Component Relationships and Requirements

o       [language] A model is the model for one and only one ontological language. Models are required to declared their associated language, either by indexing it or embedding it. The same comment applies to ontologies. The embedding of a language within an ontology can be either concentrated in one location or distributed throughout the ontology.

o       [satisfaction] An ontology is a collection of expressions of the associated language that are regarded as assertions or constraints. The (meta) assertion that a model satisfies an expression (or more generally, an ontology) can only be made when both have the same associated language. When a model is asserted to satisfy an ontology, but has not declared a language, the language of the ontology is implicitly declared for the model.

o       [truth context] An ontological language defines a (formal) context called the truth context. This context is a (meta) classification, whose instances are models for the language, whose types are expressions of the language, and whose classification relation is satisfaction between models and expressions.

o       [type equivalence] Ordinary assertions appear in ontologies, not languages. However, synonymic type equivalence is a special assertion that appears in languages, and is inherited by their ontologies and models. In a language the assertions of synonymic relation type equivalence must be compatible with the assertions of synonymic entity type equivalence.

o       [language extension] Along with language inclusion, synonymic type equivalence defines morphisms of languages. The assertion that language1 extends language0 means that all type symbol declarations and type equivalence assertions made in language0 are type symbols and type equivalences of language1; but that there may be further type symbol declarations and type equivalence assertions made in language1. Language extension is a morphism of languages.

o       [truth infomorphism] A language morphism from language0 to language1 defines a (meta) infomorphism from truth0 to truth1, consisting of an expression map from expression(language0) to expression(language1) and a (functorial) passage from model(language1) to model(language0).

o       [ontology extension] The (meta) assertion that ontology1 extends ontology0 means language1 extends language0 and the satisfaction closure of ontology1 includes the satisfaction closure of ontology0.


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Copyright 2000 TOC (The Ontology Consortium). All rights reserved. Revised: July 2000