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A rational analysis of the selection task as optimal data selection

by Mike Oaksford, Nick Chater - 67 – 215535 Deliverable 4.1 , 1994
"... Human reasoning in hypothesis-testing tasks like Wason's (1966, 1968) selection task has been depicted as prone to systematic biases. However, performance on this task has been assessed against a now outmoded falsificationist philosophy of science. Therefore, the experimental data is reassessed ..."
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of rationality: To be rational is to reason according to rules (Brown, 1989). Logic and mathematics provide the normative rules that tell us how we should reason. Rationality therefore seems to demand that the human cognitive system embodies the rules of logic and mathematics. However, results in the psychology

Mathematical Applications of Inductive Logic Programming

by Simon Colton, Stephen Muggleton
"... Abstract. The application of Inductive Logic Programming to scientific datasets has been highly successful. Such applications have led to breakthroughs in the domain of interest and have driven the development of ILP systems. The application of AI techniques to mathematical discovery tasks, however, ..."
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Abstract. The application of Inductive Logic Programming to scientific datasets has been highly successful. Such applications have led to breakthroughs in the domain of interest and have driven the development of ILP systems. The application of AI techniques to mathematical discovery tasks, however

INDUCTIVE LOGIC AND STATISTICS

by Jan-willem Romeijn
"... There are strong parallels between statistics and inductive logic. An inductive logic is a system of inference that describes the relation between propositions on data, and propositions that extend beyond the data, such as predictions over future data, and general conclusions on data. Statistics, on ..."
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on future samples, and so on. Both inductive logic and statistics are calculi for getting from the given data to propositions or results that transcend the data. Despite this fact, inductive logic and statistics have evolved more or less separately. This is partly because there are objections to viewing

An Application-based Comparison of Automated Theory Formation and Inductive Logic Programming

by Simon Colton - Linkoping Electronic Articles in Computer and Information Science (special issue: Proceedings of Machine Intelligence , 2000
"... Automated theory formation involves the production of examples, concepts and hypotheses about the concepts. The HR program performs automated theory formation and has used to form theories in mathematical domains. In addition to providing a plausible model for automated theory formation, HR has been ..."
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Automated theory formation involves the production of examples, concepts and hypotheses about the concepts. The HR program performs automated theory formation and has used to form theories in mathematical domains. In addition to providing a plausible model for automated theory formation, HR has

Materials for an exploratory theory of the network society.

by Manuel Castells , Anthony Giddens , Alain Touraine , Anthony Smith , Benjamin Barber , Peter Hall , Roger-Pol Droit , Sophie Watson , Frank Webster , Krishan Kumar , David Lyon , Craig Calhoun , Jeffrey Henderson , Ramon Ramos , Jose E Rodrigues-Ibanez , Jose F Tezanos , Mary Kaldor , Stephen Jones , Christopher Freeman - The British Journal of Sociology , 2000
"... ABSTRACT This article aims at proposing some elements for a grounded theor y of the network society. The network society is the social structure characteristic of the Information Age, as tentatively identi ed by empirical, cross-cultural investigation. It permeates most societies in the world, in v ..."
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mediations, imposes its structural determination to relationships of production. More speci cally, global nancial markets and their management networks constitute an automated network, governed by interactions between its multiple nodes, propelled by a combination of market logic, information turbulences

Automated theorem proving: mapping logic into AI

by D. W. Loveland - Proceedings of the International Symposium on Methodologies for Intelligent Systems , 1986
"... ABSTRACT. Logic can be defined as the formal study of reasoning; if we replace "for-mal " by "mechanical " we can place almost the entire set of methodologies used in the field of automated theorem proving (ATP) within the scope of logic. Because of the goals of A ..."
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ABSTRACT. Logic can be defined as the formal study of reasoning; if we replace "for-mal " by "mechanical " we can place almost the entire set of methodologies used in the field of automated theorem proving (ATP) within the scope of logic. Because of the goals

Schemata: the Concept of Schema in the History of Logic

by John Corcoran - Bulletin of Symbolic Logic 12
"... Abstract. Schemata have played important roles in logic since Aristotle’s Prior Analytics. The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 19 ..."
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1927 von Neumann paper [31]. Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski’s 1933 Convention T [42]. Mathematical logicians recognize the role of schemata in first-order number theory where Peano’s second-order Induction Axiom

Automating recursive Definitions and Termination Proofs in Higher-Order Logic

by Alexander Krauss , 2009
"... The aim of this thesis is to provide an infrastructure for general recursive function definitions in a proof assistant based on higher-order logic (HOL) that has no native support for recursion or pattern matching. In the first part we develop a tool that automates recursive function definitions and ..."
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The aim of this thesis is to provide an infrastructure for general recursive function definitions in a proof assistant based on higher-order logic (HOL) that has no native support for recursion or pattern matching. In the first part we develop a tool that automates recursive function definitions

Automated Theory Formation in Bioinformatics

by Simon Colton
"... A theory learned by an inductive logic programming (ILP) system such as Progol [5] usually comprises a set of concepts, expressed as logic programs, which can be employed for a classification task. This classifying ability can, in turn, be used for prediction tasks. A scientific theory, however, com ..."
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A theory learned by an inductive logic programming (ILP) system such as Progol [5] usually comprises a set of concepts, expressed as logic programs, which can be employed for a classification task. This classifying ability can, in turn, be used for prediction tasks. A scientific theory, however

Axiomatic proofs through automated reasoning

by Branden Fitelson, Larry Wos - Bulletin of the Section of Logic
"... A search of the seminal papers and significant books devoted to the study of various types of logic reveals that many proofs are missing. Indeed, if one seeks an axiomatic proof (of the type that Hilbert enjoyed) relying solely on, say, condensed detachment, in many cases one finds that none is offe ..."
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. 1. Nature, Incentive, and Perspective Papers in logic and in mathematics abound with lists of lemmas, corollaries, and theorems, none, some, or all of which are accompanied by a proof. The nature and type of proof vary widely. At one end of the spectrum, in both logic and mathematics, one finds
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