Frequently Asked Questions

What is the Information Flow Framework?

The Information Flow Framework (IFF) provides the terminology, semantics and principled foundation for a metalevel ontological framework – a framework for sharing ontologies, manipulating ontologies as objects, relating ontologies through morphisms, partitioning ontologies, composing ontologies via colimits, discussing ontological structure, noting dependencies between ontologies, declaring the use of other ontologies, etc.

What is the philosophy and approach of the IFF?

The IFF advocates a building blocks approach to ontology construction and management. In the IFF approach, ontologies are organized in an extension hierarchy called a lattice of theories. Ontologies can be assembled from building blocks using structural summation and structural quotienting (the colimit construction). Continuing the analogy, the IFF understands that the mortar between the blocks must be strong and resilient in order to adequately support the building. This mortar is corresponds to the semantic integration of ontologies. The IFF defines the structure of object level ontologies by relating ontologies using morphisms and composing ontologies using colimits (fusion). The morphic aspect of ontologies is manifested by the lattice of IFF theories in the small and the context of IFF theories in the large. The colimit aspect of ontologies is manifested by the IFF approach to semantic integration.

What are some possible object level building block ontologies?

Some of the many upper object level ontologies that could be used as building blocks include: Sowa's upper ontology, Russell and Norvig’s ontology, Casati and Varzi’s theory of holes, Allen’s temporal axioms, Smith’s and Guarino’s mereotopologies, the Core Plan Representation, a Simple-Time ontology, a Standard-Units ontology, an Agents ontology, the Numbers ontology (from the Ontolingua server), and the Natural-Kinds and Positions ontology (authored by the Ontology Group at ITBM-CRN),

Why is a monolithic upper level ontology considered harmful?

One technique for ontology creation and management is the development of a monolithic upper level ontology filled with various top-level categories that would be used to generate others. The IFF regards this as a recipe for failure, and advocates its rejection. Throughout history, new conceptions have continually arisen that caused total disruption of the status quo (the currently formalized conceptions). Recent disruptive conceptions in science and technology include: from Physics the concepts of relativity and quantum mechanics; from Biology the cell concept, energy and photosynthesis, respiration, energy and ecosystems, the genetic control of development, Mendelian heredity, and Darwinian evolution; from Computer Systems the concept of an algorithm, the stored program concept, the compilation of higher level programming languages; etc. New disruptive conceptions cause communities to reformulate their knowledge space. This will continue into the future. More important than the monolithic approach is a framework that relates ontologies to each other and builds new ontologies based on common agreement. The IFF is such a framework, with ontologies connected by morphisms and constructed through colimits (a fusion process).

When will the IFF be complete?

The top IFF metalevel consisting of only the Top Core (meta) ontology is finished. The upper IFF metalevel consisting of the Upper Core, Category Theory and Upper Classification (meta) ontologies is complete. The lower IFF metalevel is still being built – it will contain Lower Core, Lower Classification, Model Theory, Algebraic Theory and Ontology (meta) ontologies. It is anticipated that the first version of the complete IFF will be finished by summer or fall of 2003.

I have heard that the IFF uses category theory. Why is this?

The IFF is based upon category theory. This is the appropriate foundation for the IFF, since the IFF relates ontologies via morphisms and composes ontologies using colimits. Compare this to the Kestrel Institutes’ Specware system, which is based on category theory and supports creation and combination of specifications (read ontology, for our purposes) using powerful composition primitives and the colimit operation. An early study shows that the colimit mechanism for composing ontologies from chunks is very powerful.

What are the central concepts of the IFF and how are these represented?

The central concepts of the IFF include language, model, theory and logic. These are represented in the IFF as mathematical contexts. A mathematical context is another name for a category. Such a context axiomatizes a concept and ways to relate such concepts. For example, the theory context represents theories and theory morphisms, and the logic context represents logics and logic infomorphisms. The IFF contains other contexts, such as sets and hypergraphs, which provide support for the central concepts.

How does the IFF represent ontologies?

