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

Mill on logic

Working within the broad lines of general consensus that mark out the core features of John Stuart Mill’s (1806–1873) logic, as set forth in his A System of Logic (1843–1872), this chapter provides an introduction to Mill’s logical theory by reviewing his position on the relationship between induction and deduction, and the role of general premises and principles in reasoning. Locating induction, understood as a kind of analogical reasoning from particulars to particulars, as the basic form of inference that is both free-standing and the sole load-bearing structure in Mill’s logic, the foundations of Mill’s logical system are briefly inspected. Several naturalistic features are identified, including its subject matter, human reasoning, its empiricism, which requires that only particular, experiential claims can function as basic reasons, and its ultimate foundations in ‘spontaneous’ inference. The chapter concludes by comparing Mill’s naturalized logic to Russell’s (1907) regressive method for identifying the premises of mathematics

The effect of multiple knowledge sources on learning and teaching

Current paradigms for machine-based learning and teaching tend to perform their task in isolation from a rich context of existing knowledge. In contrast, the research project presented here takes the view that bringing multiple sources of knowledge to bear is of central importance to learning in complex domains. As a consequence teaching must both take advantage of and beware of interactions between new and existing knowledge. The central process which connects learning to its context is reasoning by analogy, a primary concern of this research. In teaching, the connection is provided by the explicit use of a learning model to reason about the choice of teaching actions. In this learning paradigm, new concepts are incrementally refined and integrated into a body of expertise, rather than being evaluated against a static notion of correctness. The domain chosen for this experimentation is that of learning to solve "algebra story problems." A model of acquiring problem solving skills in this domain is described, including: representational structures for background knowledge, a problem solving architecture, learning mechanisms, and the role of analogies in applying existing problem solving abilities to novel problems. Examples of learning are given for representative instances of algebra story problems. After relating our views to the psychological literature, we outline the design of a teaching system. Finally, we insist on the interdependence of learning and teaching and on the synergistic effects of conducting both research efforts in parallel

Facts, skills and intuition : A typology of personal knowledge

This paper introduces a knowledge model in which the types of knowledge are formed according to the nature of knowledge. First we use Ryle’s distinction of “that” and “how” knowledge, to which we add further three types. The five knowledge types are then synthesized using Polanyi’s distinction of focal and subsidiary awareness. The resulting model distinguishes three types of knowledge, the facts, the skills, and the intuition; all three having focal and subsidiary parts. We believe that this knowledge model is comprehensive in the sense that can classify any knowledge and it also has great explanatory power, as it is demonstrated through illustrative examples. Moreover, the model is elegant and easy to use, which facilitates our understanding of the domain of personal knowledge. Therefore we expect our findings to be useful for both researchers and educators in the field of knowledge and knowledge management

Classification and unjust enrichment

[First paragraph] One of the most striking changes in academic research and teaching in recent times has been the appearance of a new subject under the name of restitution or unjust enrichment. This has transformed the treatment of various areas of the common law that were historically neglected, confused and obscure, and has had, over a relatively short period, a marked effect on the approach of some judges to these areas. One of the most influential works has been Peter Birks's An Introduction to the Law of Restitution,1 originally published nearly twenty years ago. Much of the literature has been concerned with exploring issues identified by Birks, in the terminology and according to the general approach that he adopted. Birks has been influential not only through this book and the numerous articles and other books that developed and modified his views, but also through scholarship that he has facilitated and promoted: important work has been produced by his research students and by participants in academic seminars and conferences organised by him. In addition, the Restitution Law Review, which Birks helped to found, has provided a new forum for the promotion and discussion of these developments

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

Computational and Biological Analogies for Understanding Fine-Tuned Parameters in Physics

In this philosophical paper, we explore computational and biological analogies to address the fine-tuning problem in cosmology. We first clarify what it means for physical constants or initial conditions to be fine-tuned. We review important distinctions such as the dimensionless and dimensional physical constants, and the classification of constants proposed by Levy-Leblond. Then we explore how two great analogies, computational and biological, can give new insights into our problem. This paper includes a preliminary study to examine the two analogies. Importantly, analogies are both useful and fundamental cognitive tools, but can also be misused or misinterpreted. The idea that our universe might be modelled as a computational entity is analysed, and we discuss the distinction between physical laws and initial conditions using algorithmic information theory. Smolin introduced the theory of "Cosmological Natural Selection" with a biological analogy in mind. We examine an extension of this analogy involving intelligent life. We discuss if and how this extension could be legitimated. Keywords: origin of the universe, fine-tuning, physical constants, initial conditions, computational universe, biological universe, role of intelligent life, cosmological natural selection, cosmological artificial selection, artificial cosmogenesis.Comment: 25 pages, Foundations of Science, in pres

Interpretation-driven mapping: A framework for conducting search and re-representation in parallel for computational analogy in design

This paper presents a framework for the interactions between the processes of mapping and rerepresentation within analogy making. Analogical reasoning systems for use in design tasks require representations that are open to being reinterpreted. The framework, interpretation-driven mapping, casts the process of constructing an analogical relationship as requiring iterative, parallel interactions between mapping and interpreting. This paper argues that this interpretation-driven approach focuses research on a fundamental problem in analogy making: how do the representations that make new mappings possible emerge during the mapping process? The framework is useful for both describing existing analogy-making models and designing future ones. The paper presents a computational model informed by the framework Idiom, which learns ways to reinterpret the representations of objects as it maps between them. The results of an implementation in the domain of visual analogy are presented to demonstrate its feasibility. Analogies constructed by the system are presented as examples. The interpretation-driven mapping framework is then used to compare representational change in Idiom to that in three previously published systems