scholarly journals Confirmation Based on Analogical Inference: Bayes Meets Jeffrey

2019 ◽  
Vol 50 (2) ◽  
pp. 174-194
Author(s):  
Christian J. Feldbacher-Escamilla ◽  
Alexander Gebharter
Keyword(s):  
Analogical Reasoning ◽  
Moral Reasons ◽  
Analogical Inference ◽  
Jeffrey Conditionalization ◽  
Bayesian Update

AbstractCertain hypotheses cannot be directly confirmed for theoretical, practical, or moral reasons. For some of these hypotheses, however, there might be a workaround: confirmation based on analogical reasoning. In this paper we take up Dardashti, Hartmann, Thébault, and Winsberg’s (2019) idea of analyzing confirmation based on analogical inference Bayesian style. We identify three types of confirmation by analogy and show that Dardashti et al.’s approach can cover two of them. We then highlight possible problems with their model as a general approach to analogical inference and argue that these problems can be avoided by supplementing Bayesian update with Jeffrey conditionalization.

Inferring Causal Relations by Analogy

2017 ◽  
Author(s):  
Keith J. Holyoak ◽  
Hee Seung Lee
Keyword(s):  
Analogical Reasoning ◽  
Causal Model ◽  
Causal Knowledge ◽  
Common Pattern ◽  
Causal Relations ◽  
Analogical Inference ◽  
Psychological Evidence ◽  
Inductive Inferences ◽  
Novel Target ◽  
Constituent Elements

When two situations share a common pattern of relationships among their constituent elements, people often draw an analogy between a familiar source analog and a novel target analog. This chapter reviews major subprocesses of analogical reasoning and discusses how analogical inference is guided by causal relations. Psychological evidence suggests that analogical inference often involves constructing and then running a causal model. It also provides some examples of analogies and models that have been used as tools in science education to foster understanding of critical causal relations. A Bayesian theory of causal inference by analogy illuminates how causal knowledge, represented as causal models, can be integrated with analogical reasoning to yield inductive inferences.

Relational Reasoning in a Neurally Plausible Cognitive Architecture

2005 ◽  
Vol 14 (3) ◽  
pp. 153-157 ◽  
Author(s):  
John E. Hummel ◽  
Keith J. Holyoak
Keyword(s):  
Analogical Reasoning ◽  
A Priori ◽  
Cognitive Architecture ◽  
Relational Reasoning ◽  
Natural Basis ◽  
Analogical Inference ◽  
Analogical Mapping ◽  
Design Requirements ◽  
Human Thinking ◽  
Propositional Structures

Human mental representations are both flexible and structured—properties that, together, present challenging design requirements for a model of human thinking. The Learning and Inference with Schemas and Analogies (LISA) model of analogical reasoning aims to achieve these properties within a neural network. The model represents both relations and objects as patterns of activation distributed over semantic units, integrating these representations into propositional structures using synchrony of firing. The resulting propositional structures serve as a natural basis for memory retrieval, analogical mapping, analogical inference, and schema induction. The model also provides an a priori account of the limitations of human working memory and can simulate the effects of various kinds of brain damage on thinking.

Multiple analogical proportions

2021 ◽  
pp. 1-18
Author(s):  
Henri Prade ◽  
Gilles Richard
Keyword(s):  
Artificial Intelligence ◽  
Linear Algebra ◽  
Building Block ◽  
Analogical Reasoning ◽  
Weak Form ◽  
Boolean Logic ◽  
Real Numbers ◽  
Analogical Inference ◽  
Logical Modeling

Analogical proportions are statements of the form “a is to b as c is to d”, denoted a : b : : c : d, that may apply to any type of items a, b, c, d. Analogical proportions, as a building block for analogical reasoning, is then a tool of interest in artificial intelligence. Viewed as a relation between pairs ( a , b ) and ( c , d ), these proportions are supposed to obey three postulates: reflexivity, symmetry, and central permutation (i.e., b and c can be exchanged). The logical modeling of analogical proportions expresses that a and b differ in the same way as c and d, when the four items are represented by vectors encoding Boolean properties. When items are real numbers, numerical proportions – arithmetic and geometric proportions – can be considered as prototypical examples of analogical proportions. Taking inspiration of an old practice where numerical proportions were handled in a vectorial way and where sequences of numerical proportions of the form x 1 : x 2 : ⋯ : x n : : y 1 : y 2 : ⋯ : y n were in use, we emphasize a vectorial treatment of Boolean analogical proportions and we propose a Boolean logic counterpart to such sequences. This provides a linear algebra calculus of analogical inference and acknowledges the fact that analogical proportions should not be considered in isolation. Moreover, this also leads us to reconsider the postulates underlying analogical proportions (since central permutation makes no sense when n ⩾ 3) and then to formalize a weak form of analogical proportion which no longer obeys the central permutation postulate inherited from numerical proportions. But these weak proportions may still be combined in multiple weak analogical proportions.

scholarly journals Analogical Reasoning as an Inference Scheme

Dialogue ◽  
2021 ◽  
pp. 1-21
Author(s):  
Bernard Walliser ◽  
Denis Zwirn ◽  
Hervé Zwirn
Keyword(s):  
Analogical Reasoning ◽  
General Scheme ◽  
Formal Representation ◽  
Analogical Inference ◽  
Different Types

Abstract Despite its importance in various fields, analogical reasoning has not yet received a unified formal representation. Our contribution proposes a general scheme of inference that is compatible with different types of logic (deductive, probabilistic, non-monotonic). Firstly, analogical assessment precisely defines the similarity of two objects according to their properties, in a relative rather than absolute way. Secondly, analogical inference transfers a new property from one object to a similar one, thanks to an over-hypothesis linking two sets of properties. The belief strength in the conclusion is then directly related to the belief strength in this meta-hypothesis.

scholarly journals Analogical Reasoning as an Inference Scheme

2021 ◽  
Author(s):  
Bernard Walliser ◽  
Denis ZWIRN ◽  
Hervé ZWIRN
Keyword(s):  
Analogical Reasoning ◽  
Single Case ◽  
Point Of View ◽  
Analogical Inference ◽  
The Difference ◽  
Definition Of

Abstract 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.

scholarly journals In Defense of Analogical Reasoning

2008 ◽  
Vol 28 (3) ◽  
pp. 229 ◽  
Author(s):  
Steven Gamboa
Keyword(s):  
Analogical Reasoning ◽  
Scientific Models ◽  
Existence Proof ◽  
Analogical Inference

I offer a defense of ana-logical accounts of scientific models by meeting certain logical objections to the legitimacy of analogical reasoning. I examine an argument by Joseph Agassi that purports to show that all putative cases of analogical inference succumb to the following dilemma: either (1) the reasoning remains hopelessly vague and thus establishes no conclusion, or (2) can be analyzed into a logically preferable non-analogical form. In rebuttal, I offer a class of scientific models for which (a) there is no satisfactory non-analogical analysis, and (b) we can gain sufficient clarity for the legitimacy of the inference to be assessed. This result constitutes an existence proof for a class of analogical models that escape Agassi’s dilemma.

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