Type theory (with dependent types) was introduced by Per Martin-Löf with the intention of providing a foundation for constructive mathematics. A part of constructive mathematics is type theory itself, hence we should be able to say what type theory is using the formal language of type theory. In addition, metatheoretic properties of type theory such as normalisation should be provable in type t...

The syntax and semantics of human language can illuminate many individual psychological differences and important dimensions of social interaction. Accordingly, psychological and psycholinguistic research has begun incorporating sophisticated representations of semantic content to better understand the connection between word choice and psychological processes. In this work we introduce Convers...

In this paper we develop the a posteriori error estimation of hp–version discontinuous Galerkin composite finite element methods for the discretization of second–order elliptic partial differential equations. This class of methods allows for the approximation of problems posed on computational domains which may contain a huge number of local geometrical features, or microstructures. While stand...

This paper proposed a method that can automatically detect syntax errors in Chinese sentences. The algorithm for identifying syntax errors proposed in this study is known as KNGED, which uses a large database of rules to identify whether syntax errors exist in a sentence. The rules were generated either manually or automatically. This paper further proposed an algorithm for identifying the type...

Core to the mathematical innovations of space syntax is the concept of graph-radius. In this paper, the authors propose a new mathematical mechanism to provide a relative measure for the local/global configuration of an axial line. We propose that cumulative depth be redefined as CD = Sum (1/((di-1)^k)) where d is the depth from node i to the origin and k is a constant factor. This method is ba...

In this paper we introduce the hp–version discontinuous Galerkin composite finite element method for the discretization of second–order elliptic partial differential equations. This class of methods allows for the approximation of problems posed on computational domains which may contain a huge number of local geometrical features, or micro-structures. While standard numerical methods can be de...

When a compiler encounters a syntax error, it usually attempts to restart parsing to check the remainder of the input for any further errors. One common method of recovering from syntax errors is to repair the incorrect input string, allowing parsing to continue. This research presents a language independent method for repairing the input string to an LALR(1) parser. The method results in much ...