cle it is, of course, much more recommended to link dividuals: often most of them are already completely DBox, except the one of (quickly) retrieving lists means of a relational database, and queries to the such a way that a uniform query function, based on data from these databases to our knowledge bases. { i.e., belonging to a unary table/view { or being in be collected ex-novo it can be to manage convenient5 over, they are automatically kept updated as far as description we say also that the set of data ex- W3; These conditions are of the kind of being in a class separately exist, for both the ABox and the DBox, most of them by means of a DBMS.
DBox can be done in SQL. Therefore in the followas it can be, for example, expressed in SQL. Since the two answering functions, can be implemented. ing we will refer to tables/views { or simply tables { minimum the eort of transferring data and, moreWe do not require any special capability from the of tuples of items satisfying requested conditions. a knowledge base KB = hT ; W; Di can be dened in suming that two complete query answering functions relation with other items { i.e., belonging to a binary table/view { and logical combinations of these, to those of SQL.4 complex, but can also involve a large number of inexperience suggests that, in realis- [Bresciani,1992] as they usually are intended in relational databases, the linked databases are. But also when data must tic applications, knowledge bases not only can be and to the query answering function of the DBox as the databases to the knowledge bases. Using a DBox paradigm we obtain the advantage of reducing to the SQL, we assume that D is somehow represented by pressed in a DBox constitutes a data base D. Asour implementation relies, in fact, on a DBMS with several times, in the past, the task of transferring and suitably described in some database. We faced >From the point of view of users of KBMS, our Using the techniques described in the present artisingle instances are, therefore, already placed in the As mentioned, in our KB, D is assumed to contain This corresponds to having each table of D associated with a primitive of T . We will show how term6 not supposed to have any inferential power. The completely a-priori realized under the right concept. no structural knowledge, but just raw data, and is right tables. That is, speaking in KR terms, they are the association of those terms in T whose extensions set of all the terms classied under t in T (includM : T ! s.t. M (t) = fP M (x) j x 2 2DBtable, diate db extension condition above. Therefore, tables of records of data, without any reasoning cative terms in T , and DBtable the set of tables in homogeneous extension hypothesis can always be are in D with the corresponding tables in the DB.
DBtable is given, where PT is the set of primiwe assume that a partial mapping P M : PT ! satised. The db isolation and the non intermeKB = hT ; W; D;P M i. for each class of individuals present in D: by this the ing t). The marking function gives the (possibly pability.
To this extent it is enough to know this association empty) set of tables necessary to retrieve all the insubs(t) and P M (x) is dened g, where subs(t) is the esis that D is just a at collection of unstructured stances (pairs) of a given concept (relation). Thereneeded to correctly drive the query mechanism is fore, it is an important part of our KB, whose deUnder these assumptions, all the information such a way that a primitive term is introduced in T for those terms that are leaf, for the non intermenition, to be more precise, has now to be rephrased: Consider that it is not dicult to design KB in the DB. So, we can dene the marking function diate db extension conditions reect the h ypothselector similar to those in select-body, correspondtively; field1 corresponds to the rst occurence of tively. The from-body is the list of all the tables inbindings via the variables in x. For simplicity, let each use of constants. In both the forms field2 is a variable in x, according to the fact that the vari- xi the variable. translated into an equivalent SQL query. Of course, where the select-body is a list of column names of the of SQL where-conditions of the kind field2=field1 with the union set of tables : : : ; and their fT1; Thg us suppose that the tables returned by M are comtion (let them be called left and right). The SQL or field2=constant, where the rst form has to be used for each variable that is used more than once, volved { i.e., all the M The where-body is a list (Pi). able appears for the rst time in the predicate xi kind M ):left or M ):right, one for each (Pxi (Pxi SELECT DISTINCT select-body can be made correspond to a set of tables in the FROM f rom-body ing to positions in the query where the