Abstraction Within Partial Deduction for Linear Logic - Artificial Intelligence and Symbolic Computation - page 64

automate the formation of abstraction spaces, but only partially automated the
process. Besides, ABSTRIPS produced only relaxed models [6], by abstracting
away literals in preconditions, thus the problem space was not abstracted at all.
However, the algorithm, we apply here, produces reduced models , where literals
are abstracted away at particular abstraction level from all formulae. Other
approaches to automatic construction of abstraction spaces include [1, 2, 12].
In this paper we presented a method to apply abstractions to PD problems
by using information about dependencies between literals. Then through hierar-
chical PD the complexity of overall theorem proving would be decreased.
If an abstract space is formed by dropping conditions from the original prob-
lem space as we did, information is lost and axioms in the abstract space can
be applied in situations in which they cannot be applied in the original space.
Thus, using an abstraction space formed by dropping information, it is dicult
to guarantee that if there exists an abstract solution, there exists also a solution
in the base space. This problem is called the false proof problem [14, 4].
Acknowledgements
This work is partially supported by the Norwegian Research Foundation in the
framework of Information and Communication Technology (IKT-2010) program
- the ADIS project. I would like to thank the anonymous referees for their
constructive comments and suggestions.
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