LoLa: A Modular Ontology of Logics, Languages, and Translations

The Distributed Ontology Language (DOL) is currently being standardised within the OntoIOp (Ontology Integration and Interoperability) activity of ISO/TC 37/SC 3. It aims at providing a unified framework for (1) ontologies formalised in heterogeneous logics, (2) modular ontologies, (3) links between ontologies, and (4) annotation of ontologies. This paper focuses on building an ontology that formally describes DOL’s vocabulary for logics, ontology languages (and their serialisations), as well as logic translations, called LoLa. Interestingly, to adequately formalise the logical relationships between these notions, LoLa itself needs to be axiomatised heterogeneously—a task for which we choose DOL. Namely, we use the logic RDF for Abox assertions, OWL for basic axiomatisations of various modules concerning logics, languages, and translations, FOL for capturing certain closure rules that are not expressible in OWL, and circumscription for minimising the extension of concepts describing default translations. 1 The Distributed Ontology Language (DOL) – Overview An ontology in the Distributed Ontology Language (DOL) consists of modules formalised in basic ontology languages, such as OWL (based on description logic) or Common Logic (based on first-order logic with some second-order features). These modules are serialised in the existing syntaxes of these languages in order to facilitate reuse of existing ontologies. DOL adds a meta-level on top, which allows for expressing heterogeneous ontologies and links between ontologies.4 Such links include (heterogeneous) imports and alignments, conservative extensions (important for the study of ontology modules), and theory interpretations (important for reusing proofs). Thus, DOL gives ontology interoperability a formal grounding and makes heterogeneous ontologies and services based on them amenable to automated verification. DOL is currently being standardised within the OntoIOp (Ontology Integration and Interoperability) activity of ISO/TC 37/SC 35. The international 4 The languages that we call “basic” ontology languages here are usually limited to one logic and do not provide meta-theoretical constructs. 5 TC = technical committee, SC = subcommittee working group comprises around 50 experts (around 15 active contributors so far), representing a large number of communities in ontological research and application, such as different (1) ontology languages and logics (e.g. Common Logic and OWL), (2) conceptual and theoretical foundations (e.g. model theory, proof theory), (3) technical foundations (e.g. ontology engineering methodologies and linked open data), and (4) application areas (e.g. manufacturing, biomedicin, etc.). For details and earlier publications, see the OntoIOp project page at http://ontolog.cim3.net/cgi-bin/wiki.pl?OntoIOp. The OntoIOp/DOL standard is currently in its final working draft stage and will be submitted as a committee draft (the first formal ISO standardisation stage) in August 2012.6 The final international standard ISO 17347 is scheduled for 2015. The standard specifies syntax, semantics, and conformance criteria: Syntax: abstract syntax of distributed ontologies and their parts; three concrete syntaxes: a text-oriented one for humans, XML and RDF for exchange among tools and services, where RDF particularly addresses exchange on the Web. In this paper, we will use the DOL text syntax in listings but also explain the RDF vocabulary; for further details on the DOL syntaxes, see [5]. Semantics: (1) a direct set-theoretical semantics for the core of the language, extended by an institutional and category-theoretic semantics for advanced features such as ontology combinations (technically co-limits), where basic ontologies keep their original semantics; (2) a translational semantics, employing the semantics of the expressive Common Logic ontology language for all basic ontologies, taking advantage of the fact that for all basic ontology languages known so far translations to Common Logic have been specified or are known to exist7; (3) finally, there is the option of providing a collapsed semantics, where the semantics of the meta-theoretical language level provided by DOL (logically heterogeneous ontologies and links between them) is not just specified on paper in semiformal mathematical textbook style, but once more formalised in Common Logic, thus in principle allowing for machine verification of meta properties. For details about the semantics, see [8]. Conformance criteria provide for DOL’s extensibility to other basic ontology languages than those considered so far, including possible future languages. (1) A basic ontology language conforms with DOL if its underlying logic has a set-theoretic or, for the extended DOL features, an institutional semantics. Similar criteria apply to translations between languages. (2) A concrete syntax (serialisation) of a basic ontology language conforms if it supports IRIs (Unicode-aware Web-scalable identifers) for symbols and satisfies some further well-formedness criteria. (3) A document conforms if it is well-formed w.r.t. one of the DOL concrete syntaxes, which particularly requires explicitly mentioning all logics and translations employed. (4) An application 6 The standard draft itself is not publicly available, but negotiations are under way to make the final standard document public, as has been done with the related Common Logic standard [2]. 7 Even for higher-order logics this works, in principle, by using combinators. essentially conforms if it is capable of processing conforming documents, and providing logical information that is implied by the formal semantics. 2 A Graph of Logic Translations