Strong Equivalence of TAG and CCG

Tree-adjoining grammar (TAG) and combinatory categorial grammar (CCG) are two well-established mildly context-sensitive grammar formalisms that are known to have the same expressive power on strings (i.e., generate the same class of string languages). It is demonstrated that their expressive power on trees also essentially coincides. In fact, CCG without lexicon entries for the empty string and only first-order rules of degree at most 2 are sufficient for its full expressive power.

Resolving Interoperability Issues of Precision and Array with Null Value of Web Services Using WSIG-JADE Framework

Web services and agent technology play a significant role while resolving the issues related to platform interoperability. Web service interoperability organization (WS-I) provided the guidelines to remove the interoperability issues using basic profile 1.1/1.2 product. However, issues are still arising while transferring the precision values and an array with null values between different platforms like JAVA and .NET. As in a precision issue, JAVA supports data precision up to the 6th value and .NET up to the 5th value after the decimal and after increasing their limits, the whole number gets rounded off. In array with a null value issue, JAVA treats null as a value but .NET treats null as an empty string. To remove these issues, we use the WSIG-JADE framework that helps to build and demonstrate a multiagent system that does the mapping and conversions between agents and web services. It limits the number of digits to the 5th place after the decimal thereby increasing the precision in data sets, whereas it treats null as an empty string so that string length remains the same for both the platforms thereby helping in the correct count of data elements.

Discovering grammar of an unknown text as an optimisation problem

This paper concerns the problem of discovering an unknown grammar from a text sample. The discovering methods are formulated as optimisation problems based on a binary representation of context-sensitive grammars. The representation starts with a longest possible vector of bits to, finally, make it more compact so as to be usable in practical applications. For the sake of simplicity, considered are only noncontracting (length preserving) grammars of order 2, excluding productions of the form P:A→B and those deriving the empty string, i.e P:A→ε.

An improved prenex normal form1

Let ℒ be the set of all formulas of a given first order predicate logic (with or without identity). For each positive integer n, let ℒn be the set of all formulas φ in ℒ logically equivalent to a formula of the form where Q is a (possibly empty) string of quantifiers, m is a positive integer, and each αij is either an atomic formula or the negation of an atomic formula.