Conceptual graphs and first-order logic

Conceptual Structures (CS) Theory is a logic-based knowledge representation formalism. To show that conceptual graphs have the power of first-order logic, it is necessary to have a mapping between both formalisms. A proof system, i.e. axioms and inference rules, for conceptual graphs is also useful. It must be sound (no false statement is derived from a true one) and complete (all possible tautologies can be derived from the axioms). This paper shows that Sowa's original definition of the mapping is incomplete, incorrect, inconsistent, and unintuitive, and the proof system is incomplete too. To overcome these problems a new translation algorithm is given and a complete proof system is presented. Furthermore, the framework is extended for higher-order types

Goal driven theorem proving using conceptual graphs and Peirce logic

The thesis describes a rational reconstruction of Sowa's theory of Conceptual Graphs. The reconstruction produces a theory with a firmer logical foundation than was previously the case and which is suitable for computation whilst retaining the expressiveness of the original theory. Also, several areas of incompleteness are addressed. These mainly concern the scope of operations on conceptual graphs of different types but include extensions for logics of higher orders than first order. An important innovation is the placing of negation onto a sound representational basis. A comparison of theorem proving techniques is made from which the principles of theorem proving in Peirce logic are identified. As a result, a set of derived inference rules, suitable for a goal driven approach to theorem proving, is developed from Peirce's beta rules. These derived rules, the first of their kind for Peirce logic and conceptual graphs, allow the development of a novel theorem proving approach which has some similarities to a combined semantic tableau and resolution methodology. With this methodology it is shown that a logically complete yet tractable system is possible. An important result is the identification of domain independent heuristics which follow directly from the methodology. In addition to the theorem prover, an efficient system for the detection of selectional constraint violations is developed. The proof techniques are used to build a working knowledge base system in Prolog which can accept arbitrary statements represented by conceptual graphs and test their semantic and logical consistency against a dynamic knowledge base. The same proof techniques are used to find solutions to arbitrary queries. Since the system is logically complete it can maintain the integrity of its knowledge base and answer queries in a fully automated manner. Thus the system is completely declarative and does not require any programming whatever by a user with the result that all interaction with a user is conversational. Finally, the system is compared with other theorem proving systems which are based upon Conceptual Graphs and conclusions about the effectiveness of the methodology are drawn

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

3D interaction assistance in virtual reality: A semantic reasoning engine for context-awareness: From interests and objectives detection to adaptations

International audienceThis work aims to provide 3D interaction assistance in virtual environments depending on context. We designed and implemented a generic decision engine that can connect to our existing virtual reality applications through a set of tools. It uses an ontology and Conceptual Graphs (CGs) to represent knowledge, and First Order Logic to conduct semantic reasoning. Context information are gathered by virtual sensors in the application and interpreted by the engine. Multimodal assistance is provided by virtual actuators. Our first test scenario is about assistance to selection of objects or navigation towards objects: the engine automatically detects user's interests and manages adaptations depending on user's hand gestures, interactions history and type of task

On the Relation between Conceptual Graphs and Description Logics

Aus der Einleitung: 'Conceptual graphs (CGs) are an expressive formalism for representing knowledge about an application domain in a graphical way. Since CGs can express all of first-order predicate logic (FO), they can also be seen as a graphical notation for FO formulae. In knowledge representation, one is usually not only interested in representing knowledge, one also wants to reason about the represented knowledge. For CGs, one is, for example, interested in validity of a given graph, and in the question whether one graph subsumes another one. Because of the expressiveness of the CG formalism, these reasoning problems are undecidable for general CGs. In the literature [Sow84, Wer95, KS97] one can find complete calculi for validity of CGs, but implementations of these calculi have the same problems as theorem provers for FO: they may not terminate for formulae that are not valid, and they are very ineficient. To overcome this problem, one can either employ incomplete reasoners, or try to find decidable (or even tractable) fragments of the formalism. This paper investigates the second alternative. The most prominent decidable fragment of CGs is the class of simple conceptual graphs (SGs), which corresponds to the conjunctive, positive, and existential fragment of FO (i.e., existentially quantified conjunctions of atoms). Even for this simple fragment, however, subsumption is still an NP-complete problem [CM92]. SGs that are trees provide for a tractable fragment of SGs, i.e., a class of simple conceptual graphs for which subsumption can be decided in polynomial time [MC93]. In this report, we will identify a tractable fragment of SGs that is larger than the class of trees. Instead of trying to prove new decidability or tractability results for CGs from scratch, our idea was to transfer decidability results from description logics [DLNN97, DLNS96] to CGs. The goal was to obtain a \natural' sub-class of the class of all CGs in the sense that, on the one hand, this sub-class is defined directly by syntactic restrictions on the graphs, and not by conditions on the first-order formulae obtained by translating CGs into FO, and, on the other hand, is in some sense equivalent to a more or less expressive description logic. Although description logics (DLs) and CGs are employed in very similar applications (e.g., for representing the semantics of natural language sentences), it turned out that these two formalisms are quite different for several reasons: (1) conceptual graphs are interpreted as closed FO formulae, whereas DL concept descriptions are interpreted by formulae with one free variable; (2) DLs do not allow for relations of arity > 2 ; (3) SGs are interpreted by existential sentences, whereas almost all DLs considered in the literature allow for universal quantification; (4) because DLs use a variable-free syntax, certain identifications of variables expressed by cycles in SGs and by co-reference links in CGs cannot be expressed in DLs. As a consequence of these differences, we could not identify a natural fragment of CGs corresponding to an expressive DL whose decidability was already shown in the literature. We could, however, obtain a new tractability result for a DL corresponding to SGs that are trees. This correspondence result strictly extends the one in [CF98]. In addition, we have extended the tractability result from SGs that are trees to SGs that can be transformed into trees using a certain \cycle-cutting' operation. The report is structured as follows. We first introduce the description logic for which we will identify a subclass of equivalent SGs. In Section 3, we recall basic definitions and results on SGs. Thereafter, we introduce a syntactical variant of SGs which allows for directly encoding the support into the graphs (Section 4.1). In order to formalize the equivalence between DLs and SGs, we have to consider SGs with one distinguished node called root (Section 4.2). In Section 5, we finally identify a class of SGs corresponding to a DL that is a strict extension of the DL considered in [CF98]