The IFF represents ontologies with the concepts of theories and logics. An ontology is populated when it contains instance data. Unpopulated ontologies containing only axioms are represented by IFF theories, whereas populated ontologies are represented by IFF logics. An IFF logic has two parts, an IFF theory and an IFF model that satisfies that theory. An IFF model provides for an interpretative semantics, an IFF theory provides for a formal or axiomatic semantics, and an IFF logic provides for a combined, both formal and interpretative, semantics.

Is the lattice of theories represented in the IFF?

Yes. The lattice of theories has an initial baseline representation in the truth namespace of the IFF Ontology meta-Ontology (IFF-ONT). The terminology and axiomatization includes functionality for mapping modules into and out of lattices of theories, functionality for combining modules using lattice operators, functionality for navigating within a lattice of theories (contraction, expansion, revision, etc.), and functionality for moving between lattices of theories (analogy). The lattices of theories construction is compatible with the wider context of theories, which consists of theories and theory morphisms.

How does the IFF represent the lattice of theories?

The IFF representation for the lattice of theories is called the truth concept lattice. The truth concept lattice is equivalent to the truth classification. See the illustration on slides 5 and 6 of the SUO Workshop PowerPoint presentation. The truth classification was discussed as example 4.6 on page 71 of the book Information Flow: The Logic of Distributed Systems by Jon Barwise and Jerry Seligman. The truth concept lattice is introduced for the first time here in the SUO IFF. An element of the truth concept lattice, called a truth formal concept, is a closed theory.

How are the truth classification and the truth concept lattice connected?

The association between the truth classification and the truth concept lattice is based upon the fundamental theorem of Formal Concept Analysis. The fundamental theorem and its various mappings are represented by the IFF Upper Classification Ontology. The truth concept lattice is a potentially infinite open-ended lattice of theories. However, it is important to note is that we are dealing with a fibered structure. This is not a single lattice, but an infinite collection of lattices, where each truth classification and truth concept lattice is based upon (indexed by) a particular first order language.

How does an object level ontology appear in the lattice of theories?

Since it is represented by an IFF theory, an unpopulated object level ontology will appear as the closure of the theory, which is one element in the lattice of theories that is based at its underlying first order language. Since it is represented by an IFF logic, a populated object level ontology will appear as a path in the lattice of theories. One end of the path (the bottom end) will be located at the theory of the component model of the logic, and the other end of the path (the top end) will be located at the closure of the component theory of the logic.

Can two different lattices of theories be related?

Yes, since lattices of theories are based at first order languages, two different lattices of theories can be related through an interpretation between their underlying languages. The notion of a first order interpretation was discussed as example 4.11 on page 74 of the book by Jon Barwise and Jerry Seligman [op. cit.]. First order language interpretations, which generalize first order language morphisms, are axiomatized in the IFF Type Language Namespace. An interpretation from one language to a second language maps the relations of the first language to the expressions (formulas) of the second language. Each first order interpretation defines a truth infomorphism between the associated truth classifications (see Barwise and Seligman [op. cit.]). In turn, this truth infomorphism defines a truth concept morphism between the associated truth concept lattices, which maps between formal truth concepts (representing object level ontologies) in a very semantic way.

Does the IFF have a methodology for the semantic integration of ontologies?

Yes. The IFF methodology for the semantic integration of ontologies was discussed in a Boeing mini-workshop presentation and a Cataloging & Classification Quarterly paper. The IFF approach to the semantic integration of ontologies is the two-step process of alignment and unification.

○ Ontological alignment is the semiautomatic process of the sharing of common terminology and semantics through a mediating ontology.

○ Ontological unification, concentrated in a virtual ontology of community connections, is the automatic process of fusion of the alignment diagram of participant community ontologies.

What lower metalevel modules are being contemplated for the IFF?

A module in the lower metalevel should be based upon a well-researched area. In addition to the IFF Ontology (meta) ontology, which is based upon knowledge representation and logic, other lower metalevel modules being considered are as follows: a module for the “soft computation” of both rough sets and fuzzy logic; a module for theories of semiotics; a module for game-theoretic semantics; a module that corresponds to the Kestrel Institute’s Specware system by representing the notions of sheaves and specifications; a module corresponding to the work by Goguen and Meseguer on institutions; etc.