The IFF foundation for ontological knowledge organization

Cataloging and Classification Quarterly

Volumn 37, Issue 1-2, 2003, Pages 187-203

  Kent, Robert E ^a,b,c  

^a Standard Upper Ontology (SUO) working group   (United States)

^b Information Flow Framework (IFF)   (United States)

^c NONE   (United States)

Author keywords

Alignment; Classification; Information flow; Knowledge organization; Logic; Model; Ontology; Semantic integration; Semantics; Theory; Unification

Indexed keywords

EID: 84856465811     PISSN: 01639374     EISSN: 15444554     Source Type: Journal    
DOI: 10.1300/J104v37n01_13     Document Type: Article

References (11)

1. Kent, Robert E., 2000. “The information flow foundation for conceptual knowledge organization. In”. In Dynamism and Stability in Knowledge Organization:Proceedings of the 6th International Conference of the International Society for Knowledge Organization (ISKO) (10–13 July 2000) Toronto, Würzburg, DE, Canada:Ergon Verlag.
2. Kent, Robert E., 2001. The Information Flow Framework Starter document for IEEE P1600.1, the IEEE Standard Upper Ontology Working Group, http://suo.ieee.org/IFF/.
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5. It has been the opinion of many that the best way to handle the multivalent relations in ontologies is with hypergraphs. A first order IFF type language is equivalent to the notion of a hypergraph. It consists of sets for variables, entity types corresponding to hypergraph nodes, and relation types corresponding to hyperedges, and functions for defining the signature and arity of relation types. The set of entity types linked by a relation type is called its signature. Type languages are related through type language morphisms. A type language morphism from source type language to target type language maps source entity (relation) types to target entity (relation) types, preserving signature and arity. In contrast to the notion of a hypergraph, any type language is extended to a type language of expressions, which has the same sets for variables and entity types, but has expressions as its relation types. The set of expressions is defined recursively and is the disjoint union of atomic expression, negation conjunction, disjunction, implication, existential and universal quantifications, and substitutions. There is an embedding type language morphism from any type language to its expression type language
6. Sowa, John F., 2000. Knowledge representation:logical, philosophical, and computional foundations. Pacific Grove, CA:Brooks/Cole.
7. Edghill, E. M., Aristotle. 350 B.C.E. Categories.http://classics.mit.edu/Aristotle/categories.html. Translated by
8. A hypergraph is similar to a graph but allows edges that link more than two nodes. The set of nodes linked by a hyperedge is called its tuple. An IFF hypergraph consists of sets for names, nodes, and hyperedges, and functions for defining the tuple and arity of hyperedges. Hypergraphs are related through hypergraph morphisms. A hypergraph morphism from source hypergraph to target hypergraph maps source nodes (hyperedges) to target nodes (hyperedges), preserving tuple and arity
9. The IFF gives a (somewhat novel) category-theoretic axiomatization for first-order model theory based upon the two fundamental ideas of classification and hypergraph (see the two dimensional structure in Figure 2a formed out of classifications along one dimension and hypergraphs along the other dimension). In one sense, an IFF model is a hypergraph of classifications. In place of nodes, there is a classification of entities, and in place of hyperedges, there is a classification of relations. The set of entity instances is called the universe of discourse, and the set of relation instances is called the tuple space. In another sense, an IFF model is a classification of hypergraphs-the instance aspect of a model forms an instance hypergraph, and dually the type aspect of a model forms a type language. IFF models are equivalent to the models of traditional many-sorted logic. In this equivalence, the extent functions of the entity, relation and expression classifications are regarded as interpretation functions. The IFF has a lax notion of satisfaction for tuples. For a tuple to satisfy an expression, or that expression to hold for the tuple, we only require that the arity of the expression be a subset of the arity of the tuple and that the restriction of the tuple to that subset satisfy the expression in the usual sense. There is an expression classification, where an expression classifies a tuple when the expression holds for that tuple. A model satisfies an expression in its type language when that expression holds for all tuples; i.e., has maximal extent in the expression classification. A model for a theory is a model that satisfies every axiom of that theory. Satisfaction is defined recursively. Models are related through model infomorphisms. A model infomorphism is a classification infomorphism along the classification dimension and a hypergraph morphism along the hypergraph dimension. Models and model infomorphisms form the Model context
10. Barwise, Jon, and Seligman, Jerry. 1997. Information flow:the logic of distributed systems. Cambridge University Tracts in Theoretical Computer Science 44 Cambridge:Cambridge University Press.
11. Ganter, Bernhard, and Wille, Rudolf. 1999. Formal concept analysis:mathematical foundations Heidelberg:Springer.