Conceptual graph-based knowledge representation for supporting reasoning in African traditional medicine

Although African patients use both conventional or modern and traditional healthcare simultaneously, it has been proven that 80% of people rely on African traditional medicine (ATM). ATM includes medical activities stemming from practices, customs and traditions which were integral to the distinctive African cultures. It is based mainly on the oral transfer of knowledge, with the risk of losing critical knowledge. Moreover, practices differ according to the regions and the availability of medicinal plants. Therefore, it is necessary to compile tacit, disseminated and complex knowledge from various Tradi-Practitioners (TP) in order to determine interesting patterns for treating a given disease. Knowledge engineering methods for traditional medicine are useful to model suitably complex information needs, formalize knowledge of domain experts and highlight the effective practices for their integration to conventional medicine. The work described in this paper presents an approach which addresses two issues. First it aims at proposing a formal representation model of ATM knowledge and practices to facilitate their sharing and reusing. Then, it aims at providing a visual reasoning mechanism for selecting best available procedures and medicinal plants to treat diseases. The approach is based on the use of the Delphi method for capturing knowledge from various experts which necessitate reaching a consensus. Conceptual graph formalism is used to model ATM knowledge with visual reasoning capabilities and processes. The nested conceptual graphs are used to visually express the semantic meaning of Computational Tree Logic (CTL) constructs that are useful for formal specification of temporal properties of ATM domain knowledge. Our approach presents the advantage of mitigating knowledge loss with conceptual development assistance to improve the quality of ATM care (medical diagnosis and therapeutics), but also patient safety (drug monitoring)

A different perspective on canonicity

One of the most interesting aspects of Conceptual Structures Theory is the notion of canonicity. It is also one of the most neglected: Sowa seems to have abandoned it in the new version of the theory, and most of what has been written on canonicity focuses on the generalization hierarchy of conceptual graphs induced by the canonical formation rules. Although there is a common intuition that a graph is canonical if it is "meaningful'', the original theory is somewhat unclear about what that actually means, in particular how canonicity is related to logic. This paper argues that canonicity should be kept a first-class notion of Conceptual Structures Theory, provides a detailed analysis of work done so far, and proposes new definitions of the conformity relation and the canonical formation rules that allow a clear separation between canonicity and truth

Knowledge formalization in experience feedback processes : an ontology-based approach

Because of the current trend of integration and interoperability of industrial systems, their size and complexity continue to grow making it more difficult to analyze, to understand and to solve the problems that happen in their organizations. Continuous improvement methodologies are powerful tools in order to understand and to solve problems, to control the effects of changes and finally to capitalize knowledge about changes and improvements. These tools involve suitably represent knowledge relating to the concerned system. Consequently, knowledge management (KM) is an increasingly important source of competitive advantage for organizations. Particularly, the capitalization and sharing of knowledge resulting from experience feedback are elements which play an essential role in the continuous improvement of industrial activities. In this paper, the contribution deals with semantic interoperability and relates to the structuring and the formalization of an experience feedback (EF) process aiming at transforming information or understanding gained by experience into explicit knowledge. The reuse of such knowledge has proved to have significant impact on achieving themissions of companies. However, the means of describing the knowledge objects of an experience generally remain informal. Based on an experience feedback process model and conceptual graphs, this paper takes domain ontology as a framework for the clarification of explicit knowledge and know-how, the aim of which is to get lessons learned descriptions that are significant, correct and applicable

Continuous Improvement Through Knowledge-Guided Analysis in Experience Feedback

Continuous improvement in industrial processes is increasingly a key element of competitiveness for industrial systems. The management of experience feedback in this framework is designed to build, analyze and facilitate the knowledge sharing among problem solving practitioners of an organization in order to improve processes and products achievement. During Problem Solving Processes, the intellectual investment of experts is often considerable and the opportunities for expert knowledge exploitation are numerous: decision making, problem solving under uncertainty, and expert configuration. In this paper, our contribution relates to the structuring of a cognitive experience feedback framework, which allows a flexible exploitation of expert knowledge during Problem Solving Processes and a reuse such collected experience. To that purpose, the proposed approach uses the general principles of root cause analysis for identifying the root causes of problems or events, the conceptual graphs formalism for the semantic conceptualization of the domain vocabulary and the Transferable Belief Model for the fusion of information from different sources. The underlying formal reasoning mechanisms (logic-based semantics) in conceptual graphs enable intelligent information retrieval for the effective exploitation of lessons learned from past projects. An example will illustrate the application of the proposed approach of experience feedback processes formalization in the transport industry sector