Conceptual Graphs for Modelling and Computing with Generally Quantified Statements

Conceptual graphs and fuzzy logic are two logical formalisms that emphasize the target of natural language, where conceptual graphs provide a structure of formulas close to that of natural language sentences while fuzzy logic provides a methodology for computing with words. This paper proposes fuzzy conceptual graphs as a knowledge representation language that combines the advantages of both the two formalisms for artificial intelligence approaching human expression and reasoning. Firstly, the conceptual graph language is extended with functional relation types for representing functional dependency, and conjunctive types for joining concepts and relations. Then fuzzy conceptual graphs are formulated as a generalization of conceptual graphs where fuzzy types and fuzzy attribute-values are used in place of crisp types and crisp attribute-values. Projection and join as basic operations for reasoning on fuzzy conceptual graphs are defined, taking into account the semantics of fuzzy set-based values.

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It is well-known that problems like validity and subsumption of general CGs are undecidable, whereas subsumption is NP-complete for simple conceptual graphs (SGs) and tractable for SGs that are trees. We will employ results on decidable fragments of first-order logic to identify a natural and expressive fragment of CGs for which validity and subsumption is decidable in EXPTIME. In addition, we will extend existing work on the connection between SGs and description logics (DLs) by identifying a DL that corresponds to the class of SGs that are trees. This yields a tractability result previously unknown in the DL community.

This paper presents a new ontology mapping method. This method addresses the case in which a non-structured ontology is to be mapped with a structured one. Both ontologies are composed of triplets of the form (object, characteristic, value). Structured means that the values describing the objects according to a given characteristic are hierarchically organized using the a kind of relation. The proposed method uses fuzzy conceptual graphs [8] to represent and map objects from a source ontology to a target one. First, we establish a correspondence between characteristics of the source ontology and characteristics of the target ontology based on the comparison of their associated values. Then, we propose an original way of translating the description of an object of the source ontology using characteristics and values of the target ontology. The description thus translated is represented as a fuzzy conceptual graph. Finally, a new projection operation is used to find mappings between translated objects and actual objects of the target ontology. This method has been implemented and the results of an experimentation concerning the mapping of ontologies in the field of risk in food are presented.KeywordsRelevance ScoreConceptual GraphConcept TypeProjection OperationMilk CheeseThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This paper presents a flexible querying system of fuzzy RDF annotations which consists in translating fuzzy RDF annotations into fuzzy conceptual graphs and using an “approximate”-projection operation in order to compare fuzzy query graphs with fuzzy annotation graphs. The fuzzy sets in the query graphs having a semantic of preferences are compared with the fuzzy sets in the annotation graphs having a semantic of similarity or imprecision. These comparisons deliver several scores which are used by our flexible querying system to sort the answers according to a total order even if these scores are not commensurable.

Fuzzy engineering design semantics elaboration and application

Conceptual graphs as a universal knowledge representation

This paper describes two approaches to the automatic generation of behavioral VHDL models from descriptions written in natural language. Both approaches are based on a modeling style in which behavior is represented by a system of interconnected processes. The first approach employs a semantic grammar to directly generate a single VHDL process from a paragraph written in a restricted English called ModelSpeak. The second approach accepts more general English and generates models consisting of multiple processes. series of sentences describing the behavior of a single process and generated correct VHDL code for it. This interface requires the behavior be expressed in a highly restricted English called ModelSpeak (10). Conditional expressions (if statements) may be nested to two levels, and interaction is invoked by the interface to resolve scope ambiguity of loops. This interface is implemented with a semantic grammar (3) in Prolog. The second interface (Approach II) to the Modeler's Assistant for natural language is substantially more complex, but accepts more general English expressions and generates multiple-process models. In this approach, each sentence is parsed by a bottom-up, parallel chart parser to generate a set of valid parse trees. The trees are examined by a Semantic Analyzer (7) to determine one which is semantically correct, and a conceptual graph (14) (semantic network) of its meaning is generated. Once the conceptual graph of individual sentences are joined together (12), a program called the Linker (8) analyzes the graph to produce a Process Model Graph and VHDL process code for the Modeler's Assistant. Nodes in the conceptual graph representing verbs typically generate processes or the conditions which govern them. Nodes representing objects generate signals. The modeling style underlying the Linker produces a sizable collection of processes, each consisting of a single if_then statement. To avoid unnecessary bus resolutions, multiple processes assigning to the same signal are merged. Since signal types are generally not expressed in the English description, they may be added interactively later. Before describing the approaches in more detail, related research on natural language interfaces is reviewed briefly.

