We discuss some of the recent controversies concerning the DLP fragment of OWL. We argue that it is a meaningful fragment and can serve as a basic interoperability layer between OWL and logic programming-based ontology languages.
DLP — Description Logic Programs — has originally been conceived in [
We think that DLP isn’t so bad after all. It is limited, yes, but useful to
understand the relationships between ontology languages such as OWL and F-Logic.
Further it is a constructive approach to establishing interoperability among them
on a well-defined level. Indeed, we claim that the semantic issues concerning logic
programming, OWL, and their intersection DLP are not as fuzzy as they seem
and are often displayed as. We believe that DLP can serve as a very basic
interoperability layer between OWL and logic programming-based ontology languages,
although in a way which yet remains to be worked out in detail, and which will
most likely be of a very restricted nature.
? The authors acknowledge support by the German Federal Ministry of Education and
Research (BMBF) under the SmartWeb project, and by the European Commission
under contract IST-2003-506826 SEKT and under the KnowledgeWeb Network of
Excellence. The expressed content is the view of the authors but not necessarily the
view of any of the projects as a whole.
1 The dissertation [
An exhaustive and entirely satisfactory definition of DLP is not straightforward,
as argued in [
As such, any DLP ontology can be converted syntactically into a set of Horn clauses. A source of confusion comes from the fact that Horn clauses are also used for the syntactic representation of logic programs, more precisely, of definite logic programs (i.e. not containing any form of negation). This in turn motivates reasoning with DLP using logic programming systems. Whether this form of reasoning is reasonable, is the central point which is being discussed. It is being argued, for example, that logic programming semantics is based on the closed world assumption (CWA), while OWL (and therefore DLP) is based on the open world assumption (OWA) — which may lead one to the arguable consequence that the semantics are fundamentally different and thus incompatible.
The relation between Horn logic programming semantics and the first-order
predicate logic semantics, however, is not as complicated as the OWA vs. CWA
debate might suggest. If we go back to the roots of logic programming, then it
indeed came into existence due to efforts of automatizing resolution, which is a
sound and complete proof theory for first-order predicate logic. Proof procedures
implemented in standard Prolog systems (like SLD- or SLG-resolution) build on
this and trade completeness of reasoning for speed. The proof-theoretic semantics
of such systems is thus an approximation of the rfist-order semantics in the sense
that it is sound but not complete, and this is entirely reasonable as predicate
logic is not decidable (but only semi-decidable) to start with. It can indeed be
understood as approximation in a very formal (and logical!) sense by means of
standard perspectives of denotational semantics i.e. domain theory (see e.g. [
An issue likely to be brought into the discussion is that of negation. Standard logic programming systems tend to answer No to queries if they (finitely) fail to prove them. Naively understood, this may prompt the user to think that the negation of the query be true, although under first-order predicate logic semantics the query simply fails to be a logical consequence of the knowledge base. Interpreting the No as truth of the negation of the query indeed is the step which leads us into CWA reasoning, and thus differs from OWA reasoning.
The problem, however, is not on the side of the semantics of Horn logic programming. It is rather in our interpretation of procedural system behaviour. A No answer to a query simply means that the query cannot be proven, and 4 The omission of occurs check and corresponding lazy unification causes systems to be unsound. But this is not a problem in practice and can be rectified easily. that furthermore, it can be shown that the query cannot be proven. It is thus a system response which can also be interpreted in an OWA fashion, namely as Query cannot be proven, together with some information on the procedural aspects of the underlying reasoning. As such, Horn logic progamming is fully compatible with OWA, and there is no fundamental difference to OWA reasoning as applied e.g. in OWL.
But what about negation as failure, or default negation, or other kinds of
nonmonotonic negation? They don’t play a role in our context, as DLP — properly
translated into Horn clause syntax — does not contain any such negation. If
nonmonotonic negation is used on top of DLP, then this should be perceived as a
nonmonotonic extension of DLP, in the sense in which non-monotonic extensions of
OWL are being studied, e.g. in [
Some of the currently discussed proposals for a standardized rule language for the Semantic Web5 aim at establishing a logic programming-based rule ontology language as an alternative to the already denfied standard OWL. This in part mirrors the actual situation within the Semantic Web community, where both paradigms are currently being used. An obvious question being asked in this case is to what extent interoperability accross the paradigms would be possible in case such an alternative standard were to be defined. Some proposals, such as WRL, state that DLP would serve as interoperability layer between paradigms.
We have already noted that semantic compatibility between the two perspectives on DLP — Horn logic programming and rfist-order predicate logic — is basically given. However, it can still be argued whether DLP is a reasonable interoperability layer between OWL and F-Logic-based languages. Indeed, DLP appears to be a rather restricted fragment which lacks in expressivity.
There are two aspects to this. The first is that many available ontologies use
only very few constructs outside the DLP fragment (see [
The second argument is that DLP serves only as a common fragment of
OWL and F-Logic, and rather not as something which makes interoperability
between the frameworks possible in a reasonable sense. Agreed! — so far. But
we believe that this is only a first step towards a larger interoperability which
can be established by using DLP as a base, e.g. by using DL-safe rules [
Indeed, as OWL can be perceived as an extension of DLP, F-Logic (or WRL)
can be perceived as an extension of DLP in a different direction. Indeed, OWL
semantics is that of first-order predicate logic, and F-Logic semantics is different,
as it involves CWA and well-founded (non-monotonic) negation.7 But the latter
has been developed on the basis of classical logic and relates to it in a formal
way. Admittedly, the study of the exact relationships between non-monotonic
semantics and first-order predicate logic semantics has been neglected in the
past, and consequently the relations are not well understood. However, there do
exist investigations, e.g. [
The underlying vision is straightforward: Given ontologies from different sources, written in different languages (say, OWL and WRL), it is reasonable to expect that a merging of the knowledge is possible in some reasonable way, namely such that at least some meaningful consequences can be drawn from the combined knowledge, which cannot be derived from any of the ontologies looked at in isolation. Realizing interoperability in this sense has to be approached by studying the exact relationships between the semantics of the frameworks, and it is reasonable to expect that such efforts would produce meaningful – albeit restricted – outcomes. 4
Summarizing, we conclude that OWL and F-Logic indeed are basically compatible if restricted to DLP. Furthermore, we see that interoperability between frameworks is possible and in our opinion needs to be researched and realized.
We would indeed be very happy to see more efforts in establishing
constructive relationships between paradigms as the Semantic Web can and should be
expected to be very heterogenous. We would also be happy to see many more
constructive discussions as they may lead to improved systems and
interoperability, and ultimately to improved perception of our community in other research
communities and the industry.
6 http://kaon2.semanticweb.org
7 Note that the different semantics proposed for F-Logic coincide on ground
consequences of the Horn fragment.
8 We remark here that there is a natural limit to possible interoperability due to the
fact that the well-founded semantics is in general not semi-decidable [