Induction and decision procedures

PNA. Revista de Investigación en Didáctica de la Matemática

We present an analysis of the inductive reasoning of twelve Spanish secondary students in a mathematical problem-solving context. Students were interviewed while they worked on two different problems. Based on Polya´s steps and Reid’s stages for a process of inductive reasoning, we propose a more precise categorization for analyzing this kind of reasoning in our particular context. In this paper we present some results of a wider investigation (Cañadas, 2002). Una propuesta de categorización para analizar el razonamiento inductivo Presentamos un análisis del razonamiento inductivo de doce estudiantes de educación secundaria en un contexto de resolución de problemas matemáticos. Los estudiantes fueron entrevistados mientras trabajaban en dos problemas diferentes. Basándonos en los pasos considerados por Pólya y Reid para un proceso de razonamiento inductivo, proponemos una categorización más precisa para analizar este tipo de razonamiento en nuestro contexto particular. En este docum...

Philosophy, Logic, and Artificial Intelligence, 1999

Non-Axiomatic Reasoning System (NARS) is designed to be a general-purpose intelligent reasoning system, which is adaptive and works under insu cient knowledge and resources. This paper focuses on the components of NARS that contribute to the system's induction capacity, and shows how the traditional problems in induction are addressed by the system. The NARS approach of induction uses an term-oriented formal language with an experience-grounded semantics that consistently interprets various types of uncertainty. An induction rule generates conclusions from common instance of terms, and a revision rule combines evidence from di erent sources. In NARS, induction and other types of inference, such as deduction and abduction, are based on the same semantic foundation, and they cooperate in inference activities of the system. The system's control mechanism makes knowledge-driven, context-dependent inference possible.

Communications of the ACM, 1995

Techniques of machine learning have been successfully applied to various problems . Most of these applications rely on attribute-based learning, exemplified by the induction of decision trees as in the program C4.5 . Broadly speaking, attribute-based learning also includes such approaches to learning as neural networks and nearest neighbor techniques. The advantages of attribute-based learning are: relative simplicity, efficiency, and existence of effective techniques for handling noisy data. However, attribute-based learning is limited to non-relational descriptions of objects in the sense that the learned descriptions do not specify relations among the objects' parts. Attribute-based learning thus has two strong limitations:

This is part II in a series of papers outlining Abstraction Theory, a theory that I propose provides a solution to the characterisation or epistemological problem of induction. Logic is built from first principles severed from language such that there is one universal logic independent of specific logical languages. A theory of (non-linguistic) meaning is developed which provides the basis for the dissolution of the 'grue' problem and problems of the non-uniqueness of probabilities in inductive logics. The problem of counterfactual conditionals is generalised to a problem of truth conditions of hypotheses and this general problem is then solved by the notion of abstractions. The probability calculus is developed with examples given. In future parts of the series the full decision theory is developed and its properties explored.

1993

A for-loop is somewhat similar to an inductive argument. Just as the truth of a proposition P(n + 1) depends on the truth of P(n), the correctness of iteration n+1 of a for-loop depends on iteration n having been completed correctly. This paper presents the induce-construct, a new programming construct based on the form of inductive arguments. It is more expressive than the for-loop yet less expressive than the while-loop. Like the for-loop, it is always terminating. Unlike the for-loop, it allows the convenient and concise expression of many algorithms. The for-loop traverses a set of consecutive natural numbers, the induce-construct generalizes to other data types. The induce-construct is presented in two forms, one for imperative languages and one for functional languages. The expressive power of languages in which this is the only recursion construct is greater than primitive recursion, namely it is the multiply recursive functions in the rst order case and the set of functions expressible in G odel's system T in the general case. 0 Data Types We consider languages in which some of the data types are de ned by recursion as in Hoare's`Recursive Data Types' 8] or the language ML. The example in this paper use the following (polymorphic) types. tree 2() = empty j node(; tree 2(); tree 2()) list() = nil j :list() tree n() = empty j node(; list(tree n())) natural = 0 j natural 0 This article was processed using the L a T E X macro package with LLNCS style View publication stats View publication stats

Citeseer

Learning problems can be difficult for many reasons, one of them is inadequate representation space or description language. Features can be considered as a representational language; when this language contains more features than necessary, subset selection helps ...

Studia Logica - An International Journal for Symbolic Logic, 2011

The paper contains a survey of (mainly unpublished) adaptive logics of inductive generalization. These defeasible logics are precise formula- tions of certain methods. Some attention is also paid to ways of handling background knowledge, introducing mere conjectures, and the research guiding capabilities of the logics.

IEEE Expert / IEEE Intelligent Systems, 1998

rithms enable the learner to extend its vocabulary with new terms if, for a given a set of training examples, the learner's vocabulary is too restncted to solve the learning task. We propose a filter that selects potentially relevant terms from the set of constructed terms and eliminates terms that are irrelevant for the learning task. Restricting constructive induction (or predicate invention) to relevant terms allows a much larger explored space of constructed terms. The elimination of irrelevant terms is especially well-suited for learners of large time or space complexity, such as genetic algorithms and artificial neural networks.

International Joint Conference on Artificial Intelligence, 1995