A Logical Approach to Reasoning by Analogy

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 (2) 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

Logical Comparison of Cases

Comparison between cases is a core issue in case-based reasoning. In this paper, we discuss a logical comparison approach in terms of the case model formalism. By logically generalizing the formulas involved in case comparison, our approach identifies analogies, distinctions and relevances. An analogy is a property shared between cases. A distinction is a property of one case ruled out by the other case, and a relevance is a property of one case, and not the other, that is not ruled out by the other case. The comparison approach is applied to HYPO-style comparison (where distinctions and relevances are not separately characterized) and to the temporal dynamics of case-based reasoning using a model of real world cases.</p

Teaching Legal Reasoning in Law School

With the understanding that reasonable scholars and critics may differ, it is nevertheless this article\u27s contention that law schools today must still strive to teach the basic logical principles-and process-of legal reasoning. By analogy, a swimmer must learn at least a few basic strokes in order to survive in his new environment. The same is true with law students and legal reasoning. An elementary foundation in legal reasoning skills, limited though it may be, is still better than nothing at all-especially when the latter alternative offers only confusion and misunderstanding. The purpose of this article is to discuss one such approach in teaching the principles and process of legal reasoning to first year students at the University of Richmond Law School. Although the author realizes that this is only one of many approaches to the subject in question, it is hoped that some of the fundamental assumptions within this discussion may serve as a catalyst for teaching legal reasoning techniques in other schools as well

PROFIL PENALARAN ANALOGI SISWA DALAM PEMECAHAN MASALAH MATEMATIKA DITINJAU DARI KEMAMPUAN MATEMATIKA

Analogy reasoning is the process of thinking logically and analytically in drawing conclusions based on the similarities between the two things being compared. The purpose of this study is to describe the analogy reasoning of students in solving mathematical problems in terms of high, medium, and low mathematical abilities. This research is a descriptive study with a qualitative approach. Data collection was carried out in class IX-H of SMP Negeri 5 Surabaya in the 2019/2020 school year by 33 students and each subject was selected for each category of mathematical ability. The results of the analysis of Problem Solving Tests and interviews show that students with high, medium, and low mathematical abilities mention information that is known and what is asked for logical reasons on the source and target problem, and explain the relations between the information. This indicates that each subject has an encoding process. Each subject also mentions and explains the concepts used to solve source problems, which means each subject has an inferring process. The difference is, subjects with high mathematical ability mention the same concepts between the source problem and the target problem and explain the concepts used to solve the target problem, then students can complete the target problem. This means that the subject is doing two other processes, namely mapping and applying. Subjects with medium mathematical abilities are mentioning the same concept between the source problem and the target problem but cannot explain the concept used in the target problem. However, the subject only did one of the two indicators in the mapping process, so the analogy reasoning process carried out by the subject was encoding and inferring. While students with low mathematical abilities are stopped in the encoding and inferring processes. Keywords: Analogy Reasoning, Mathematical Abiliti

Reasoning by Analogy in a Multi-Level System Architecture for the Design of Mechanisms

Since the first attempts to integrate AI technology and engineering design nearly two decades ago, few expert systems have been shown to demonstrate sufficient reasoning capabilities to solve real-world design problems. The complex nature of design, the lack of understanding of the design process, and the limitations of current expert system technology have all been shown to have adverse effects on the maturity of this research area. Therefore, our direction in this research concentrates on understanding the design process, investigating a novel area of research focusing on creative design, and incorporating the results into a system model feasible for production use. The model presented is based on the concept of reusing past experience and existing cases to solve future design problems in different application domains. The resulting system performs its task by reasoning and learning by ANALOGY while utilizing the Logical-Building Block approach to design. Our method demonstrates the use of a case-based reasoner in conjunction with other existing techniques, such as heuristic reasoning and first principle reasoning, to produce a system with three levels of reasoning strategies. Such a system will exhibit a learning capability by which its performance is enhanced with repeated use. A prototype has been implemented and tested for the synthesis of various mechanisms

