TY - JOUR
T1 - Representation theory for default logic
AU - Marek, V. Wiktor
AU - Treur, Jan
AU - Truszczyński, Mirosław
PY - 1997
Y1 - 1997
N2 - Default logic can be regarded as a mechanism to represent families of belief sets of a reasoning agent. As such, it is inherently second-order. In this paper, we study the problem of representability of a family of theories as the set of extensions of a default theory. We give a complete solution to the problem of representability by means of default theories with finite set of defaults, and by means of normal default theories. We obtain partial results on representability by arbitrary (infinite, non-normal) default theories. We construct examples of denumerable families of non-including theories that are not representable. We also study the concept of equivalence between default theories.
AB - Default logic can be regarded as a mechanism to represent families of belief sets of a reasoning agent. As such, it is inherently second-order. In this paper, we study the problem of representability of a family of theories as the set of extensions of a default theory. We give a complete solution to the problem of representability by means of default theories with finite set of defaults, and by means of normal default theories. We obtain partial results on representability by arbitrary (infinite, non-normal) default theories. We construct examples of denumerable families of non-including theories that are not representable. We also study the concept of equivalence between default theories.
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U2 - 10.1023/a:1018977721624
DO - 10.1023/a:1018977721624
M3 - Article
AN - SCOPUS:21944453136
SN - 1012-2443
VL - 21
SP - 343
EP - 358
JO - Annals of Mathematics and Artificial Intelligence
JF - Annals of Mathematics and Artificial Intelligence
IS - 2-4
ER -