Interface of global and local semantics in a self-navigating system based on the concept lattice

Abstract

If the syntax–semantics interaction is driven by the interface, it also interrupts the interaction on its own right. Because the syntax is verified to be isomorphic to the semantics, the interaction is open to the diagonal argument leading to a contradiction. That is why it is necessary to introduce a particular interface to drive the interface to make the interaction possible despite the contradiction. In this context we propose the system implemented with the syntax–semantics loop by using a concept lattice and a particular weak quantifier. This system is expressed as the self-navigating system which wanders in a two-dimensional space, encounters some landmarks, constructs the relationship among landmarks to which decision making with respect to the move is referred. The syntax of this system is defined as two-dimensional move and the semantics is defined as a concept lattice [B. Ganter, R. Wille, Formal Concept Analysis, Springer, Berlin, 1999] constructed by the binary relation between landmarks and some properties of landmarks, and by Galois connection. To implement the interface driving and interrupting the interaction between syntax and semantics, we divided semantics into local and global concept lattices, and introduce a weak quantifier to connect a local with a global lattice. Because the contradiction results from diagonal argument or using a normal quantifier ∀, the use of a quantifier is restricted dependent on the situation to avoid a contradiction. It is shown that due to the role of a weak quantifier our self-navigating system is both robust and open to the emergent property through simulating studies.