The shallow processing of logical negation

The aim of this study is to introduce a novel reasoning phenomenon concerned with the shallow processing of negation in the context of sentential reasoning. By analogy to other psychological explanations that account for superficial responses with conditionals, this study proposes an account for biconditionals derived from a recent theory of negation. This theory predicts that the psychological use of negation returns small scope products. This would happen because the human mind tends to avoid the working memory overload by simplifying its reasoning processes. A within-subjects experimental design was applied to test this conjecture. Results were consistent with such small scope negation prediction. The obtained evidence extends the observation of shallow reasoning processes to the negation of conjunctions and disjunctions that take the form of biconditionals. The results of this study support a mental models approach to account for the psychology of logical negation.Fil: Macbeth, Guillermo Eduardo. Universidad Nacional de Entre Rios; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Razumiejczyk, Eugenia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Entre Rios; ArgentinaFil: Crivello, María del Carmen. Universidad Nacional de Entre Rios; ArgentinaFil: Fioramonti, Mauro Bruno. Universidad Nacional de Entre Rios; ArgentinaFil: Pereyra Girardi, Carolina Iris. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires; Argentin

Circles and analogies in public health reasoning

The study of the fallacies has changed almost beyond recognition since Charles Hamblin called for a radical reappraisal of this area of logical inquiry in his 1970 book Fallacies. The “witless examples of his forbears” to which Hamblin referred have largely been replaced by more authentic cases of the fallacies in actual use. It is now not unusual for fallacy and argumentation theorists to draw on actual sources for examples of how the fallacies are used in our everyday reasoning. However, an aspect of this move towards greater authenticity in the study of the fallacies, an aspect which has been almost universally neglected, is the attempt to subject the fallacies to empirical testing of the type which is more commonly associated with psychological experiments on reasoning. This paper addresses this omission in research on the fallacies by examining how subjects use two fallacies – circular argument and analogical argument – during a reasoning task in which subjects are required to consider a number of public health scenarios. Results are discussed in relation to a view of the fallacies as cognitive heuristics that facilitate reasoning in a context of uncertainty

The Generalised Liar Paradox: A Quantum Model and Interpretation

The formalism of abstracted quantum mechanics is applied in a model of the generalized Liar Paradox. Here, the Liar Paradox, a consistently testable configuration of logical truth properties, is considered a dynamic conceptual entity in the cognitive sphere. Basically, the intrinsic contextuality of the truth-value of the Liar Paradox is appropriately covered by the abstracted quantum mechanical approach. The formal details of the model are explicited here for the generalized case. We prove the possibility of constructing a quantum model of the m-sentence generalizations of the Liar Paradox. This includes (i) the truth-falsehood state of the m-Liar Paradox can be represented by an embedded 2m-dimensional quantum vector in a (2m)^m dimensional complex Hilbert space, with cognitive interactions corresponding to projections, (ii) the construction of a continuous 'time' dynamics is possible: typical truth and falsehood value oscillations are described by Schrodinger evolution, (iii) Kirchoff and von Neumann axioms are satisfied by introduction of 'truth-value by inference' projectors, (iv) time invariance of unmeasured state.Comment: 13 pages, to be published in Foundations of Scienc

Iteratively Learning Embeddings and Rules for Knowledge Graph Reasoning

Reasoning is essential for the development of large knowledge graphs, especially for completion, which aims to infer new triples based on existing ones. Both rules and embeddings can be used for knowledge graph reasoning and they have their own advantages and difficulties. Rule-based reasoning is accurate and explainable but rule learning with searching over the graph always suffers from efficiency due to huge search space. Embedding-based reasoning is more scalable and efficient as the reasoning is conducted via computation between embeddings, but it has difficulty learning good representations for sparse entities because a good embedding relies heavily on data richness. Based on this observation, in this paper we explore how embedding and rule learning can be combined together and complement each other's difficulties with their advantages. We propose a novel framework IterE iteratively learning embeddings and rules, in which rules are learned from embeddings with proper pruning strategy and embeddings are learned from existing triples and new triples inferred by rules. Evaluations on embedding qualities of IterE show that rules help improve the quality of sparse entity embeddings and their link prediction results. We also evaluate the efficiency of rule learning and quality of rules from IterE compared with AMIE+, showing that IterE is capable of generating high quality rules more efficiently. Experiments show that iteratively learning embeddings and rules benefit each other during learning and prediction.Comment: This paper is accepted by WWW'1