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Published in:
2010 | OriginalPaper | Chapter
Closeness and Distance Relations in Order of Magnitude Qualitative Reasoning via PDL
Authors : Alfredo Burrieza, Emilio Muñoz-Velasco, Manuel Ojeda-Aciego
Published in: Current Topics in Artificial Intelligence
Publisher: Springer Berlin Heidelberg
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The syntax, semantics and an axiom system for an extension of Propositional Dynamic Logic (PDL) for order of magnitude qualitative reasoning which formalizes the concepts of closeness and distance is introduced in this paper. In doing this, we use some of the advantages of PDL: firstly, we exploit the possibility of constructing complex relations from simpler ones for defining the concept of closeness and other programming commands such as
while ... do
and
repeat ... until
; secondly, we employ its theoretical support in order to show that the satisfiability problem is decidable and the completeness of our system. Moreover, the specific axioms of our logic have been obtained from the
minimal
set of formulas needed in our definition of qualitative sum of small, medium and large numbers. We also present some of the advantages of our approach on the basis of an example.