems with Associative Networks in the Course of Knowledge Representation

Abstract

This article aims to study of the use Associative (Semantic) networks in the course of Knowledge representation that is taught at the University of Ostrava. In the course was created logic puzzles of type Zebra from simple to more complex levels (Einstein's problems). Associative networks have been used to solve logic puzzles. KEYWORD: Associative networks; semantic networks; graph theory; logic puzzle; zebra; representation knowledge International Conference on Industrial Technology and Management Science (ITMS 2015) © 2015. The authors Published by Atlantis Press 121 3 LOGIC TASK OF THE ZEBRA TYPE Logic tasks of ZEBRA type are well-known particularly from the field of recreational mathematics. They are generally classified as difficult tasks. An obvious reason of „difficulty “is a difficult communicability of individual steps of the logic procedure and a considerable degree of abstraction. However, solving this task type can be approached from the perspective of different strategies. By applying basics of structural and graphical methods in order to achieve solution, tasks become accessible not only for gifted students. [4] Individual steps are easier to be communicated and can be discussed. However there still remains some space for own personal presentations of students. This article deals with solutions for tasks of the ZEBRA type in more detail. Besides the intuitive problem-solving approach the attention is also paid to both the structural approach (solving tasks using a system of tables with logical relationships) and graphical approach (solving tasks using a a node graph). 4 ASSOCIATIVE NETWORK Associative networks which are based on a graph representation of knowledge can be considered a tool for solving logic tasks. Associative networks, also well-known as semantic networks, are suitable as a tool for representing relationships (connections) among individual elements in the assignment. The first mention of associative networks can be found in 1968 when they were designed as a model for human associative memory and have still been used to solve various tasks and problems; they have also been transferred to computer science. [4] Logics [2] and semantic networks have a different formalism to represent knowledge. Several authors demonstrate that simple semantic networks may be expanded in the way that they, for example, are enhanced by an expressive power of the predicate logic. It means that the knowledge representation is based, equally as predicate logic, on atoms representing basic network statement by means of appropriately selected predicates. These statements are of vector nature ( ). See Figure 1. Figure 1. Vector of statement Semantic network is an enhanced oriented graph consisting of nodes and edges. Each node represents an object (individuum) and each edge represents a relationship between two objects. Relationships between statements are of our interest because they provide basic structure for organized knowledge. In associative networks the relationships can be well expressed by a set of inclusion and affiliation in a set; both the unique and general concepts can be represented here. Relationships of a set of inclusion and affiliation to a class enable to represent a taxonomic (hierarchical) arrangement of objects effectively. Thus deriving by specialization or by generalization can be carried out straightforwardly. As for specialization the information in taxonomy is transformed from general types to the specialized ones; as for generalization it is the contrary. Within one semantic network knowledge can be associated from many different perspectives. [3] Semantic (associative) network is an enhanced oriented graph consisting of nodes, enhanced by terms, and of edges, enhanced by binary predicate symbols where the edges join some pairs of nodes. Language of associative networks disposes of the following types of symbols: