Logic-Based Analogical Reasoning and Learning

Analogy-making is at the core of human intelligence and creativity with applications to such diverse tasks as commonsense reasoning, learning, language acquisition, and story telling. This paper contributes to the foundations of artificial general intelligence by developing an abstract algebraic framework for logic-based analogical reasoning and learning in the setting of logic programming. The main idea is to define analogy in terms of modularity and to derive abstract forms of concrete programs from a `known' source domain which can then be instantiated in an `unknown' target domain to obtain analogous programs. To this end, we introduce algebraic operations for syntactic program composition and concatenation and illustrate, by giving numerous examples, that programs have nice decompositions. Moreover, we show how composition gives rise to a qualitative notion of syntactic program similarity. We then argue that reasoning and learning by analogy is the task of solving analogical proportions between logic programs. Interestingly, our work suggests a close relationship between modularity, generalization, and analogy which we believe should be explored further in the future. In a broader sense, this paper is a first step towards an algebraic and mainly syntactic theory of logic-based analogical reasoning and learning in knowledge representation and reasoning systems, with potential applications to fundamental AI-problems like commonsense reasoning and computational learning and creativity

Developing The Attitude And Creativity In Mathematics Education

The structures in a traditionally-organized classroom of mathematics teaching can usually be linked readily with the routine classroom activities of teacher-exposition and teacher-supervised desk work, teacher’s initiation, teacher’s direction and strongly teacher’s expectations of the outcome of student learning. If the teacher wants to develop appropriate attitude and creativities in mathematics teaching learning it needs for him to develop innovation in mathematics teaching. The teacher may face challenge to develop various style of teaching i.e. various and flexible method of teaching, discussion method, problem-based method, various style of classroom interaction, contextual and or realistic mathematics approach. To develop mathematical attitude and creativity in mathematics teaching learning processes, the teacher may understand the nature and have the highly skill of implementing the aspects of the following: mathematics teaching materials, teacher’s preparation, student’s motivation and apperception, various interactions, small-group discussions, student’s works sheet development, students’ presentations, teacher’s facilitations, students’ conclusions, and the scheme of cognitive development.In the broader sense of developing attitude and creativity of mathematics learning, the teacher may needs to in-depth understanding of the nature of school mathematics, the nature of students learn mathematics and the nature of constructivism in learning mathematics. Key Word: mathematical attitude, creativity in mathematics, innovation of mathematics teaching,school mathematics

Understanding analogical reasoning : viewpoints from psychology and related disciplines

Analogy and metaphor have a long history of study in linguistics, education, philosophy and psychology. Consensus over what analogy is or how analogy functions in language and thought, however, has been elusive. This paper, the first in a two part series, examines these various research traditions, attempting to bring out major lines of agreement over the role of analogy in individual human experience. As well as being a general literature review which may be helpful for newcomers to the study of analogy, this paper attempts to extract from these literatures existing theories, models and concepts which may be interesting or useful for computational studies of analogical reasoning

The challenge of complexity for cognitive systems

Complex cognition addresses research on (a) high-level cognitive processes – mainly problem solving, reasoning, and decision making – and their interaction with more basic processes such as perception, learning, motivation and emotion and (b) cognitive processes which take place in a complex, typically dynamic, environment. Our focus is on AI systems and cognitive models dealing with complexity and on psychological findings which can inspire or challenge cognitive systems research. In this overview we first motivate why we have to go beyond models for rather simple cognitive processes and reductionist experiments. Afterwards, we give a characterization of complexity from our perspective. We introduce the triad of cognitive science methods – analytical, empirical, and engineering methods – which in our opinion have all to be utilized to tackle complex cognition. Afterwards we highlight three aspects of complex cognition – complex problem solving, dynamic decision making, and learning of concepts, skills and strategies. We conclude with some reflections about and challenges for future research

Theory blending: extended algorithmic aspects and examples

In Cognitive Science, conceptual blending has been proposed as an important cognitive mechanism that facilitates the creation of new concepts and ideas by constrained combination of available knowledge. It thereby provides a possible theoretical foundation for modeling high-level cognitive faculties such as the ability to understand, learn, and create new concepts and theories. Quite often the development of new mathematical theories and results is based on the combination of previously independent concepts, potentially even originating from distinct subareas of mathematics. Conceptual blending promises to offer a framework for modeling and re-creating this form of mathematical concept invention with computational means. This paper describes a logic-based framework which allows a formal treatment of theory blending (a subform of the general notion of conceptual blending with high relevance for applications in mathematics), discusses an interactive algorithm for blending within the framework, and provides several illustrating worked examples from mathematics

Aha? Is Creativity Possible in Legal Problem Solving and Teachable in Legal Education?

