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On Cascade Products of Answer Set Programs

Published online by Cambridge University Press:  21 July 2014

CHRISTIAN ANTIĆ
CHRISTIAN ANTIĆ*
Affiliation:
Institute of Information Systems, Vienna University of Technology, Favoritenstraβe 9-11, A-1040 Vienna, Austria (e-mail: christian.antic@icloud.com)
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Abstract

Describing complex objects by elementary ones is a common strategy in mathematics and science in general. In their seminal 1965 paper, Kenneth Krohn and John Rhodes showed that every finite deterministic automaton can be represented (or “emulated”) by a cascade product of very simple automata. This led to an elegant algebraic theory of automata based on finite semigroups (Krohn-Rhodes Theory). Surprisingly, by relating logic programs and automata, we can show in this paper that the Krohn-Rhodes Theory is applicable in Answer Set Programming (ASP). More precisely, we recast the concept of a cascade product to ASP, and prove that every program can be represented by a product of very simple programs, the reset and standard programs. Roughly, this implies that the reset and standard programs are the basic building blocks of ASP with respect to the cascade product. In a broader sense, this paper is a first step towards an algebraic theory of products and networks of nonmonotonic reasoning systems based on Krohn-Rhodes Theory, aiming at important open issues in ASP and AI in general.

Keywords

Answer Set Programming (ASP)Krohn-Rhodes TheoryAutomata
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 14 , Special Issue 4-5: 30th International Conference on Logic Programming , July 2014 , pp. 711 - 723
Copyright
Copyright © Cambridge University Press 2014 

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