An Algebraic Approach to Knowledge Representation

Nearlattices with an Overriding Operation

“…The three conditions in (5) below were used as axioms of the overriding operation in [10]. Therefore, the next lemma shows that the present paper and [10] deal essentially with the same notion of overriding.…”

“…The operation ← − ∪ , usually restricted to records with finite domain, has been termed overriding in computer science literature [7] (the notation ϕ ← − ∪ ψ then reads as 'ϕ overrided by ψ'). We extend use of the term also to general tolerance spaces, and, following [10], apply it to the "abstract" operation in an arbitrary nearlattice as well.…”

“…Our main goal in this paper initially was study of elementary properties of overriding and giving full proofs to several results announced in [10]; among them, Theorem 3 therein, which says when a Boolean overriding nearlattice is representable as an algebra of functions. However, in the final version of the paper, we have followed the suggestions of one of the anonymous referees and, instead of some of these proofs, have given more attention to general properties of overriding nearlattices.…”

“…Example 1.5 [10] A tolerance space is a pair (T, ∼), where T is a non-empty set and ∼ is a reflexive and symmetric binary relation (tolerance) on X. Given subsets X and…”

“…The subject of this paper is nearlattices in which a b exists for all a and b . A few preliminary results concerning such nearlattices were announced in [10]; some motivation for choice of nearlattices as the underlaying structures for the operation also can be found there.…”