This article continues and expands on my earlier project of seeking to describe how legal negotiation should be understood conceptually and undertaken behaviorally to produce better solutions to legal problems. As structured problem solving requires interests, needs and objectives identification, so too must creative solution seeking have its structure and elements in order to be effectively taught. Because research and teaching about creativity and how we think has expanded greatly since modern legal negotiation theory has been developed, it is now especially appropriate to examine how we might harness this new learning to how we might examine and teach legal creativity in the context of legal negotiation and problem solving. This article explores both the cognitive and behavioral dimensions of legal creativity and offers suggestions for how it can be taught more effectively in legal education, both within the more narrow curricula of negotiation courses and more generally throughout legal education

Towards creative information exploration based on Koestler's concept of bisociation

Creative information exploration refers to a novel framework for exploring large volumes of heterogeneous information. In particular, creative information exploration seeks to discover new, surprising and valuable relationships in data that would not be revealed by conventional information retrieval, data mining and data analysis technologies. While our approach is inspired by work in the field of computational creativity, we are particularly interested in a model of creativity proposed by Arthur Koestler in the 1960s. Koestler’s model of creativity rests on the concept of bisociation. Bisociative thinking occurs when a problem, idea, event or situation is perceived simultaneously in two or more “matrices of thought” or domains. When two matrices of thought interact with each other, the result is either their fusion in a novel intellectual synthesis or their confrontation in a new aesthetic experience. This article discusses some of the foundational issues of computational creativity and bisociation in the context of creative information exploration

Marketing Management Support Systems and Their Implications for Marketing Research

Marketing decision makers are responsible for the design and execution of marketing programs for products or brands. They operate under different names, such as product manager, brand manager, marketing manager, marketing director, or commercial director. They choose the target markets and segments for their products and services and develop and implement marketing mixes. Because of the proliferation of products and brands, the fragmentation of markets in an ever growing number of different segments, the fierceness of competition, and the overall acceleration of change, marketing decisions are becoming increasingly complex. Furthermore, decisions have to be made under increasing time pressure. Product life cycles are getting shorter, and competition occurs not only within countries but also increasingly at an international and even global level. New markets are rapidly opening up, existing markets are being deregulated, and new distribution channels such as the Internet have developed. The question now is, how can these decision makers be supported to become more effective

Towards a computational- and algorithmic-level account of concept blending using analogies and amalgams

Concept blending–a cognitive process which allows for the combination of certain elements (and their relations) from originally distinct conceptual spaces into a new unified space combining these previously separate elements, and enables reasoning and inference over the combination–is taken as a key element of creative thought and combinatorial creativity. In this article, we summarise our work towards the development of a computational-level and algorithmic-level account of concept blending, combining approaches from computational analogy-making and case-based reasoning (CBR). We present the theoretical background, as well as an algorithmic proposal integrating higher-order anti-unification matching and generalisation from analogy with amalgams from CBR. The feasibility of the approach is then exemplified in two case studies

Students' Analogical Reasoning in Solving Trigonometric Problems in Terms of Cognitive Style: A Case Study

This article discusses the analogical reasoning of students' types in solving trigonometric problems based on cognitive styles. This research was conducted at MAN I Probolinggo, eighteen students was asked to complete cognitive style tests and math ability tests. It was found that students' answers can be grouped into two types of cognitive styles, namely systematic and intuitive. From each group, one student was taken to be interviewed with the aim of getting a more detailed explanation of each type of analogical reasoning. The results show that the two types can be explained as follows, first, the type of systematic cognitive style, students can understand the problem given, mention in detail all the information that is known and asked, use all known information about the problem, read and understand the problem, map the structure relational problems, applying a structured way to solve problems that have been planned in advance. In the intuitive cognitive style type, students can understand the problem only by reading the problem once, mention some information that is known about the problem, use the information that is known in the problem, read and understand the problem, apply problem-solving methods. pre-planned but unstructured. Therefore, teachers must encourage and enable students to use analogical reasoning optimally in learning mathematics