J.F. Sowa has defined a FOL semantics for Simple Conceptual Graphs and proved the soundness of the graph operation called projection with respect to this semantics. M. Chein and M.L. Mugnier have proved the completeness result, with a restriction on the form of the target graph of the projection. I propose here another FOL semantics for Simple Conceptual Graphs corresponding to a slightly different interpretation of a Conceptual Graph. Soundness and completeness of the projection with respect to this semantics are true without any restriction. I extend the definitions and results on both semantics to Conceptual Graphs containing co-reference links and to Nested Conceptual Graphs.KeywordsGeneric NodeDescription GraphConceptual GraphConcept NodeConcept TypeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Indexing and retrieval by color descriptions are very important to finding certain web resources, which is typical in the example of online clothing search. However, both keyword matching and semantic mediation by the current ontologies may suffer from the semantic gap between the similarity evaluation and the human perception, which requests the exploitation of “deeper” semantics of color descriptions to reduce this gap. Considering the inherent variability and imprecision characterizing color naming, this paper proposes a novel approach to define (1) the fuzzy semantics of color names on the HSL color space together with their knowledge representation in fuzzy conceptual graphs, and (2) the associated measures to evaluate the similarity between fuzzified color descriptions. The experimental results rendered by the prototype clothing search system have preliminarily shown the strength of the deeper semantics surpassing the ability of both keywords and a concept hierarchy, in handling the matching problem of color descriptions in the targeted web resource search.

The analysis of medical narratives and the generation of natural language expressions are strongly dependent on the existence of an adequate representation language. Such a language has to be expressive enough in order to handle the complexity of human reasoning in the domain. Sowa's Conceptual Graphs (CG) are an answer, and this paper presents a multilingual implementation, using French, English and German. Current developments demonstrate the feasibility of an approach to natural Language Understanding where semantic aspects are dominant, in contrast to syntax driven methods. The basic idea is to aggregate blocks of words according to semantic compatibility rules, following a method called Proximity Processing. The CG representation is gradually built, starting from single words in a semantic lexicon, to finally give a complete representation of the sentence under the form of a single CG. The process is dependent on specific rules of the medical domain, and for this reason is largely controlled by the declarative knowledge of the medical Linguistic Knowledge Base.

In this article a theory of distributed systems consisting of formal contexts which was introduced by Barwise and Seligman is translated to distributed systems consisting of concept graphs. The aim is to construct for every distributed system a channel consisting of a concept graph representing the distributed system and a set concept graph morphisms representing the relation between the parts of the system and the whole system. To reach this aim two operations for constructing new concept graphs, the semiproduct and the quotient by an invariant, are introduced. These operations are the basis for constructing the concept graph of the channel which represents a distributed system as a whole.

A method of acquiring knowledge from natural language (NL) and multiple experts into a standard knowledge representation is provided by the PCCG (Personal Constructs as Conceptual Graphs) operational tracked grid. A tracked grid is similar to a repertory grid with the difference that operational synthetic problems can be acquired naturally via an NL interface. The PCCG tracked grid provides an ability to guide a semi-automatic process of converting NL phrases to conceptual graphs. These phrases may be either stand-alone sentences or the elements and constructs of a tracked grid. If the phrases are from grids and from different experts then the PCCG operational grid will use graph similarity in close conjunction with case based (CB) reasoning to guide consistency checking and integration of the knowledge of the different experts.KeywordsNatural LanguageKnowledge AcquisitionCase Base ReasoningPersonal ConstructOperational GridThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A learning model is considered in terms of formal concept analysis (FCA). This model is generalized for objects represented by sets of graphs with partially ordered labels of vertices and edges (these graphs can be considered as simple conceptual graphs). An algorithm that computes all concepts and the linear (Hasse) diagram of the concept lattice in time linear with respect to the number of concepts is presented. The linear diagram gives the structure of the set of all concepts with respect to the partial order on them and provides a useful tool for browsing or discovery of implications (associations) in data.

This paper discusses a technique that effectively combines conceptual graph theory with fuzzy logic for 3D object recognition. The suitability of fuzzy conceptual graphs for learning continuous valued features is brought out with a machine vision system that employs model-based object recognition. The object recognition system learns instances of segmented range objects from different views, represented in terms of fuzzy conceptual graphs as a memory aggregate. Recognition is done by deriving a conceptual graph for a query and performing graph matching. The technique is found suitable for continuous valued concepts and hence used as with a powerful capability for learning. >