A Causal Approach to Analogy

Analogical reasoning addresses the question how evidence from various phenomena can be amalgamated and made relevant for theory development and prediction. In the first part of my contribution, I review some influential accounts of analogical reasoning, both historical and contemporary, focusing in particular on Keynes, Carnap, Hesse, and more recently Bartha. In the second part, I sketch a general framework. To this purpose, a distinction between a predictive and a conceptual type of analogical reasoning is introduced. I then take up a common intuition according to which (predictive) analogical inferences hold if the differences between source and target concern only irrelevant circumstances. I attempt to make this idea more precise by addressing possible objections and in particular by specifying a notion of causal irrelevance based on difference making in homogeneous contexts

A Causal Approach to Analogy

Analogical reasoning addresses the question how evidence from various phenomena can be amalgamated and made relevant for theory development and prediction. In the first part of my contribution, I review some influential accounts of analogical reasoning, both historical and contemporary, focusing in particular on Keynes, Carnap, Hesse, and more recently Bartha. In the second part, I sketch a general framework. To this purpose, a distinction between a predictive and a conceptual type of analogical reasoning is introduced. I then take up a common intuition according to which (predictive) analogical inferences hold if the differences between source and target concern only irrelevant circumstances. I attempt to make this idea more precise by addressing possible objections and in particular by specifying a notion of causal irrelevance based on difference making in homogeneous contexts

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 associations in the frame of a “neoclassical” semiotic theory

It has been a long time since the concept of iconic signs was proposed by C. S. Peirce. From that time on, we have been increasingly realizing that semiotic systems are for the most part established just on some type of similarity. But the more we see the sphere of analogical signification expanding its realm, the more we become aware of how inadequate is the notion of a simple relationship connecting locally a physical object with a second object, or with a mental entity. There is, on the other hand, the more refined theory of sign conceived by Ferdinand de Saussure, but this theory, by its very definition, addresses a restricted domain, and definitely does not include the field of those signs which rest on analogical associations. The main purpose of this article is then to show how the more polished Saussurean model can act as a starting point for a general restatement, primarily intended to embrace the signs that rest on an analogical basis. We may so speak of a “neoclassical”, innovative semiotic theory, able to join the latest “sociosemiotic” approach with the most precious foundations of our discipline

The Problem of Analogical Inference in Inductive Logic

We consider one problem that was largely left open by Rudolf Carnap in his work on inductive logic, the problem of analogical inference. After discussing some previous attempts to solve this problem, we propose a new solution that is based on the ideas of Bruno de Finetti on probabilistic symmetries. We explain how our new inductive logic can be developed within the Carnapian paradigm of inductive logic-deriving an inductive rule from a set of simple postulates about the observational process-and discuss some of its properties.Comment: In Proceedings TARK 2015, arXiv:1606.0729

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

Error analysis of expressive analogy task in Spanish-English bilingual school age children with and without specific language impairment

textPurpose: The relational shift hypothesis (RSH) states that, as children age, the way in which they interpret analogies shifts from a focus on object similarities to relational aspects of objects. This study investigated the validity of the RSH by describing the error patterns of typically developing (TD), low normal (LN), and language impaired (LI) bilingual school-age children when completing an expressive analogy task in A:B::C:D format (e.g. good:bad::happy:_____) in English and Spanish. Method: Participants included a total of 49 Spanish-English bilingual children between the ages of 7;4 and 8; 9 (mean = 8; 1). Ten children were identified as LI, ten scored in the LN range, and 29 were TD. Children were administered English and Spanish versions of the item twice, initially during the second grade and once again approximately one year later. Responses were recorded verbatim and coded as correct (C), thematic/category error (THEM/CAT), wrong object, correct relationship error (WO-CR), unrelated error (UNREL), or repetition/no response (REP/NR). Results: A repeated measures ANOVA was used to compare children’s analogy scores by time, ability, and language. Results demonstrated significant differences for ability. Four chi square tests investigated the error patterns of TD, LN, and LI bilingual children in English and Spanish. We compared responses provided children by response type (C, THEM/CAT, WO-CR, UNREL, or REP/NR). Results from the Spanish analogical reasoning task indicated a decrease in THEM/CAT with age for the LN and TD children. Results from the English analogical reasoning task were inconsistent. Conclusions: Results provide partial support for the RSH in LN and TD children, but not in children with LI. This difference in error patterns may provide insight into the validity of the RSH in bilingual children with specific language impairment and typically developing second language learners.Communication Sciences and Disorder

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