Marie-Laure Mugnier

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.

Sound and Complete Forward and backward Chainingd of Graph Rules

This paper presents graph operations for processing conceptual graph rules in forward chaining and backward chaining. In both cases the operations provide sound and complete procedures with respect to first-order logic deduction. First we present our framework: simple conceptual graphs, rules as couples of lambda-abstractions, knowledge base, logical semantics. Next we focus on forward chaining. In particular, using the notion of redundancy, we exactly characterize when the application of a rule to a graph enriches or not this graph with a “new” information. The forward mechanism is complete if the knowledge base is in normal form. Basic notions (cut points, pieces, compatible partitions, unification) for backward chaining are detailed. A parallel with previous works on backward chaining is done, in particular with the work of B.C. Ghosh and V. Wuwongse, which is close to ours. The main difference is that we do not split the goals into trivial subgraphs (a relation and its neighbours). Instead, we determine cut points, which define arbitrary complex subgraphs, called pieces, that can be processed as a whole.

Walking the complexity lines for generalized guarded existential rules

We establish complexities of the conjunctive query entailment problem for classes of existential rules (i.e. Tuple-Generating Dependencies or Datalog+/- rules). Our contribution is twofold. First, we introduce the class of greedy bounded treewidth sets (gbts), which covers guarded rules, and their known generalizations, namely (weakly) frontier-guarded rules. We provide a generic algorithm for query entailment with gbts, which is worst-case optimal for combined complexity with bounded predicate arity, as well as for data complexity. Second, we classify several gbts classes, whose complexity was unknown, namely frontier-one, frontier-guarded and weakly frontier-guarded rules, with respect to combined complexity (with bounded and unbounded predicate arity) and data complexity.

Conceptual Structures: Common Semantics for Sharing Knowledge

Invited Papers.- Patterns for the Pragmatic Web.- Conceptual Graphs for Semantic Web Applications.- Knowledge Representation and Reasoning in (Controlled) Natural Language.- What Is a Concept?.- Applications of Description Logics: State of the Art and Research Challenges.- Methodologies for the Reliable Construction of Ontological Knowledge.- Using Formal Concept Analysis and Information Flow for Modelling and Sharing Common Semantics: Lessons Learnt and Emergent Issues.- On the Need to Bootstrap Ontology Learning with Extraction Grammar Learning.- Conzilla - A Conceptual Interface to the Semantic Web.- Theoretical Foundations.- Variables in Concept Graphs.- Arbitrary Relations in Formal Concept Analysis and Logical Information Systems.- Merge-Based Computation of Minimal Generators.- Representation of Data Contexts and Their Concept Lattices in General Geometric Spaces.- Local Negation in Concept Graphs.- Morphisms in Context.- Contextual Logic and Aristotles Syllogistic.- States of Distributed Objects in Conceptual Semantic Systems.- Knowledge Engineering and Tools.- Hierarchical Knowledge Integration Using Layered Conceptual Graphs.- Evaluation of Concept Lattices in a Web-Based Mail Browser.- D-SIFT: A Dynamic Simple Intuitive FCA Tool.- Analyzing Conflicts with Concept-Based Learning.- Querying a Bioinformatic Data Sources Registry with Concept Lattices.- How Formal Concept Lattices Solve a Problem of Ancient Linguistics.- A New Method to Interrogate and Check UML Class Diagrams.- Knowledge Acquisition and Ontologies.- Language Technologies Meet Ontology Acquisition.- Weighted Pseudo-distances for Categorization in Semantic Hierarchies.- Games of Inquiry for Collaborative Concept Structuring.- Toward Cooperatively-Built Knowledge Repositories.- What Has Happened to Ontology.- Enhancing the Initial Requirements Capture of Multi-Agent Systems Through Conceptual Graphs.- Outline of trikonic?* k: Diagrammatic Trichotomic.

Knowledge Representation and Reasonings Based on Graph Homomorphism

The main conceptual contribution in this paper is to present an approach to knowledge representation and reasonings based on labeled graphs and labeled graph homomorphism. Strengths and weaknesses of this graph-based approach are discussed. Main technical contributions are the followings. Fundamental results about the kernel of this approach, the so-called simple graphs model are synthesized. It is then shown that the basic deduction problem on simple graphs is essentially the same problem as conjunctive query containment in databases and constraint satisfaction; polynomial parcimonious transformations between these problems are exhibited. Grounded on the simple graphs model, a knowledge representation and reasoning model allowing to deal with facts, production rules, transformation rules, and constraints is presented, as an illustration of the graph-based approach.

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 sound and complete backward chaining algorithm for existential rules

We address the issue of Ontology-Based Data Access which consists of exploiting the semantics expressed in ontologies while querying data. Ontologies are represented in the framework of existential rules, also known as Datalog+/-. We focus on the backward chaining paradigm, which involves rewriting the query (assumed to be a conjunctive query, CQ) into a set of CQs (seen as a union of CQs). The proposed algorithm accepts any set of existential rules as input and stops for so-called finite unification sets of rules (fus). The rewriting step relies on a graph notion, called a piece, which allows to identify subsets of atoms from the query that must be processed together. We first show that our rewriting method computes a minimal set of CQs when this set is finite, i.e., the set of rules is a fus. We then focus on optimizing the rewriting step. First experiments are reported.

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.