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

Children’s spontaneous comparisons from 26 to 58 months predict performance in verbal and non-verbal analogy tests in 6th grade

Comparison supports the development of children’s analogical reasoning. The evidence for this claim comes from laboratory studies. We describe spontaneous comparisons produced by 24 typically developing children from 26 to 58 months. Children tend to express similarity before expressing difference. They compare objects from the same category before objects from different categories, make global comparisons before specific comparisons, and specify perceptual features of similarity/difference before non-perceptual features. We then investigate how a theoretically interesting subset of children’s comparisons – those expressing a specific feature of similarity or difference – relates to analogical reasoning as measured by verbal and non-verbal tests in 6th grade. The number of specific comparisons children produce before 58 months predicts their scores on both tests, controlling for vocabulary at 54 months. The results provide naturalistic support for experimental findings on comparison development, and demonstrate a strong relationship between children’s early comparisons and their later analogical reasoning

Penalaran Analogi Peserta Didik SMP dalam Menyelesaikan Dua Masalah dengan Kesamaan Permukaan Rendah

Analogical reasoning is a process of identifying two problems that aim to produce knowledge by associating relevant concepts and facts and adapting them so that they can solve more complex problems. Low surface similarity does not play a significant role in solving analogical reasoning. This type of research was carried out descriptively with qualitative methods with the aim of describing students' reasoning in solving analogy problems with low surface similarity. The research was conducted at one of the junior high schools in Sidoarjo with three selected students. Research data were analyzed using indicators that had been made by researchers. The data from the research results gave rise to three students who have uniqueness in analogical reasoning. There are two peculiarities found, namely the peculiarities with general cases and the peculiarities with special cases. The low surface similarity in analogy problems has an impact on students in the form of different stages of analogical reasoning that are passed by the three students. Students with general characteristics have stages of linear analogy reasoning. Students with special case characteristics have dynamic analogical reasoning stages. Identifying is done by students by identifying characteristics and concluding the relationship between the two problems. Mapping is done by students by mapping information related to analogy problems. At the time of applying the answers to the source problem to the target problem, there were two students with special characteristics who returned to the previous stage because they found it difficult. Verifying has been done by each student, but students with special cases have beliefs that are contrary to the results of the answers. So, the use of source problems and target problems that have low surface similarities can be used with the condition that the structure of the answers between the two problems must be analogous to each other

Zero-shot visual reasoning through probabilistic analogical mapping

Human reasoning is grounded in an ability to identify highly abstract commonalities governing superficially dissimilar visual inputs. Recent efforts to develop algorithms with this capacity have largely focused on approaches that require extensive direct training on visual reasoning tasks, and yield limited generalization to problems with novel content. In contrast, a long tradition of research in cognitive science has focused on elucidating the computational principles underlying human analogical reasoning; however, this work has generally relied on manually constructed representations. Here we present visiPAM (visual Probabilistic Analogical Mapping), a model of visual reasoning that synthesizes these two approaches. VisiPAM employs learned representations derived directly from naturalistic visual inputs, coupled with a similarity-based mapping operation derived from cognitive theories of human reasoning. We show that without any direct training, visiPAM outperforms a state-of-the-art deep learning model on an analogical mapping task. In addition, visiPAM closely matches the pattern of human performance on a novel task involving mapping of 3D objects across disparate categories

Analogy

This essay (a revised version of my undergraduate honors thesis at Stanford) constructs a theory of analogy as it applies to argumentation and reasoning, especially as used in fields such as philosophy and law. The word analogy has been used in different senses, which the essay defines. The theory developed herein applies to analogia rationis, or analogical reasoning. Building on the framework of situation theory, a type of logical relation called determination is defined. This determination relation solves a puzzle about analogy in the context of logical argument, namely, whether an analogous situation contributes anything logically over and above what could be inferred from the application of prior knowledge to a present situation. Scholars of reasoning have often claimed that analogical arguments are never logically valid, and that they therefore lack cogency. However, when the right type of determination structure exists, it is possible to prove that projecting a conclusion inferred by analogy onto the situation about which one is reasoning is both valid and non-redundant. Various other properties and consequences of the determination relation are also proven. Some analogical arguments are based on principles such as similarity, which are not logically valid. The theory therefore provides us with a way to distinguish between legitimate and illegitimate arguments. It also provides an alternative to procedures based on the assessment of similarity for constructing analogies in artificial intelligence systems

Analogical Reasoning

Analogical reasoning is the ability to perceive and use relational commonality between two situations. Most commonly, analogy involves mapping relational structures from a familiar (base situation to an unfamiliar situation (target). For example, solving the analogy “chicken is to chick like tiger is to___?” requires perceiving the relation parent–offspring in the base domain (chicken:chick) and mapping the same relation to the target (tiger:__?) to get to the answer cub. Relational similarity is the crux of analogical reasoning; what is crucial here is the sameness of the relation, not of other similarities—chickens and tigers do not look alike

Analogical Reasoning in Mathematical Theorems

Analogical reasoning is one of the most powerful tools of mathematical thinking. For example, to prove a theorem it is necessary to see similarities with the previous theorem. This study aims to classify analogies in mathematics courses and examples. This classification is based on research results. The research was conducted use qualitative research. The research subjects are 12 lecturers who teach mathematics courses and study program managers. Analogical reasoning instruments are unstructured interview guidelines and observation sheets. Interview guides and observation sheets were made to be able to reveal mathematics analogical reasoning in the Mathematics Education Study Program course. The results of the research show that there are 3 types of analogy classifications in mathematics courses, namely definition analogy, theorem-defining analogy, and theorem analogy. First, the definition of similarity in the same or different courses. Second, the similarities between definitions and theorems in the same or different courses. Third, the theorem similarities in the same or different subjects. Our classification is related to theorems and analogical properties in several courses in the curriculum of the Mathematics Education Study Program. The analogy can be applied to certain mathematical topics related to real life. Meanwhile, to analyze other aspects of reasoning through analogy needs to be studied further