Upper Ontology Summit Discussion (KF3)
- In support of the UpperOntologySummit (KF4)
- NOTE: for definitions of terms used in these discussions, see the /UosGlossary page (LKJ)
(1) Proposed Methodology Outline (KFX)
- A suggested methodology for finding the maximum commonality among ontologies: (KF6)
- By Michael Uschold (KFY)
- I have long believed that the best solution for reaching agreement on
ontologies at any level is: (KF7)
- Agree on everything/anything that you can that is uncontentious [or contentious only at a superficial level] in terms of the 'things of interest'. (KF8)
- If you can also agree on the same terms for the things of interest, then great. If not, then use different terms and map/record them as synonyms. (KF9)
- Agree to disagree on other things, when there are good reasons for different stakeholders that have different needs (e.g. 3d/4d) (KFA)
- where possible, map between the diff 'things of interest' so that a user can to the maximal extent possible, enjoy the experience of a virtual CEO, even though it is more messy under the bonnet/hood. If a lattice of theories works for this, then great. (KFB)
-- Michael Uschold (L42)
* * * * * * * * * * * * * * * * * * * * * * * (L43)
- Patrick Cassidy Commented: (KFZ)
- Mike's four suggested stages might well serve as an outline of the process that will succeed. I would only add that the custodians of the existing upper ontologies may conclude that small modifications of their own ontologies in the interest of increasing the level of commonality would create significant benefits with minimal cost. (KG0)
(2) Theoretical Relations among ontologies (KFC)
- By Michael Gruninger (KFD)
The notes for the Upper Ontology Summit contain two key ideas: -develop methods to relate the existing upper ontologies to each other. - create a common subset ontology that is compatible with all of the linked upper ontologies. (KFE)
- There are two fundamental relationships between ontologies that we need to consider: (KFF)
- First, a few definitions: (KFI)
- A theory is a set of sentences in a language conformant with Common Logic. (KFJ)
- An ontology is a set of theories. (KFK)
- Suppose that the nonlogical lexicon of a theory T2 is a subset of the nonlogical lexicon of the a theory T1. T1 is an extension of T2 if the axioms in T1 entail the axioms in T2. (KFL)
- T1 is definably interpretable in T2 iff for each symbol in the nonlogical lexicon of T1 the relation/function/constant denoted by the symbol is definable by a sentence S in the language of T2. (KFM)
- Theory T1 generalizes theory T2 iff T1 is definably interpretable in a theory T3 and T2 is a consistent extension of T3. (KFN)
- (The intuition is that the more general a theory, the weaker it is, so that theories are extensions of the theories in the Common Subset Ontology (CSO), with definable interpretation being used in cases where different nonlogical lexicons are used.) (KFO)
- The idea is that we can design a Common Subset Ontology (CSO) by solving the following problem for the theories contained in the set of existing upper, mid-level, and domain-specific ontologies: (KFP)
- Given two theories T1 and T2, determine whether there exists a theory that generalizes both. (KFQ)
- Theories that do not have any generalizations are candidates for inclusion in the CSO. (KFR)
- Additional Comments (KFS)
- 1. This is a well-posed problem with a definite solution; it is not a matter of philosophical differences. (KFT)
- 2. Evaluation of the relationships between ontologies is made using their axioms alone; it cannot rely on intended models of concepts that are not axiomatized. If the axioms of an ontology are insufficient to capture their users' intended semantics, then there is little progress that can be made towards integration; we risk descent into logomachy, as far too many previous efforts have done. (KFU)
- 3. Theories may be generalizations of each other. For example, Hilbert's geometry and Tarski's geometry are definably interpretable in each other, even though they have different primitives and different relations. In such cases, either or both theories could be included in the CSO. (KFV)
- michael gruninger (KFW)
(3) Relative roles of a Common Upper Ontology and automated mapping (L3R)
- Patrick Cassidy discusses the advantage of a CUO over automated mapping: (L3S)
The difficulty in other approaches to Semantic Interoperability that makes a Common Upper Ontology the best method (IMO by a very large margin) is that ontologies developed separately just don't have the information required for accurate mapping. Using a CUO to specify the meanings of ontology elements in disparate ontologies makes the process simple and accurate because all of the basic assumptions and all of the compound concepts used to build up even more complex concepts are identical. Whatever nuances of fundamental meaning are merged or omitted in one ontology will be merged or omitted in the other as well, because the meaning for any ontology element in a specialized ontology based on a CUO comes from the basic CUO elements of which it is composed. (L3T)
