Extensions of Simple Conceptual Graphs: the Complexity of Rules and Constraints

Simple conceptual graphs are considered as the kernel of most knowledge representation formalisms built upon Sowa's model. Reasoning in this model can be expressed by a graph homomorphism called projection, whose semantics is usually given in terms of positive, conjunctive, existential FOL. We present here a family of extensions of this model, based on rules and constraints, keeping graph homomorphism as the basic operation. We focus on the formal definitions of the different models obtained, including their operational semantics and relationships with FOL, and we analyze the decidability and complexity of the associated problems (consistency and deduction). As soon as rules are involved in reasonings, these problems are not decidable, but we exhibit a condition under which they fall in the polynomial hierarchy. These results extend and complete the ones already published by the authors. Moreover we systematically study the complexity of some particular cases obtained by restricting the form of constraints and/or rules

Default Conceptual Graph Rules: Preliminary Results for an Agronomy Application

International audienceIn this paper, we extend Simple Conceptual Graphs with Reiter's default rules. The motivation for this extension came from the type of reasonings involved in an agronomy application, namely the simulation of food processing. Our contribution is many fold: rst, the expressivity of this new language corresponds to our modeling purposes. Second, we provide an effective characterization of sound and complete reasonings in this language. Third, we identify a decidable subclass of Reiter's default logics. Last we identify our language as a superset of SREC-, and provide the lacking semantics for the latter language

RDF Entailment as a Graph Homomorphism

baget2005aInternational audienceSemantic consequence (entailment) in RDF is ususally computed using Pat Hayes Interpolation Lemma. In this paper, we reformulate this mechanism as a graph homomorphism known as projection in the conceptual graphs community. Though most of the paper is devoted to a detailed proof of this result, we discuss the immediate benefits of this reformulation: it is now easy to translate results from different communities (e.g. conceptual graphs, constraint programming,... ) to obtain new polynomial cases for the NP-complete RDF entailment problem, as well as numerous algorithmic optimizations

Improving maintenance strategies from experience feedback

A huge amount of rough data is available in companies on past maintenance activities as a result of the implementation of CMMS (Computerized Maintenance Management System). In that context, we focus on an experience feedback system dedicated to maintenance, allowing the capitalization of past interventions by means of a formal knowledge representation language, and the extraction from these interventions of new knowledge for future reuse

Griwes: Generic Model and Preliminary Specifications for a Graph-Based Knowledge Representation Toolkit

International audienceGriwes is an initiative to develop a common model and an open-source freeware platform shared by different graph-based frameworks. We provide an overview of its objectives, architecture and specifications. We detail some of the basic mathematical structures that are used to characterize the primitives for graph-based knowledge representation. We then propose to factorize recurrent knowledge representation primitives that can be shared across specific graph-based languages and we provide a proof of concept by showing how two languages (Simple Conceptual Graphs and RDF) can be described in this framework

Improving the Forward Chaining Algorithm for Conceptual Graphs Rules

baget2004bInternational audienceSimple Conceptual Graphs (SGs) are used to represent entities and relations between these entities: they can be translated into positive, conjunctive, existential first-order logics, without function symbols. Sound and complete reasonings w.r.t. associated logic formulas are obtained through a kind of graph homomorphism called projection. Conceptual Graphs Rules (or CG rules) are a standard extension to SGs, keeping sound and complete reasonings w.r.t. associated logic formulas (they have the same form as tuple generating dependencies in database): these graphs represent knowledge of the form ''IF ... THEN''. We present here an optimization of the natural forward chaining algorithm for CG rules. Generating a graph of rules dependencies makes the following sequences of rule applications far more efficient, and the structure of this graph can be used to obtain new decidability results

Free nilpotent and HH-type Lie algebras. Combinatorial and orthogonal designs

The aim of our paper is to construct pseudo $H$-type algebras from the covering free nilpotent two-step Lie algebra as the quotient algebra by an ideal. We propose an explicit algorithm of construction of such an ideal by making use of a non-degenerate scalar product. Moreover, as a bypass result, we recover the existence of a rational structure on pseudo $H$-type algebras, which implies the existence of lattices on the corresponding pseudo $H$-type Lie groups. Our approach substantially uses combinatorics and reveals the interplay of pseudo $H$-type algebras with combinatorial and orthogonal designs. One of the key tools is the family of Hurwitz-Radon orthogonal matrices

Generating Knowledge in Maintenance from Experience Feedback

Knowledge is nowadays considered as a significant source of performance improvement, but may be difficult to identify, structure, analyse and reuse properly. A possible source of knowledge is in the data and information stored in various modules of industrial information systems, like CMMS (Computerized Maintenance Management Systems) for maintenance. In that context, the main objective of this paper is to propose a framework allowing to manage and generate knowledge from information on past experiences, for improving the decisions related to the maintenance activity. In that purpose, we suggest an original Experience Feedback process dedicated to maintenance, allowing to capitalize on past interventions by i) formalizing the domain knowledge and experiences using a visual knowledge representation formalism with logical foundation (Conceptual Graphs); ii) extracting new knowledge thanks to association rules mining algorithms, using an innovative interactive approach; iii) interpreting and evaluating this new knowledge thanks to the reasoning operations of Conceptual Graphs. The suggested method is illustrated on a case study based on real data dealing with the maintenance of overhead cranes