# Conceptual Graph

A Conceptual Graph is a semantic network where graph nodes represent concepts and graph edges represent semantic relations.

## References

### 2009

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Conceptual_graphs
• A conceptual graph (CG) is a notation for logic based on the existential graphs of Charles Sanders Peirce and the semantic networks of artificial intelligence. In the first published paper on CGs, John F. Sowa used them to represent the conceptual schemas used in database systems. The first book on CGs (Sowa 1984) applied them to a wide range of topics in artificial intelligence, computer science, and cognitive science. A linear notation, called the Conceptual Graph Interchange Format (CGIF), has been standardized in the ISO standard for Common Logic.

### 2008

• (Corbett, 2008) ⇒ Dan R. Corbett. (2008). “Graph-based Representation and Reasoning for Ontologies.” In: Studies in Computational Intelligence, Springer. [http://dx.doi.org/10.1007/978-3-540-78293-3 10.1007/978-3-540-78293-3 doi:[http://dx.doi.org/10.1007/978-3-540-78293-3 10.1007/978-3-540-78293-3)
• A Conceptual Graph with respect to a canon is a tuple G=(C,R, type, referent, arg1, ..., argm), where
• $\displaystyle{ C }$ is the set of concepts ; type : $\displaystyle{ C }$$\displaystyle{ T }$ indicates the type of a concept, and referent : $\displaystyle{ C }$ → $I$ indicates the referent marker of a concept.
• $\displaystyle{ R }$ is the set of conceptual relations, type : $\displaystyle{ R }$$\displaystyle{ T }$ indicates the type of relation, and each argi : $\displaystyle{ R }$$\displaystyle{ C }$ is a partial function where argi(r) indicates the i-th argument of the relation r. The argument functions are partial as they are undefined for arguments higher than the relation’s ‘arity’. We adopt the convention that arg0 indicates the (at most) one incoming arc. If there is no incoming arc to the relation, then arg0 is undefined. We also define the function arity(r) which returns an integer value representing the number of arguments that the relation $\displaystyle{ r }$ has.
• … Description Logics are useful and efficient at categorizing objects and creating a hierarchy of types. They can classify new concepts and specify constraints on the type hierarchy. But is this enough? … Using Conceptual Graphs to represent the underlying ontology, we have demonstrated a method for automated reasoning on ontologies. Type hierarchies and the canonical formation rules efficiently specialize graphs into concrete instances. A simple unification operation, using join and type subsumption, is used to perform knowledge conjunction of the concepts represented as graphs. The significance of our work is that the previously static knowledge representation of ontology is now a dynamic, functional reasoning system.

### 2000

• (Mineau et al., 2000) ⇒ Guy W. Mineau, Akshay Bissoon, and Robert Godin. (2000). “Pre and Post-Pruning Techniques for Large Conceptual Clustering Structures.” In: Electronic Transactions on Artificial Intelligence, 4.
• A conceptual graph (CG) is made of two types of nodes: concepts representing objects (either concrete or abstract), and relations representing semantic links between concepts. Both nodes are typed; types come from a thesaurus called a type hierarchy T. Identifiable individuals are referred to by individual markers. I is the set of all individual markers. All concept nodes in a CG represents an individual of some type, either represented by an individual marker (if explicitly known) or by a quantified variable (otherwise). When the variable is existentially quantified, then the * symbol, called the generic marker, may be used. An individual represented by a concept node is said to conform to the type of the concept. To that effect, a conformity relation :: is defined between elements of T and I ? {*}. We call the elements of I ? {*} referents. A concept is thus described using a type t and a referent which conforms to t.
• Arcs connect concept nodes to relation nodes in a non-ambiguous way, as described in B, the canonical basis of the system. B encodes the signature of each relation. For each relation r, B gives the number of parameters of r, their order, and the maximal type of each parameter (which are all concept nodes). By doing so, overgeneralizations are avoided. Canonical formation operators define how concepts and relations may be connected to form new graphs. Consequently, all graphs represented in a CG system are derived from <T,I,::,B>, the canon of the system

### 1984

• (Sowa, 1984) ⇒ J. F. Sowa. (1984). “Conceptual Structures: Information Processing in Mind and Machine. Addison Wesley.
• Conceptual graphs form a knowledge representation language based on linguistics, psychology, and philosophy. In the graphs, concept nodes, represent entities, attributes, states and events, and relation nodes show how the concepts are interconnected.
• 3.1.2 Assumption. A conceptual graph is a finite, connected, bipartite graph. … If a relation node has narcs, it is said to be n-adic.
• Only three assumptions, which were analyzed in Section 2.3, are necessary to justify Assumption 3.1.2:
• Concepts are discrete units.
• Combinations of concepts are not diffuse mixtures, but ordered structures.
• Only discrete relations are recorded in concepts. Continuous forms must be approximated by patterns of discrete units.