Querying Geometric Figures Using a Controlled Language, Ontological Graphs and Dependency Lattices

Dynamic geometry systems (DGS) have become basic tools in many areas of geometry as, for example, in education. Geometry Automated Theorem Provers (GATP) are an active area of research and are considered as being basic tools in future enhanced educational software as well as in a next generation of mechanized mathematics assistants. Recently emerged Web repositories of geometric knowledge, like TGTP and Intergeo, are an attempt to make the already vast data set of geometric knowledge widely available. Considering the large amount of geometric information already available, we face the need of a query mechanism for descriptions of geometric constructions. In this paper we discuss two approaches for describing geometric figures (declarative and procedural), and present algorithms for querying geometric figures in declaratively and procedurally described corpora, by using a DGS or a dedicated controlled natural language for queries.Comment: 14 pages, 5 figures, accepted at CICM 201

CAISL: Simplification Logic for Conditional Attribute Implications

In this work, we present a sound and complete axiomatic system for conditional attribute implications (CAIs) in Triadic Concept Analysis (TCA). Our approach is strongly based on the Simplification paradigm which offers a more suitable way for automated reasoning than the one based on Armstrong’s Axioms. We also present an automated method to prove the derivability of a CAI from a set of CAI s.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Formal Concept Analysis Methods for Description Logics

This work presents mainly two contributions to Description Logics (DLs) research by means of Formal Concept Analysis (FCA) methods: supporting bottom-up construction of DL knowledge bases, and completing DL knowledge bases. Its contribution to FCA research is on the computational complexity of computing generators of closed sets