Mapping techniques are attractive in the situation where there is no existing de facto common upper ontology -- so that using some UO as a reference would seem to be a waste of time, as it provides little interoperability benefit for the effort expended in using it (it could provide other benefits). That is the current situation and is the reason that so much effort is being expended on those mapping tactics. It is also the problem that we are trying to solve by finding a way to relate the existing upper ontologies, and thereby develop a de facto (widely used) CUO. The de facto CUO may emerge as a common subset ontology or as a set of mappings of ontology elements among the existing UOs. Such a de facto CUO would optimally provide enough axiomatization to make the meanings of the elements unambiguous. The linked UOs could provide additional knowledge that is valuable for reasoning, and would provide additional value for those whose tasks could use the additional knowledge. (L3U)
If one thinks that mapping, alignment or integration techniques that do not use a CUO are equal to or preferred to the CUO approach, consider the possible future (inevitable and near, I believe) where there is at least one widely used CUO with interface utilities (e.g. a controlled English knowledge entry and query system) that make the CUO as easy to use as Java, and several open-source applications that perform useful tasks beyond just searching the knowledge base itself. Would anyone then building an ontology and anticipating that it would need to communicate with several other ontologies, build it in isolation and then try mapping? Would any sane businessman fund such an endeavor? (L3V)
If there are legacy ontology-based applications, or ontologies built in isolation for whatever reasons their builders may have, then mapping to the CUO might well be helped by mapping tools. Thus mapping may have a role to play even when a widely-used CUO is available. But in the absence of such a CUO, one should not assign significance to the fact that people are trying to map without using a CUO. (L3W)
An approach to integration using an interlingua is discussed by Michael Gruninger in the extended abstract of his Dagstuhl paper: http://drops.dagstuhl.de/opus/volltexte/2005/39/pdf/04391.GruningerMichael3.Paper.39.pdf The interlingua serves some of the same functions that a CUO would serve, though that mapping approach does not demand that the mapped ontologies be specified using the terms in the interlingua. As he points out, "automated and correct approaches to semantic integration will require ontologies with a deeper formal grounding". The best way to assure that the formal grounding of both ontologies is adequate is by specifying the meanings of those ontologies using a CUO. The mapping of domain ontologies to the CUO-interlingua then becomes relatively simple and highly accurate. (L3X)
Why settle for less? (L3Y)
A CUO is an engineering artifact. Its value can only be tested by building it and seeing how well it performs its intended function. The existing upper ontologies were also built in the hope that they would gain a large user base. Up to now the complexity of the larger of these ontologies and the diversity of approaches to UO have made the use of these ontologies difficult and their utility uncertain to those who don't have time to explore them in depth. If it proves possible to find useful relations among the existing CUOs, that should help on both counts - for complexity, by providing a lower barrier to use of the existing upper ontologies by developing a subset ontology or a set of mappings for a subset of compatible ontology elements; for uncertainty, by providing a public consensus of the most expert developers of UOs assuring potential users that the effort expended in learning to use the UOs will not be rapidly made futile by the emergence of some other standard UO. (L3Z)
There is ample experience now on hand among the UO builders to create powerful systems that can encode knowledge and permit sophisticated reasoning with it. Finding relations among the UOs will help to make that capability more accessible to a wider user base. A consequence we can anticipate is that there will be a larger number of applications that can test those ontologies and help increase their level of "maturity". (L40)
-- Patrick Cassidy (L41)