Large-Scale Analogical Reasoning

Analogy plays an important role in science as well as in non-scientific domains such as taxonomy or learning. We make explicit the difference and complementarity between the concept of analogical statement, which merely states that two objects have a relevant similarity, and the concept of analogical inference, which relies on the former in order to draw a conclusion from some premises. For the first, we show that it is not possible to give an absolute definition of what it means for two objects to be analogous; a relative definition of analogy is introduced, only relevant from some point of view. For the second, we argue that it is necessary to introduce a background over-hypothesis relating two sets of properties; the belief strength of the conclusion is then directly related to the belief strength of the over-hypothesis. Moreover, we assert the syntactical identity between analogical inference and one case induction despite important pragmatic differences.

Motivation -The purpose of this article is to reinvigorate debate concerning the nature of analogy and broaden the scope of current conceptions of analogy. Research approach -An analysis of the history of the concept of analogy, case studies on the use of analogy in problemsolving, cognitive research on analogy comprehension, and a naturalistic inquiry into the various functions of analogy. Findings and Implications -Psychological theories and computational models have generally relied on: (a) A single set of ontological concepts (a property called "similarity" and a structuralist categorization of types of semantic relations) (b) A single form category (i.e., the classic four-term analogy), and (c) A single set of morphological distinctions (e.g., verbal versus pictorial analogies). The taxonomy presented here distinguishes functional kinds of analogy, each of which presents an opportunity for research on aspects of reasoning that have been largely unrecognized. Originality/Value -The various functional kinds of analogy will each require their own treatment in macrocognitive theories and computational models. Take away message -The naturalistic investigation of the functions of analogy suggests that analogy is a macrocognitive phenomenon derivative of number of supporting processes, including the apperception of resemblances and distinctions, metaphor, and the balancing of semantic flexibility and inference constraint.

Human reasoning applies argumentation patterns to draw conclusions about a particular subject. These patterns represent the structure of the arguments in the form of argumentation schemes which are useful in AI to emulate human reasoning. A type of argument schema is that what allow to analyze the similarities and differences between two arguments, to find a solution to a new problem from an already known one. Researchers in the heavily studied field of analogies in discourse have recognized that there is not a full and complete definition to indicate when two arguments are considered analogous. Our proposal presents an initial attempt to formalize argumentation schemes based on analogies, considering a relationship of analogy between arguments. This will contribute to the area increasing such schemes usefulness in Artificial Intelligence (AI), since it can be implemented later in Defeasible Logic Programming (DeLP).

Journal of Mathematical Modelling and Application, 2012

Much of our cognitive activity depends on our ability to reason analogically. When we encounter a new problem we are often reminded of similar problems solved in past and may use the solution procedure of an old problem to solve the new one (analogical problem solving). In this paper we develop two mathematical models for the description of the process of analogical problem solving. The first one is a stochastic model constructed by introducing a finite, ergodic Markov chain on the steps of the analogical reasoning process. Through this we obtain a measure of the solvers' difficulties during the process. The second is a fuzzy model constructed by representing the main steps of the process as fuzzy subsets of a set of linguistic labels characterizing the individuals' performance in each of these steps. In this case we introduce the Shannon's entropy (total probabilistic uncertainty)properly modified for use in a fuzzy environment-as a measure of the solvers' performance. The two models are compared to each other by listing their advantages and disadvantages. Classroom experiments are also performed to illustrate their use in practice.

2008

Human-level reasoning is manifold and comprises a wide variety of different reasoning mechanisms. So far, artificial intelligence has focused mainly on using the classical approaches deduction, induction, and abduction to enable machines with reasoning capabilities. However, the approaches are limited and do not reflect the mental, cognitive process of human reasoning very well. We contend that analogical reasoning is the driving force behind human thinking and therefore propose analogy as an integrating framework for the variety of human-level reasoning mechanisms.

Foundations of Science, 1999

This paper aims at integrating the work onanalogical reasoning in Cognitive Science into thelong trend of philosophical interest, in this century,in analogical reasoning as a basis for scientificmodeling. In the first part of the paper, threesimulations of analogical reasoning, proposed incognitive science, are presented: Gentner's StructureMatching Engine, Mitchel's and Hofstadter's COPYCATand the Analogical Constraint Mapping Engine, proposedby Holyoak and Thagard. The differences andcontroversial points in these simulations arehighlighted in order to make explicit theirpresuppositions concerning the nature of analogicalreasoning. In the last part, this debate in cognitivescience is applied to some traditional philosophicalaccounts of formal and material analogies as a basisfor scientific modeling, like Mary Hesse`s, and tomore recent ones, that already draw from the work inArtificial Intelligence, like that proposed byAronson, Harré and Way.

