Complexity of Grammar Induction for Quantum Types

Most categorical models of meaning use a functor from the syntactic category to the semantic category. When semantic information is available, the problem of grammar induction can therefore be defined as finding preimages of the semantic types under this forgetful functor, lifting the information flow from the semantic level to a valid reduction at the syntactic level. We study the complexity of grammar induction, and show that for a variety of type systems, including pivotal and compact closed categories, the grammar induction problem is NP-complete. Our approach could be extended to linguistic type systems such as autonomous or bi-closed categories.Comment: In Proceedings QPL 2014, arXiv:1412.810

An independent axiomatisation for free short-circuit logic

Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. Free short-circuit logic is the equational logic in which compound statements are evaluated from left to right, while atomic evaluations are not memorised throughout the evaluation, i.e., evaluations of distinct occurrences of an atom in a compound statement may yield different truth values. We provide a simple semantics for free SCL and an independent axiomatisation. Finally, we discuss evaluation strategies, some other SCLs, and side effects.Comment: 36 pages, 4 tables. Differences with v2: Section 2.1: theorem Thm.2.1.5 and further are renumbered; corrections: p.23, line -7, p.24, lines 3 and 7. arXiv admin note: substantial text overlap with arXiv:1010.367

F-structure transfer-based statistical machine translation

In this paper, we describe a statistical deep syntactic transfer decoder that is trained fully automatically on parsed bilingual corpora. Deep syntactic transfer rules are induced automatically from the f-structures of a LFG parsed bitext corpus by automatically aligning local f-structures, and inducing all rules consistent with the node alignment. The transfer decoder outputs the n-best TL f-structures given a SL f-structure as input by applying large numbers of transfer rules and searching for the best output using a log-linear model to combine feature scores. The decoder includes a fully integrated dependency-based tri-gram language model. We include an experimental evaluation of the decoder using different parsing disambiguation resources for the German data to provide a comparison of how the system performs with different German training and test parses

Machine Learning and the Cognitive Basis of Natural Language

Articl

Packed rules for automatic transfer-rule induction

We present a method of encoding transfer rules in a highly efficient packed structure using contextualized constraints (Maxwell and Kaplan, 1991), an existing method of encoding adopted from LFG parsing (Kaplan and Bresnan, 1982; Bresnan, 2001; Dalrymple, 2001). The packed representation allows us to encode O(2n) transfer rules in a single packed representation only requiring O(n) storage space. Besides reducing space requirements, the representation also has a high impact on the amount of time taken to load large numbers of transfer rules to memory with very little trade-off in time needed to unpack the rules. We include an experimental evaluation which shows a considerable reduction in space and time requirements for a large set of automatically induced transfer rules by storing the rules in the packed representation