Conceptual graphs and formal concept analysis (original) (raw)
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Simple concept graphs: A logic approach
Lecture Notes in Computer Science, 1998
Conceptual Graphs and Formal Concept Analysis are combined by developing a logical theory for concept graphs of relational contexts. Therefore, concept graphs are introduced as syntactical constructs, and their semantics is de ned based on relational contexts. For this contextual logic, a sound and complete system of inference rules is presented and a standard graph is introduced that entails all concept graphs being valid in a given relational context. A possible use for conceptual knowledge representation and processing is suggested.
Arbitrary Relations in Formal Concept Analysis and Logical Information Systems
Lecture Notes in Computer Science, 2005
A logical view of formal concept analysis considers attributes of a formal context as unary predicates. In a first part, we propose an augmented definition that handles binary relations between objects. A Galois connection is defined on augmented contexts. It represents concept inheritance as usual, but also relations between concepts. As usual, labeling operators are also defined. In particular, concepts and relations are visible and labeled in a single structure. In a second part, we show how relations can be used for navigating in an augmented concept lattice. This part augments the theory of Logical Information Systems. An implementation is sketched, and first experimental results are presented.
Simple Conceptual Graphs and Simple Concept Graphs
2006
Sowa's Conceptual Graphs and Formal Concept Analysis have been combined into another knowledge representation formalism named Concept Graphs. In this paper, we compare Simple Conceptual Graphs with Simple Concept Graphs, by successively studying their different syntaxes, semantics, and entailment calculus. We show that these graphs are almost identical mathematical objects, have equivalent semantics, and similar inference mechanisms. We highlight the respective benefits of these two graph-based knowledge representation formalisms, and propose to unify them.
Semantics of Conceptual Graphs
1979
Conceptual graphs are both a language for representing knowledge and patterns for constructing models. They form models in the AI sense of structures that approximate some actual or possible system in the real world. They also form models in the logical sense of structures for which some set of axioms are true. When combined with recent developments in nonstandard logic and semantics, conceptual graphs can form a bridge between heuristic techniques of AI and formal techniques of model theory.
Formal Concept Analysis – Overview and Applications
Procedia Engineering, 2014
In this article we give a brief overview of the theory behind the formal concept analysis, a novel method for data representation and analysis. From given tabular input data this method finds all formal concepts and computes a concept lattice, a directed, acyclic graph, in which all formal concepts are hierarchically ordered. We describe the link between this method and formal logic, as well as graph theory. Finally we present one example of an application of this method in the field of computer aided learning.
1ST Order Logic Formal Concept Analysis: From Logic Programming to Theory
Computer and Information Science, 1998
In this paper, we analyze and de ne the introduction of 1st order logic in Formal Concept Analysis (FCA); the aims are both theoretical (as a complete model is needed) and applied (so as to improve expression power of FCA as a knowledge mining tool and the relevance of its results).
Conceptual Graphs, Metamodeling, and Notation of Concepts
Lecture Notes in Computer Science, 2000
We study Sowa's conceptual graphs (CGs) with both existential and universal quantifiers. We explore in detail the existential fragment. We extend and modify Sowa's original graph derivation system with new rules and prove the soundness and completeness theorem with respect to Sowa's standard interpretation of CGs into first order logic (FOL). The proof is obtained by reducing the graph derivation to a question-answering problem. The graph derivation can be equivalently obtained by querying a Definite Horn Clauses program by a conjunction of positive atoms. Moreover, the proof provides an algorithm for graph derivation in a pure proof-theoretic fashion, namely by means of a slight enhancement of the standard PROLOG interpreter. The graph derivation can be rebuilt step-by-step and constructively from the resolution-based proof. We provide a notion of CGs in normal form (the table of the conceptual graph) and show that the PROLOG interpreter also gives a projection algorithm between normal CGs. The normal forms are obtained by extending the FOL language by witnesses (new constants) and extending the graph derivation system. By applying iteratively a set of rules the reduction process terminates with the normal form of a conceptual graph. We also show that graph derivation can be reduced to a question-answering problem in propositional datalog for a subclass of simple CGs. The embedding into propositional datalog makes the complexity of the derivation polynomial.
Conceptual graphs as a universal knowledge representation
Computers & Mathematics with Applications, 1992
Conceptual graphs are a knowledge representation language designed as a synthesis of several different traditions. First are the semantic networks, which have been used in machine translation and computational linguistics for over thirty years. Second are the logic-based techniques of unification, lambda calculus, and Peirce's existential graphs. Third is the linguistic research based on Tosni~re's dependency graphs and various forms of case grammar and thematic relations. Fourth are the dataflow diagrams and Petri nets, which provide a computational me,~hani,m for relating conceptual graphs to external procedures and databases. The result is a highly expressive system of logic with a direct mapping to and from natural languages. The lambda calculus supports the definitions for a taxonomic system and provides a general mecha~m for restructuring knowledge bases. With the definitional mechanisms, conceptual graphs can be used as an intermediate stage between natural languages and the rules and frames of expert systems-an important feature for knowledge acquisition and for help and exphaatious. During the past five years, conceptual graphs have been applied to almost every aspect of AI, ranging from expert systems and natural langm~e to computer vision and neural networks. This paper surveys conceptual graphs, their development from each of these traditions, and the applications based on them.
International Handbooks on Information Systems
A conceptual graph (CG) is a graph representation for logic based on the semantic networks of artificial intelligence and the existential graphs of Charles Sanders Peirce. Several versions of CGs have been designed and implemented over the past thirty years. The simplest are the typeless core CGs, which correspond to Peirce's original existential graphs. More common are the extended CGs, which are a typed superset of the core. The research CGs have explored novel techniques for reasoning, knowledge representation, and natural language semantics. The semantics of the core and extended CGs is defined by a formal mapping to and from ISO standard 24707 for Common Logic, but the research CGs are defined by a variety of formal and informal extensions. This article surveys the notation, applications, and reasoning methods used with CGs and their mapping to and from other versions of logic. This is a preprint of Chapter 5 of the Handbook of Knowledge Representation, ed. by F. van Harmelen, V. Lifschitz, and B. Porter, Elsevier, 2008, pp. 213−237. It has been updated with some recent references and an Appendix with the CGIF grammar.
Conceptual graphs for representing conceptual structures
Conceptual Structures in Practice, 2009
A conceptual graph (CG) is a graph representation for logic based on the semantic networks of artificial intelligence and the existential graphs of Charles Sanders Peirce. CG design principles emphasize the requirements for a cognitive representation: a smooth mapping to and from natural languages; an "iconic" structure for representing patterns of percepts in visual and tactile imagery; and cognitively realistic operations for perception, reasoning, and language understanding. The regularity and simplicity of the graph structures also support efficient algorithms for searching, pattern matching, and reasoning. Different subsets of conceptual graphs have different levels of expressive power: the ISO standard conceptual graphs express the full semantics of Common Logic (CL), which includes the subset used for the Semantic Web languages; a larger CG subset adds a context notation to support metalanguage and modality; and the research CGs are exploring an open-ended variety of extensions for aspects of natural language semantics. Unlike most notations for logic, CGs can be used with a continuous range of precision: at the formal end, they are equivalent to classical logic; but CGs can also be used in looser, less disciplined ways that can accommodate the vagueness and ambiguity of natural languages. This chapter surveys the history of conceptual graphs, their relationship to other knowledge representation languages, and their use in the design and implementation of intelligent systems.