Advances in connectionist and neural computation …, 1994

IEEE Transactions on Systems, Man, and Cybernetics, 1988

in L. Magnani e C. Casadio (eds.), Model-Based Reasoning in Science and Technology – Logical, Epistemological and Cognitive Issues, Series: Studies in Applied Philosophy, Epistemology and Rational Ethics, Vol. 27, Springer International Publishing AG, Cham, 2016

Generally speaking, model-based reasoning refers to every reasoning that involves model of reality or physical world, and it is especially involved in scientific discovery. Analogy is a cognitive process involved in scientific discovery as well as in everyday thinking. I suggest to consider analogy as a type of model-based reasoning and in relation with models. Analogy requires models in order to connect a source situation and a target situation. A model in an analogy is required to establish salient properties and, mostly, relations that allow transfer of knowledge from the source domain to the target domain. In another sense, analogy is the model itself, or better, analogy provides the elements of model of reality that enable the processes of scientific discovery or knowledge increase. My suggestion is that some insight on how an analogy is a model and is connected to model-based reasoning is provided by recently proposed theories about analogy as a cat-egorization phenomenon. Seeing analogy as a categorization phenomenon is a fruitful attempt to solve the problem of feature relevance in analogies, especially in the case of conceptual innovation and knowledge increase in scientific domain.

We analyze the logical form of the domain knowledge that grounds analogical inferences and generalizations from a single instance. The form of the assumptions which justify analogies is given schematically as the "determination rule", so called because it expresses the relation of one set of variables determining the values of another set. The determination relation is a logical generalization of the different types of dependency relations defined in database theory. Specifically, we define determination as a relation between schemata of first order logic that have two kinds of free variables: (1) object variables and what we call "polar" variables, which hold the place of truth values. Determination rules facilitate sound rule inference and valid conclusions projected by analogy from single instances, without implying what the conclusion should be prior to an inspection of the instance. They also provide a way to specify what information is sufficiently relevant to decide a question, prior to knowledge of the answer to the question. 1

Humans use analogies to communicate, reason, and learn. But while the human brain excels at creating and understanding analogies, it does not easily recall useful analogies created or learned over time. General purpose tools and methods are needed that assist humans in representing, storing, and recalling useful analogies. Additionally, such tools must take advantage of the World Wide Web's ubiquity, global reach, and universal standards. We first identify commonly occurring patterns of analogy structure. Because understanding of instructional analogies is significantly improved when their structure is visualized, we develop a compact and general representation for analogies using XML, and demonstrate general methods for visualizing the structure of analogy expressions in Web-based environments.

2016

Humans regularly exploit analogical reasoning to generate potentially novel and useful inferences. We outline the Dr Inventor model that identifies analogies between research publications, describing recent work to evaluate the inferences that are generated by the system. Its inferences, in the form of subjectverb-object triples, can involve arbitrary combinations of source and target information. We evaluate three approaches to assess the quality of inferences. Firstly, we explore an n-gram based approach (derived from the Dr Inventor corpus). Secondly, we use ConceptNet as a basis for evaluating inferences. Finally, we explore the use of Watson Concept Insights (WCI) to support our inference evaluation process. Dealing with novel inferences arising from an ever growing corpus is a central concern throughout.

Dialogue, 2021

Analogy plays an important role in science as well as in non-scientific domains such as taxonomy or learning. We make explicit the difference and complementarity between the concept of analogical statement, which merely states that two objects have a relevant similarity, and the concept of analogical inference, which relies on the former in order to draw a conclusion from some premises. For the first, we show that it is not possible to give an absolute definition of what it means for two objects to be analogous; a relative definition of analogy is introduced, only relevant from some point of view. For the second, we argue that it is necessary to introduce a background over-hypothesis relating two sets of properties; the belief strength of the conclusion is then directly related to the belief strength of the over-hypothesis. Moreover, we assert the syntactical identity between analogical inference and single case induction despite important pragmatic differences.

American Psychologist, 1997

1. Analogy is a powerful cognitive mechanism that people use to make inferences and learn new abstractions. The history of work on analogy in modern cognitive science is sketched, focusing on contributions from cognitive psychology, artificial intelligence, and philosophy of science. This review sets the stage for the 3 articles that follow in this Science Watch section.(PsycINFO Database Record (c) 2012 APA, all rights reserved)