Common Logic and The Formal Perspective on Ontologies

Common Logic and The “Formal” Perspective on Ontologies

Ontological Engineering • Needs to become a mature engineering discipline with rigorous mathematical foundations ‣ Those foundations are mathematical logic ‣ As fundamental to Ontological Engineering as the calculus is to Mechanical or Electrical Engineering • Common Logic was designed to serve as a rigorous standard for writing in mathematical logic ontologies and exchanging them on the World Wide Web

What Common Logic Is • CL is an ISO standard ‣ ISO Project 24707 – Common Logic: A Framework for a Family of Logic-based Languages. ISO/IEC JTC 1/SC 32 ‣ http: //common-logic. org • CL is a logic framework for exchanging and transmitting information • CL is a specification of a large class of formal languages and their semantics. ‣ In particular, a wide variety of first-order languages or dialects, including KIF-style (CLIF) and XML-style (XCL) ‣ There is no privileged dialect

What Common Logic Is Not • CL is not itself a language ‣ Again, it encompasses a large class of languages • CL not itself an ontology ‣ Ontologies require nonlogical axioms ‣ CL presupposes only a standard “logical” ontology of individuals, properties, and relations. • CL is not a panacea! ‣ It is a tool like any other; useful for some purposes, not useful for others ‣ But it is very good for some purposes! : -)

Design Goals of CL • Rigorous classical syntax and semantics ‣ Clear definitions of validity, subsumption, equivalence, etc. • Maximal expressiveness ‣ CL dialects can render any content expressible in RDF, RDFS, or OWL • Minimal syntactic restrictions (unless desired) • “Web/Network” sensitive ‣ - Numerals for denoting integers - Quotation for denoting strings Provisions for importing and transmitting content on the WWW using XML.

an engineering artifact and its content Engineering Ontologies ‣ Formal semantics only provides rigorous meanings for the logical vocabulary of a language ‣ Intuitive content can only be expressed via axioms • Beyond axioms, “intended” or “intuitive” meanings and other informal, quasiphilosophical notions cannot be captured formally. • We need a very clear division between the ontologies as engineering artifacts and any less formal notions. ‣ I will call these “engineering ontologies”. • Proposal: An engineering ontology is a set of statements in a formal language that has a well -defined syntax and a well-defined declarative

“Engineering Ontology”: A proposal • Proposal: An engineering ontology is a set of statements in a formal language that has a well -defined syntax and a well-defined declarative semantics. ‣ Any set of statements - ‣ Though one might reasonably add the provision that the statements must not be logically true relative to the language’s semantics By translating into a Common Logic dialect: - Ontologies can be shown to be equivalent (or not); - Relations between classes (across or within ontologies) can be made explicit (subsumption, overlap, equivalence)

Virtues of the Proposal • Formally precise ‣ Provides ONE clear and useful notion of “ontology” • Encompasses anything that can be considered a formal ontology • Does not privilege one representational framework over another ‣ So long as it has a rigorous syntax and semantics