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Computational Abstraction.

Raymond Turner1

  • 1School of Computer Science and Electronic Engineering, University of Essex, Colchester CO4 3SQ, UK.

Entropy (Basel, Switzerland)
|February 13, 2021
PubMed
Summary
This summary is machine-generated.

This study analyzes data abstraction in computer science, differentiating it from representation. It proposes a mathematical framework for abstraction using Frege's ideas within type theory, highlighting their distinct philosophical roles.

Keywords:
Fregeabstractioncomputationrepresentationspecification

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Area of Science:

  • Computer Science
  • Philosophy of Mathematics
  • Type Theory

Background:

  • Representation and abstraction are foundational to high-level programming.
  • Formal accounts of representation are common, but abstraction is less formally defined.
  • Existing programming paradigms rely on both concepts for bridging machine code and mathematical exercises.

Purpose of the Study:

  • To provide a formal analysis of data abstraction.
  • To explore the philosophical differences between representation and abstraction.
  • To adapt Frege's approach to abstraction within type theory.

Main Methods:

  • Analysis of contemporary work in the philosophy of mathematics.
  • Mathematical interpretation, modification, and extension of Frege's abstraction principles.
  • Integration of these principles into type theory.

Main Results:

  • A mathematical account of data abstraction is presented.
  • Representation and abstraction are shown to be mathematically related but philosophically distinct.
  • The abstract/physical interface is identified as a key area of interest.

Conclusions:

  • Abstraction and representation, while siblings in mathematics, have fundamentally different philosophical implications.
  • Frege's approach to abstraction can be formalized and extended within type theory.
  • Understanding the abstract/physical interface is crucial for both representing abstract structures and abstracting physical systems.