We present a new framework for discovering knowledge from two-dimensional structured data by using Inductive Logic Programming.
Two-dimensional graph structured data such as image or map data are widely used for representing relations and distances between
various objects. First, we define a layout term graph suited for representing twodimensional graph structured data. A layout
term graph is a pattern consisting of variables and two-dimensional graph structures. Moreover, we propose Layout Formal Graph
System (LFGS) as a new logic programming system having a layout term graph as a term. LFGS directly deals with graphs having
positional relations just like first order terms. Second, we show that LFGS is more powerful than Layout Graph Grammar, which
is a generating system consisting of a context-free graph grammar and positional relations. This indicates that LFGS has the
richness and advantage of representing knowledge about two-dimensional structured data.
Finally, we design a knowledge discovery system, which uses LFGS as a knowledge representation language and refutably inductive
inference as a learning method. In order to give a theoretical foundation of our knowledge discovery system, we give the set
of weakly reducing LFGS programs which is a sufficiently large hypothesis space of LFGS programs and show that the hypothesis
space is refutably inferable from complete data.