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SCIENCE CHINA Information Sciences, Volume 61, Issue 4: 042101(2018) https://doi.org/10.1007/s11432-017-9199-8

A computational framework for Karl Popper's logic of scientific discovery

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  • ReceivedFeb 21, 2017
  • AcceptedJun 19, 2017
  • PublishedFeb 6, 2018

Abstract

Belief revision is both a philosophical and logical problem. From Popper's logic of scientific discovery, we know that revision is ubiquitous in physics and other sciences. The AGM postulates and $R$-calculus are approaches from logic, where the $R$-calculus is a Gentzen-type concrete belief revision operator. Because deduction is undecidable in first-order logic, we apply approximate deduction to derive an $R$-calculus that is computational and has finite injury. We further develop approximation algorithms for SAT problems to derive a feasible $R$-calculus based on the relation between deduction and satisfiability. In this manner, we provide a full spectrum of belief revision: from philosophical to feasible revision.

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