Semantic grounding in models of analogy: an environmental approach

Empirical studies indicate that analogy consists of two main processes: retrieval and mapping. While current theories and models of analogy have revealed much about the mainly structural constraints that govern the mapping process, the similarities that underpin the correspondences between individual representational elements and drive retrieval are understood in less detail. In existing models symbol similarities are externally defined but neither empirically grounded nor theoretically justified. This paper introduces a new model (EMMA: the environmental model of analogy) which relies on co‐occurrence information provided by LSA (Latent Semantic Analysis; Landauer & Dumais, 1997) to ground the relations between the symbolic elements aligned in analogy. LSA calculates a contextual distribution for each word encountered in a corpus by counting the frequency with which it co‐occurs with other words. This information is used to define a model that locates each word encountered in a high‐dimensional space, with relations between elements in this space representing contextual similarities between words. A series of simulation experiments demonstrate that the environmental approach to semantics embodied in LSA can produce appropriate patterns of analogical retrieval, but that this semantic measure is not sufficient to model analogical mapping. The implications of these findings, both for theories of representation in analogy research and more general theories of semantics in cognition, are explored.     

Bayesian analogy with relational transformations

How can humans acquire relational representations that enable analogical inference and other forms of high-level reasoning? Using comparative relations as a model domain, we explore the possibility that bottom-up learning mechanisms applied to objects coded as feature vectors can yield representations of relations sufficient to solve analogy problems. We introduce Bayesian analogy with relational transformations (BART) and apply the model to the task of learning first-order comparative relations (e.g., larger, smaller, fiercer, meeker) from a set of animal pairs. Inputs are coded by vectors of continuous-valued features, based either on human magnitude ratings, normed feature ratings (De Deyne et al., 2008), or outputs of the topics model (Griffiths, Steyvers, & Tenenbaum, 2007). Bootstrapping from empirical priors, the model is able to induce first-order relations represented as probabilistic weight distributions, even when given positive examples only. These learned representations allow classification of novel instantiations of the relations and yield a symbolic distance effect of the sort obtained with both humans and other primates. BART then transforms its learned weight distributions by importance-guided mapping, thereby placing distinct dimensions into correspondence. These transformed representations allow BART to reliably solve 4-term analogies (e.g., larger:smaller::fiercer:meeker), a type of reasoning that is arguably specific to humans. Our results provide a proof-of-concept that structured analogies can be solved with representations induced from unstructured feature vectors by mechanisms that operate in a largely bottom-up fashion. We discuss potential implications for algorithmic and neural models of relational thinking, as well as for the evolution of abstract thought.     

Creative analogy and language evolution

The English good and intensifier is discussed as an example of a form that is acceptable even though ungrammatical, both synchronically and diachronically. The construction is analyzed as a case of creative analogy: the extension of a grammatically generated form to a new function, one for which it has no direct grammatical justification. From the perspective of a dynamic theory of language acquisition and evolution, it is argued that such forms constitute a new sort of evidence regarding the nature of language universals.Previous versions of this work were presented to the LSA summer meetings in 1974 and in Carroll (1975, 1978).     

The Micro-Category account of analogy

Here, we investigate how activation of mental representations of categories during analogical reasoning influences subsequent cognitive processing. Specifically, we present and test the central predictions of the "Micro-Category" account of analogy. This account emphasizes the role of categories in aligning terms for analogical mapping. In a semantic priming paradigm, a four-word analogy task was compared to two other four-word tasks. Stimuli were identical in all tasks; only the instructions given to participants differed. Participants were instructed to identify analogy relations, category relations, or conventionalized semantic relations in the four-word sets. After each four-word set, a single target word appeared and participants named this word aloud. Target words that referred to category relations in the preceding four-word sets were primed as strongly when participants identified analogies as when participants identified categories, suggesting that activation of category concepts plays an important role in analogical thinking. In addition, priming of category-referent words in the analogy and category tasks was significantly greater than priming of these words when participants identified conventionalized semantic relations. Since identical stimuli were used in all conditions, this finding indicates that it is the activation of category relations, distinct from any effect of basic semantic association, that causes analogical reasoning to prime category-referent words. We delineate how the "Micro-Category" account of analogy predicts these phenomena and unifies findings from diverse areas of research concerning analogical reasoning.     

Components of geometric analogy solution

Geometric analogy solution was investigated as a function of systematic variations in the information structure of individual items. Latency data from the verification of true and false items indicated that individuals decompose figural patterns in a way that represents a sequential determination of the various elements that need to be isolated. They also appear to identify and evaluate the transformations applied to elements in a way that represents a sequential determination of the separate or successive transformations that fully specify an item rule. Analysis and evaluation of transformations took more time than element analysis and was the primary source of errors. The combined effects of element and transformation processing violated a simple additive model and the best fitting functions suggested that nonadditive increases in solution latency and error rates were due to working memory limitations associated with the representation and manipulation of item features at high levels of rule complexity. Correlational data also indicated that these factors partially account for individual differences in performance on psychometric tests. The latency and error data for true and false items are used to develop a general theoretical system that incorporates assumptions about the form of item representation, working memory factors, and processing components and strategies in analogical reasoning tasks.     

