3 research outputs found
Redundancy in Logic I: CNF Propositional Formulae
A knowledge base is redundant if it contains parts that can be inferred from
the rest of it. We study the problem of checking whether a CNF formula (a set
of clauses) is redundant, that is, it contains clauses that can be derived from
the other ones. Any CNF formula can be made irredundant by deleting some of its
clauses: what results is an irredundant equivalent subset (I.E.S.) We study the
complexity of some related problems: verification, checking existence of a
I.E.S. with a given size, checking necessary and possible presence of clauses
in I.E.S.'s, and uniqueness. We also consider the problem of redundancy with
different definitions of equivalence.Comment: Extended and revised version of a paper that has been presented at
ECAI 200
Redundancy in Logic III: Non-Mononotonic Reasoning
Results about the redundancy of circumscriptive and default theories are
presented. In particular, the complexity of establishing whether a given theory
is redundant is establihsed.Comment: minor correction
Redundancy in Logic II: 2CNF and Horn Propositional Formulae
We report complexity results about redundancy of formulae in 2CNF form. We
first consider the problem of checking redundancy and show some algorithms that
are slightly better than the trivial one. We then analyze problems related to
finding irredundant equivalent subsets (I.E.S.) of a given set. The concept of
cyclicity proved to be relevant to the complexity of these problems. Some
results about Horn formulae are also shown.Comment: Corrected figures on Theorem 10; added and modified some reference