variable is ing function M . At this point we have just to cope DB, where the answers have to be found, it can be each time it is reused, and the second form occurs for WHERE where-body in the rst place 7 or in the second place, respec- Pxi it be called left), and two in the case of a relafurther used or where the constant appears, respectranslation is of the kind: posed by one column in the case of a concept (let When each predicate in a query q = ^ : : : ^ x:P1 Pn the sets of tables can be easily found via the markvious that, in order to avoid the generation of huge set of the query can be unreasonably large, due that a query is unconnected when it can be split into the KBMS. Answering a query in KB means nding answer sets, free variables should not be used, i.e., hx; y; zi:A(x) ^ R(x; y) ^ C(z). All the variables call these sub-queries clusters. It is obvious that the the answers of the sub-query hzi:C(z). We say that the query body (i.e., the part at the right of the requires the merging of results from the DBMS and a set fx : : : ; x of tuples of instances s.t., for each 1; mg such a query is unconnected. More in general, we say dot). Indeed, we adopt a stronger restriction, betuple x ^ : : :^ holds in KB. We call i, x:(P1 Pn)[x i] two or more sub-queries s.t. all the variables appearcause the former one still allows for some undesired to the fact that all the answers of the sub-query Due to the denition of answ er of a query, it is obIn general answering, a query is more complex and of them its answer set. hx; yi:A(x) ^ R(x; y) have to be combined with all appear in the body, but, nevertheless, the answer situations. Let us consider, for example, the query: ing in each of them does not appear in any other. We each variable appearing in x must appear also in such tuples answers of the query and the set of all actly, if, after having reordered the variables, un unIt is now clear that unconnected queries and connected queries with only bound variables. conected query is written as ^ : : :^ x:’1(x1) ’n(xn) relevant result of answering an unconnected query is queries with unbound variables may have unreasonarately answering the clusters, in the sense that all longer than those resulting by submitting the sinresponding to the terms in T , and say that a term ables appearing in x but not in y, and T (z) = the asnwers sets of a generic cluster is xi:’i(xi) P is: The case of a connected (i.e., non unconnected) 1 li To aord the answ ering of a query we need to split { where x is the concatenation of the other veccombined by a sort of Cartesian product. More ex^ : : : ^ where top correspond to the top(z1) top(zk), gle clusters; to obtain all the tuples satisfying the the formal denition of answer, we must consider pability to the system. Therefore, we consider only is S = . j I 2 : : : ; 2 fIj11 .I jnn j11 S1; Ijnn Sng. the information is included in it. But, if we consider denition of answer the single answers have to be duced to the case of an unconnected query x:’(y)^ and the DBMS. To this extent we need, as a rst ably large answer sets, without giving any further castep, to mark all the possible atomic predicates, corT (z), where z = : : : ; contains all the vari- hz1; zki responds to the single clusters { and given that tors (x = and : : : ; cor- x1. .xn), ’1(x1); ’n(xn) it into sub-queries that can be answered by the two most generic concept in T . specialized query answering functions of the KBMS query x:’(y) with unbound variables can be reis dened . - DB-marked i for eac h t 2 subs(P )\PT P M (t) = ; : : : ; g, the answer set of the whole query Si fIi Ii the fact that the overall result must contain tuples equivalent to the union of the single results of sep4.6 RETURN the only item left in result-list. 4.1-bis Developments let 5.1 Constraints on the Form of KB 5 Conclusion and Future the individuals in KB. Using this representation for merged into a single answer set as follow: any marker, e.g., a star ‘?’. The star stands for all fact answer sets , , and can be ASxKB ASxDB ASxM the completion in step 3, it is now easy to rephrase where I ? are equivalent to I except that are lengthened by lling the k missing positions : : : ; with p1; pk step 4 of the algorithm as a merging operation. In marked term into SQL. For example, if the query is this condition. In fact, while keeping the fact that Indeed we can, at least in part, give up also with primitive, denition. To this extent we need a much ing from the DB cannot be inferred { we can allow more complex schema for translating queries on DBSQL translation could be: such term to be used inside new, eventually even non of the kind hxi:C(x) where C some(R; D), its =: coherent with the fact that the raw information comsuch term must be primitive { this is pragmatically