Michel Chein

Graph-based Knowledge Representation: Computational Foundations of Conceptual Graphs

This book addresses the question of how far it is possible to go in knowledge representation and reasoning by representing knowledge with graphs (in the graph theory sense) and reasoning with graph operations. The authors have carefully structured the book with the first part covering basic conceptual graphs, the second developing the computational aspects, and the final section pooling the kernel extensions. An appendix summarizes the basic mathematical notions. This is the first book to provide a comprehensive view on the computational facets of conceptual graphs. The mathematical prerequisites are minimal and the material presented can be used in artificial intelligence courses at graduate level upwards.

Polynomial Algorithms for Projection and Matching

The main purpose of this paper is to develop polynomial algorithms for the projection and matching operations on conceptual graphs. Since all interesting problems related to these operations are at least NP-complete — we will consider here the exhibition of a solution and counting the solutions — we propose to explore polynomial cases by restricting the form of the graphs or relaxing constraints on the operations. We examine the particular conceptual graphs whose underlying structure is a tree. Besides general or injective projections, we define intermediary kinds of projections. We then show how these notions can be extended to matchings.

Positive Nested Conceptual Graphs

This paper deals with positive (i.e. without negation) nested conceptual graphs (NCGs). We first give a general framework-graphs of graphs provided with morphism-for defining classes of NCGs. Then we define a new class of NCGs-typed NCGs- and we show that known kinds of NCGs can be described very simply as classes of the general framework. All NCG models considered generalize the simple CG model in the sense that they involve objects which are generalizations of simple CGs and reasonings on these objects are based on a graph operation (projection) which is a generalization of that used for simple CGs. Furthermore, the general framework introduced allows one to consider all these models as slight variations of a unique notion. This study has been initiated by applications we are currently involved in.

A content-search information retrieval process based on conceptual graphs

An intelligent information retrieval system is presented in this paper. In our approach, which complies with the logical view of information retrieval, queries, document contents and other knowledge are represented by expressions in a knowledge representation language based on the conceptual graphs introduced by Sowa. In order to take the intrinsic vagueness of information retrieval into account, i.e. to search documents imprecisely and incompletely represented in order to answer a vague query, different kinds of probabilistic logic are often used. The search process described in this paper uses graph transformations instead of probabilistic notions. This paper is focused on the content-based retrieval process, and the cognitive facet of information retrieval is not directly addressed. However, our approach, involving the use of a knowledge representation language for representing data and a search process based on a combinatorial implementation of van Rijsbergen’s logical uncertainty principle, also allows the representation of retrieval situations. Hence, we believe that it could be implemented at the core of an operational information retrieval system. Two applications, one dealing with academic libraries and the other concerning audiovisual documents, are briefly presented.

Conceptual Graphs are Also Graphs

The main objective of this paper is to add one more brick in building the CG model as a knowledge representation model autonomous from logic. The CG model is not only a graphical representation of logic, it is much more: it is a declarative model encoding knowledge in a mathematical theory, namely labelled graph theory, which has efficient computable forms, with a fundamental graph operation on the encodings to do reasoning, projection, which is a labelled graph morphism. Main topics of this paper are: a generalized formalism for simple CGs; a strong equivalence between CSP (Constraint Satisfaction Problem) and labelled graph morphism. This correspondence allows the transportation of efficient algorithms from one domain to the other, and confirms that projection —or more generally labelled graph morphism— firmly moors CGs to combinatorial algorithmics, which is a cornerstone of computer science. The usual sound and complete first order logic semantics for CGs is still valid for our generalized model. This, plus the ease of doing important reasonings with CGs —for instance plausible reasonings by using some maximal join operations— without, at least for the moment, logical semantics, strengthens our belief that CGs must also be studied and developed independently from logic.

Concept Types and Coreference in Simple Conceptual Graphs

This paper tackles the question of representing and reasoning with types and coreference in simple conceptual graphs (SGs). It presents a framework integrating a number of previous works. This proposal is guided by the usability of CGs in practice. In other words, notions should be easy to use in knowledge representation and operations for doing reasoning have to be efficiently realizable. We propose to use conjunctive concept types, which are conjunctions of primitive types. The conjunctive concept type set is defined by means of a primitive type set and a set of banned conjunctive types. For efficiency reasons our framework is based on projection. However it has been shown that projection is complete (w.r.t. logical deduction) only when SGs are in normal form. In some situations the original form of the SGs has to be kept; we thus define an extension of projection, called coref-projection, which is complete for SGs of any form. Coref-projection is in particular suitable for frameworks where it is not assumed that coreferent nodes are mergeable.

An Experiment in Document Retrieval Using Conceptual Graphs

In this paper an experiment using conceptual graphs to represent documents and queries is described. This paper is centred on the representation and answering language, a variant of simple CGs, and not on automatic indexing. Two important specificities of the experiment described in this paper are: first, it uses an existing general “ontology”, the thesaurus of RAMEAU, which is used in all the french universitary libraries; secondly, the CG indexation has been obtained from the existing indexation by adding a new “relational” level. The main goal of this paper is to show that it is possible to add, to general traditional document retrieval systems, a CG level, and that it is worthwhile to pay an additional cost, because, using CG for indexing documents and for representing queries, leads to significant improvements in the answers obtained.

Characterization and Algorithmic Recognition of Canonical Conceptual Graphs

This paper studies canonical graphs, which are conceptual graphs derivable from a canonical basis. We provide several characterizations of canonical graphs and prove that the correspondence between notions of a projection and a derivation sequence (specialization) holds true for canonical graphs. We propose an algorithm for deciding whether a conceptual graph is canonical relative to a given canonical basis. The complexity of this algorithm is polynomially related to the complexity of computing a projection between two conceptual graphs. When the canonical basis is a set of trees, it is polynomial.

Visual reasoning with graph-based mechanisms: the good, the better and the best

This paper presents a graph-based knowledge representation and reasoning language. This language benefits from an important syntactic operation, which is called a graph homomorphism. This operation is sound and complete with respect to logical deduction. Hence, it is possible to do logical reasoning without using the language of logic but only graphical, thus visual, notions. This paper presents the main knowledge constructs of this language, elementary graph-based reasoning mechanisms, as well as the graph homomorphism, which encompasses all these elementary transformations in one global step. We put our work in context by presenting a concrete semantic annotation application example.

The CORALI Project: From Conceptual Graphs to Conceptual Graphs via Labelled Graphs

The scientific objectives of the “Conceptual gRAphs at LIrmm” project and the method used to reach these objectives are presented.