Domain transfer via cross-domain analogy

Analogical learning has long been seen as a powerful way of extending the reach of one’s knowledge. We present the domain transfer via analogy (DTA) method for learning new domain theories via cross-domain analogy. Our model uses analogies between pairs of textbook example problems, or worked solutions, to create a domain mapping between a familiar and a new domain. This mapping allows us to initialize a new domain theory. After this initialization, another analogy is made between the domain theories themselves, providing additional conjectures about the new domain. We present two experiments in which our model learns rotational kinematics by an analogy with translational kinematics, and vice versa. These learning rates outperform those from a version of the system that is incrementally given the correct domain theory.     

Semantic Normativity and Semantic Causality

Semantic normativism, which is the view that semantic properties/concepts are some kind of normative properties/concepts, has become increasingly influential in contemporary meta‐semantics. In this paper, I aim to argue that semantic normativism has difficulty accommodating the causal efficacy of semantic properties. In specific, I raise an exclusion problem for semantic normativism, inspired by the exclusion problem in the philosophy of mind. Moreover, I attempt to show that the exclusion problem for semantic normativism is peculiarly troublesome: while we can solve (or dissolve) mental‐physical exclusion by adopting the so‐called ‘autonomy approach’, a similar autonomy solution to semantic exclusion is implausible if semantic properties are understood as normative properties.     

The parent analogy: a reassessment

According to the parent analogy, as a caretaker’s goodness, ability and intelligence increase, the likelihood that the caretaker will make arrangements for the attainment of future goods that are unnoticed or underappreciated by their dependents also increases. Consequently, if this analogy accurately represents our relationship to God, then we should expect to find many instances of inscrutable evil in the world. This argument in support of skeptical theism has recently been criticized by Dougherty. I argue that Dougherty’s argument is incomplete, for there are two plausible ways of construing the parent analogy’s conclusion. I supplement Dougherty’s case by offering a new argument against the parent analogy based on failed expectations concerning the amount of inscrutable evils encountered in the world. Consequently, there remains a significant empirical hurdle for skeptical theism to overcome if it is to maintain its status as a defeater for our reliability when tracking gratuitous evils.     

Situation semantics and models of analogy

Conclusion The preceding theory represents, I believe, a large improvement over conceptual graph theories of analogy. In particular, it is possible for analogical reasoning to be flexible or creative on this approach, an aspect of analogy that is not accounted for in conceptual graph theories. I also believe that searching by constraint violations is a more reasonable way to organize memory search than to look for properties of conceptual hierarchies. Proof of this last point, however, awaits an more detailed classification of the constraints that figure in analogical reasoning.     

Mathematical problem solving by analogy.

We report the results of 2 experiments and a verbal protocol study examining the component processes of solving mathematical word problems by analogy. College students first studied a problem and its solution, which provided a potential source for analogical transfer. Then they attempted to solve several analogous problems. For some problems, subjects received one of a variety of hints designed to reduce or eliminate the difficulty of some of the major processes hypothesized to be involved in analogical transfer. Our studies yielded 4 major findings. First, the process of mapping the features of the source and target problems and the process of adapting the source solution procedure for use in solving the target problem were clearly distinguished: (a) Successful mapping was found to be insufficient for successful transfer and (b) adaptation was found to be a major source of transfer difficulty. Second, we obtained direct evidence that schema induction is a natural consequence of analogical transfer. The schema was found to co-exist with the problems from which it was induced, and both the schema and the individual problems facilitated later transfer. Third, for our multiple-solution problems, the relation between analogical transfer and solution accuracy was mediated by the degree of time pressure exerted for the test problems. Finally, mathematical expertise was a significant predictor of analogical transfer, but general analogical reasoning ability was not. The implications of the results for models of analogical transfer and for instruction were considered.     

Partition epistemology and arguments from analogy

Nineteenth and twentieth century philosophies of science have consistently failed to identify any rational basis for the compelling character of scientific analogies. This failure is particularly worrisome in light of the fact that the development and diffusion of certain scientific analogies, e.g. Darwin’s analogy between domestic breeds and naturally occurring species, constitute paradigm cases of good science. It is argued that the interactivist model, through the notion of a partition epistemology, provides a way to understand the persuasive character of compelling scientific analogies without consigning them to an irrational or arational context of discovery.     

Enabling spontaneous analogy through heuristic change

Despite analogy playing a central role in theories of problem solving, learning and education, demonstrations of spontaneous analogical transfer are rare. Here, we present a theory of heuristic change for spontaneous analogical transfer, tested in four experiments that manipulated the experience of failure to solve a source problem prior to attempting a target problem. In Experiment 1, participants solved more source problems that contained an additional financial constraint designed to signal the inappropriateness of moves that maximized progress towards the goal. This constraint also led to higher rates of spontaneous analogical transfer to a superficially similar problem. Experiments 2 and 3 showed that the effects of this constraint extend to superficially and structurally different analogs. Experiment 4 generalized the finding to a non-analogous target problem that also benefitted from inhibiting maximizing moves. The results indicate that spontaneous transfer can arise through experience during the solution of a source problem that alters the heuristic chosen for solving both analogical and non-analogical target problems.