This paper proposes a method of incrementally constructing semantic representations. Our method is based on Steedman's Combinatory Categorial Grammar (CCG), which has a transparent correspondence between syntax and semantics. In our method, a derivation for a sentence is constructed in an incremental fashion and the corresponding semantic representation is derived synchronously. Our method uses normal form CCG derivation. This is the difference between our approach and previous ones. Previous approaches use most left-branching derivation called incremental derivation, but they cannot process coordinate structures incrementally. Our method overcomes this problem.

This paper describes a method of identifying nonlocal dependencies in incremental parsing. Our incremental parser inserts empty elements at arbitrary positions to generate partial parse trees including empty elements. To identify the correspondence between empty elements and their fillers, our method adapts a hybrid approach: slash feature annotation and heuristic rules. This decreases local ambiguity in incremental parsing and improves the accuracy of our parser.

This paper describes an incremental parser based on an adjoining operation. By using the operation, we can avoid the problem of infinite local ambiguity. This paper further proposes a restricted version of the adjoining operation, which preserves lexical dependencies of partial parse trees. Our experimental results showed that the restriction enhances the accuracy of the incremental parsing.

This paper considers the universal coding problem for stationary ergodic sources with countably infinite alphabets. We propose modified versions of LZ77 and LZ78 codes for sources with countably infinite alphabets. Then, we show that for any source µ with Eµ[log X1]<∞, both codes are asymptotically optimum, i.e. the code length per input symbol approaches its entropy rate with probability one. Further, we show that we can modify LZ77 and LZ78 codes so that both are asymptotically optimal for a family of ergodic sources satisfying Kieffer's condition.

The expected lengths of the parsed segments obtained by applying Lempel-Ziv incremental parsing algorithm for i.i.d. source satisfy simple recurrence relations. By extracting a combinatorial essence from the previous proof, we obtain a simpler derivation.