Dirigé par Alexandre Monnin (Université Paris 1 Panthéon-Sorbonne/IRI/INRIA) et Harry Halpin (IRI/W3C)
Samedi 14 avril (14h00-17h00) et Dimanche 15 avril (10h00-14h00)
Logic and the Web
Patrick J. Hayes
Institute for Human & Machine Cognition
RDF with Contexts
(Texas A&M University)
Department of Philosophy
Common Logic: An Evolutionary Tale
Traditional first-order logic (TFOL) combines a clean, well-defined, highly expressive syntax with a clear, simple semantics and any number of semantically complete proof theories. It is not without good reason, then, that TFOL is the most popular and widely used framework for representing information. As is well known, much of first-order logic can be traced back to the work of Frege (among others). Somewhat ironically, even though many of Frege’s ontological doctrines are out of fashion, certain prominent features of the syntax and semantics of TFOL bear the unmistakable imprint of these doctrines — most notably, the idea that there is an inviolable gulf between concept and object. Interestingly, however, regardless of any independent merits of Frege’s ontology, the corresponding features of TFOL are a positive liability when faced with the challenge of representing and exchanging information in an anarchic environment like the World Wide Web. The topic of my talk discusses how some of these representational challenges led to evolutionary changes in the syntax and semantics of TFOL resulting in a first-order framework (now also an ISO international standard) known as Common Logic that embodies a decidedly non-Fregean ontology.
In a bit more technical detail: In Common Logic, the traditional TFOL syntactic categories of variables, individual constants, n-place predicates and n-place function symbols are dissolved in favor of a single category of names; and the polarized ontology of concept and object is replaced by a single category of things. The traditional syntactic categories reappear only as syntactic roles that names can play in one context or another. As any string of names in this language is both a well-formed function term and a well-formed atomic formula, predication and function application are variably polyadic (e.g., « pa », « pab », « pabc » with the same name in predicate/function position are all well-formed), self-predication and self-application are possible (e.g., « pp » and « f(f,a) » are well-formed), and quantification is syntactically second-order (e.g., « ∃p∀x(px ↔ ~xx) », and indeed « ∃f f(a)x » (where « f(a) » is in predicate position) are both well-formed). Time permitting, I will also discuss some of the more advanced features of Common Logic and will briefly touch on some metatheoretic results for the logic, notably a completeness proof and a method of translating from this logic into a TFOL framework.
Cette séance aura lieu salle Lalande (17 rue de la Sorbonne, escalier C, 1er étage droite) le samedi, de 14h00 à 17h00, et dans la salle Triangle du Centre Pompidou (à droite de l’entrée) le dimanche, de 10h00 à 17h00.