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What is O-Telos?

Manfred A. Jeusfeld, ConceptBase Team
April, 1999
last modification: 2020-10-17

O-Telos is the data model underlying the ConceptBase system. It has a single base relation (P-fact P(o,x,n,y)) by which concepts at any abstraction layer (instance, class, meta class, etc.) can be defined. Deductive rules and integrity constraints extend the computational model to that of a deductive database.

The Origin of O-Telos

The direct predecessor of O-Telos is the knowledge representation language Telos (specified by John Mylopoulos, Alex Borgida, Sol Greenspan, Manolis Koubarakis, and others). Telos was designed to represent information about information systems, esp. requirements. Telos was based on CML (Conceptual Modeling Language) developed in the mid/late 1980-ties. A variant of CML was created under the label SML (System Modeling Language) and implemented by John Gallagher at SCS Hamburg. CML itself was based on RML (Requirements Modeling Language) developed at the University of Toronto by Greenspan and others.

Neither RML nor CML were implemented in 1987. They were regarded as theoretic knowledge representation languages with 'possible world semantics'. SML was implemented as a subset of CML using Prolog's SLDNF semantics.

The Route to O-Telos

In 1987, we decided to start an implementation of Telos and quickly realized that the original semantics was too complex for an efficient implementation. The temporal component of Telos included both valid time (when an information is true in the domain) and transaction time (when the information is regarded to part of the knowledge base). The temporal reasoner for the valid time was based on Allen's interval calculus and was co-NP-hard. We implemented both temporal dimensions in ConceptBase V3.0 only to see that there were undesired effects with the query evaluator and the uniform representation of information into objects. Specifically, the specialization of a class into a subclass could have a valid time which could be incomparable to the valid time of an instance of the subclass. Any change in the network of valid time intervals could change the set of instances of a class. Because of that, we dropped the valid time as a built-in feature of objects but we kept the transaction time. A few other features like the declarative TELL, UNTELL and RETELL operations as proposed by Manolis Koubarakis in his master thesis on Telos were only implemented in a rather limited way -- essentially forbidding direct updates to derived facts. On the other hand, O-Telos extends the universal object representation to any piece of explicit information and reduces the number of essential builtin objects to just five. So, some of the roots of Telos in artificial intelligence were abandoned in favor of a clear semantics and of better capabilities for meta modelling.

Since we wanted to be able to manage large knowledge bases (millions of concepts rather than a few hundred), we decided to select a semantics that allowed efficient query evaluation. Telos included already features for deductive rules and integrity constraints. Thus, the natural choice was DATALOG with perfect model semantics. The deductive rule evaluator and the integrity checker were ready in 1990. A query language ("query classes") followed shortly later. O-Telos exhibits an extreme usage of DATALOG:

there is only one base relation P(o,x,l,y) used for all objects, classes, meta classes, attributes, class membership relationships, and specialization relationships as well as for deductive rules, integrity constraints and queries.
the semantics of class membership, specialization, and attribution is encoded by around 30 axioms which are either deductive rules or integrity constraints
deductive rules ranging over more than one classification level (instances, classes, meta classes, etc.) are partially evaluated to a collection of rules (or constraints) ranging over exactly one classification level

The latter feature proved to be the key to define the semantics of abstraction principles like specialization. For example, the inheritance of class membership is defined by the rules

forall o,x,c P(o,x,in,c) ==> In(x,c)
forall x,c,d In(x,c) and Isa(c,d) ==> In(x,d)

The first rule derives the predicate In(x,c) from P-facts P(o,x,in,c). The second one then defines class membership inheritance. Given the extension of the derived predicate Isa/2, one can partially evaluate such a formula. For example, if Isa(student,person) is part of the extension, then the rule is partially evaluated to

forall x In(x,student) ==> In(x,person)

This mapping allows to represent abstract features at the level of meta classes (or even more abstract) without compromising on the efficient evaluation of queries.

O-Telos should be regarded as the data modeling language of a meta database. It is capable to represent semantic features of other (data) modeling languages like entity-relationship diagrams and data flow diagrams. Once modeled as meta classes in O-Telos, one simply has to tell the meta classes to ConceptBase to get an evironment where one can manipulate models in these modeling languages. Since all abstraction levels are supported, the models themselves can be represented in O-Telos (and thus be managed by ConceptBase).

ConceptBase's implementation of O-Telos provides a couple of features beyond the core O-Telos. First of all, there is a dedicated query language CBL, which provides a class-based interpretation for queries. Second, modules have been introduced to structure the search space. Essentially, the module identifier is added to the object identifier. Thirdly, ConceptBase supports active rules (ECA rules). And finally, ConceptBase allows the recursive definition of functions.

Structural Differences between Telos and O-Telos

Data structure for propositions: Telos represents "individual" propositions like in P(Employee,Employee,-,Employee). The object name is also its identifier. In O-Telos, we always use dedicated object identifiers, e.g. P(id_123,id_123,Employee,id_123). This allows a uniform treatment of all objects, regardless of their abstraction level. Explicit attributes, instantiations and specializations have the same abilities as "individual" (=node-like) objects.
Values: O-Telos uniformly treats all values as objects, e.g. P(id_345,_id_345,177,id_345) stands for the number 177. The class 'Integer' stands for example for the currently known instances of Integer, not for all integer numbers.
Omega-Level: The object 'Proposition' (represented as P(id_0,id_0,Proposition,id_0)) is extensible by adding new properties to it. Proposition realizes the so-called omega-level known in Telos. By making it amendable, one can define new generic relations alongside the exiting constructs for instantiation, specialization, and attribution. O-Telos opens the omega-level for user-defined models.
IsA axioms: There are additional axioms for the refinement of attributes/relations for subclasses. A refined attribute/relation is always a specialization of the attribute/relation with the same name at the super-class level. Thus, all rules and constraints defined at the superclass level carry over to subclasses.
Builtin objects: O-Telos has just 5 builtin objects: Proposition, Individual, InstanceOf, IsA, and Attribute. They stand for the constructs of O-Telos are are also shared with the original Telos. However, Telos defines many more builtin objects such as the level classes Token, SimpleClass, MetaClass, and MetametaClass. These classes may be provided in ConceptBase as user-defined classes. They are not part of the axiomatization. For example, there is no need to instantiate an object to a class Token to make it an object without instances. There are no defined levels in O-Telos.
Frame syntax: Though both languages share most of the frame syntax, they deviate in particular in the way of referring to attributes.

References

[JEUS92] M. Jeusfeld (1992). Änderungskontrolle in deduktiven Objektbanken. Infix-Verlag, St. Augustin, Germany, 1992; provided here with kind permission from AKA-Verlag, Berlin.

[JEUS92b] M. Jeusfeld (1992). O-Telos Axioms. Taken from M. Jeusfeld (ed.): ConceptBase.cc User Manual - Version 8.1.

[KBC*20] M. Koubarakis, A. Borgida, P. Constantopoulos, M. Doerr, M. Jarke, M. Jeusfeld, J. Mylopoulos, D. Plexousakis (2020). A retrospective on Telos as a metamodeling language for requirements engineering. Requirements Engineering 2020.

http://conceptbase.cc -- Contact: M. Jeusfeld, University of Skövde, Sweden
2020-10-18/M.Jeusfeld