Deafault logic, natural language and generalized quantifiers

Default logic [Reiter 80] is now commonly used in artificial intelligence systems and turns out to be one of the major research fields in knowledge representation. One of the first motivations of default logic wan to give a more accurate semantic represem tation to natural language statements of the form: Birds fl~: Mos t birds fly. or~ arguably: Typicall2o; birds lty~ The idea was to define a representation that permits ex~ ceptions to be coherent togeLher with a general statement or law. -Very soon this linguistic motivation becanm somewhat negh;cted, yielding the way to theoretical investigations in non~ monotonic reasoning and to the elaboration of automatic the~ orem prover,. For a good introduction see [Besnard 89]. The only works we are aware of in natural language processing are the use of default logic to solve anaphoras [Dunin-Keplitz 84], to model dialogs [Joshi et al. 87] and to derive presuppositions from sentences [Mercer 88]. In this contribution, we come back to the very first moti~ ration of default logic and explore its integration into natural language semantics, as introduced in [Saint-Dizier 87]. More precisely, we propose an integration of default logic into Gent. eralized Quontifiers framework [Barwise and Cooper 81]. This leads us to reformulate default logic within the framework of set theory defined on universes. We first propose several types of linguistic expressions for which a representation by a default rule turns out to be relevant. Next, we present some basic properties about truth persistence of statements represented by default logic and, finally, we propose several inferential pat~ terns which permit to derive new default rules on the one hand and new linguistic expressions on the other hand.