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

On state-alternating context-free grammars

AbstractState-alternating context-free grammars are introduced, and the language classes obtained from them are compared to the classes of the Chomsky hierarchy as well as to some well-known complexity classes. In particular, state-alternating context-free grammars are compared to alternating context-free grammars (Theoret. Comput. Sci. 67 (1989) 75–85) and to alternating pushdown automata. Further, various derivation strategies are considered, and their influence on the expressive power of (state-) alternating context-free grammars is investigated

Phrase structure grammars as indicative of uniquely human thoughts

I argue that the ability to compute phrase structure grammars is indicative of a particular kind of thought. This type of thought that is only available to cognitive systems that have access to the computations that allow the generation and interpretation of the structural descriptions of phrase structure grammars. The study of phrase structure grammars, and formal language theory in general, is thus indispensable to studies of human cognition, for it makes explicit both the unique type of human thought and the underlying mechanisms in virtue of which this thought is made possible

Bayesian Grammar Induction for Language Modeling

We describe a corpus-based induction algorithm for probabilistic context-free grammars. The algorithm employs a greedy heuristic search within a Bayesian framework, and a post-pass using the Inside-Outside algorithm. We compare the performance of our algorithm to n-gram models and the Inside-Outside algorithm in three language modeling tasks. In two of the tasks, the training data is generated by a probabilistic context-free grammar and in both tasks our algorithm outperforms the other techniques. The third task involves naturally-occurring data, and in this task our algorithm does not perform as well as n-gram models but vastly outperforms the Inside-Outside algorithm.Comment: 8 pages, LaTeX, uses aclap.st