Comparing and evaluating extended Lambek calculi

Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a logical theory). However, though it was successful in giving at least a basic treatment of many linguistic phenomena, it was also clear that a slightly more expressive logical calculus was needed for many other cases. Therefore, many extensions and variants of the Lambek calculus have been proposed, since the eighties and up until the present day. As a result, there is now a large class of calculi, each with its own empirical successes and theoretical results, but also each with its own logical primitives. This raises the question: how do we compare and evaluate these different logical formalisms? To answer this question, I present two unifying frameworks for these extended Lambek calculi. Both are proof net calculi with graph contraction criteria. The first calculus is a very general system: you specify the structure of your sequents and it gives you the connectives and contractions which correspond to it. The calculus can be extended with structural rules, which translate directly into graph rewrite rules. The second calculus is first-order (multiplicative intuitionistic) linear logic, which turns out to have several other, independently proposed extensions of the Lambek calculus as fragments. I will illustrate the use of each calculus in building bridges between analyses proposed in different frameworks, in highlighting differences and in helping to identify problems.Comment: Empirical advances in categorial grammars, Aug 2015, Barcelona, Spain. 201

Topic structures and minimal effort

The complexity of human languages has always inspired research for some human faculty that makes language learning possible. The system that generates the complexity of human languages, ideally, is simple and effective. Recent developments of the generative grammatical theory explore deeper into the issue of simplicity or economy. The Minimalist Program developed in Chomsky (1991, 1993, 1995) tries to provide contents to such notions. What does it mean to be more economic or least effort? An important instantiation of such notions is the proposal that movement is the last resort assuming that movement is more costly than non-movement. Processes occur only because they are necessary. The definition of necessity generally is cast in morphological terms. Moreover, the notion of "economy" or "least effort" is deterministic of the appropriate derivations for sentences: a shorter derivation is better than a longer one. In this work, we show that the notion of "least effort," - do minimally if possible - is manifested not only in derivations but also in other aspects of the grammar. We take Chinese as an example and show that this language exhibits the properties manifesting some "least effort" guidelines in the area of movement and reconstruction, and in the projection of syntactic positions: when there is a choice, non-application of moyement/reconstruction and non-projection of a position are adopted. These phenomena essentially are attested in topic structures. The question arises as to why topic structures exhibit such minimal effort effects. We suggest that this is due to the fact that topic structures can be derived by movement or base-generation. When there are morpho-syntactic clues that reconstruction is necessary, the structure is a movement structure. Otherwise, the less costly non-movement structure is assumed. Moreover, because of the possibility of assuming a topic NP to be base-generated, bearing a predication (or aboutness) relation with the comment clause, the argument position which otherwise would be related to the topic (conveniently termed the trace position) is not projected when there is a choice of projecting or not projecting it

Revisiting Article-S

The frst published account of relative clauses in generative grammar (Smith 1964) analyzed these elements as selected complements of the article or determiner in a nominal. In this paper we revisit the “Article-S” Analysis, examining its underlying assumptions about selection and structure and updating its technical implementation. In so doing we show that Article-S continues to be attractive from a syntactic and semantic point of view. We briefly examine two broader implications of the account for the analysis of languages claimed in the literature to be “D/DP-less” and for the analysis of restrictive modifcation generally. ---DOI: http://dx.doi.org/10.31513/linguistica.2017.v13n2a1402