Syntactico-Semantic Learning of Categorial Grammars

Natural language learning seems, from a formal point o f view, an enigma. As a matter of fact, every human being, given nearly exclusively positive examples (as psycholinguists have noticed) is able at the age o f about five to master his/her mother tongue. Though, no linguistically interesting class o f formal languages is learnable with positive data in usual models (Gold ' s (67) and Valiant 's (84)). To solve this paradox, various solutions have been proposed. Following the chomskian intuitions (Chomsky 65, 68), it can be admitted that natural languages belong to a restricted family and that the human mind includes an innate knowing o f the structure o f this class (Shinohara 90). Another approach consists in putting structural, statistical or complexi ty constraints on the examples proposed to the learner, making his/her inferences easier (Sakakibara 92). A particular family o f research, more concerned with the cognitive relevance of its models, considers that in a n a t u r a l , situations, examples are always provided with semantic and pragmatic information and tries to make profit o f it (Anderson 77; Hamburger & Wexler 75 ; Hill 83 ; Langley 82). This is the family our research belongs to. But the property o f meaningfulness o f natural languages is computationally tractable only i f we have at our disposal a theory that precisely articulates syntax and semantics. The strongest possible articulation is known as the Fredge ' s principle of compositionality. This principle has acquired an explicit formulation with the works o f Richard Montague (Dowry, Wall & Peters 81 ; Montague 74) and his inheritors. We will first briefly recall an adapted version o f this syntaetico-semantie framework, based on a type of grammars called << classical categorial g r a m m a r s , (or CCGs), and we will then show how it can been used in a formal theory o f natural language learning.