Section: New Results
Participants : Philippe de Groote, Sylvain Pogodalla.
Lambek categorial grammar as abstract categorial grammars
Abstract Categorial Grammars (ACG, for short) differ from classical categorial grammars in an essential way: the ACG type system is based on a commutative logic (namely, the implicative fragment of multiplicative linear logic). For this reason, it has been argued that the way of encoding wh-extraction in an ACG corresponds to an uncontrolled form of extraction, which results in syntactic overgeneration. In particular, an ACG could not accomodate left and right peripheral extractions like a Lambek categorial grammar (LG, for short) does. In order to challenge this claim, we have shown how LG may be encoded as ACG .
The interpretation of natural language utterances relies on two complementary elements of natural language modeling. On the one hand, the description of the combinatorics of natural language expresses how elementary units, or lexical units (typically the word), combine in order to build more complex elements, such as sentences or discourses. On the other hand, the description of these elementary units specifies how they contribute to the meaning of the whole by their lexical meaning. This specification should also take into account how the different parts of the lexical meanings combine during the composition process and how they relate to their underlying meaning concepts. For instance, the verbs buy and sell should refer to a common conceptual representation. However, their syntactic arguments (e.g., the subject) play a different (semantic) role with respect to the transaction concept that they share.
The modeling of these concepts and how they relate to each other gave rise to Frames Semantics as a representation format of conceptual and lexical knowledge , , , . Frames consists of directed graphs where nodes correspond to entities (individuals, events, ...) and edges correspond to (functional or non-functional) relations between these entities. Providing a fine-grained representation of the internal concept structure allows both for a decomposition of the lexical meaning and for a precise description of the sub-structural interactions in the semantic composition process .
Following up on our previous work based on Hybrid Logic (HL) ,  on linking Frames and truth-logical semantics, with a specific focus on explicit quantification over entities or events that are lexically triggered, we extended our model to the interaction between bounded events and for-adverbials. This interaction turns bounded events (John biked to the office) to iterated events (John biked to the office for three months), when the bounded events themselves result from coercing a progression (John biked) by addition of a prepositional phrase (to the office). We also proposed a modeling taking into account the respective scopes of the quantifiers induced by for-adverbials (over events) and quantification introduced by indefinites (over entities) . Finally, we used the flexibility of the approach to model semantic coercion as induced by verbs such as read that can syntactically have an entity as argument (John began a book) while it semantically relates to an event (e.g., reading, writing, etc.) .