Conceptual Graphs (CG, www.conceptualgraphs.org) are one of the semantic text

models related to the semantic networks. Conceptual graphs were proposed in J.

Sova’s works and now play an important role as a means of modeling structures in

such areas as mathematical linguistics, bioinformatics, mathematical logic and

artificial intelligence. CG model was considered as a compromise between a

formal language and a graphical language.

History

Graph-based semantic depiction was extremely

popular in both computational and theoretical linguistics during the 1960s. In

the early 1960s a semantic network including a lattice of concept types was

introduced by Margaret Masterman. A bit later, Silvio Ceccato came up with

correlational nets based on 56 different relations with subtypes, instances and

many kinds of attributes. David Hays followed with his presentation of dependency

graphs. Although all these graph notations represented the relational structure

semantics, none of them could express full first-order logic.

In 1970s many graph notations were introduced to

represent first-order logic or a formally defined subset. In 1976 John F. Sowa

developed his version of conceptual graphs (CGs). He emphasized by CG syntax

the features of natural language and based their logical structure on existential

graphs (EG) of Charles Sanders Peirce (1909).

The difference between the EG and CG notations

Pierce used three operators to

visualize the first-order logic (FOL) using existential graphs (EG). These

operators are:

·

an existential quantifier expressed by a bar or

linked structure of bars called a line of identity;

·

negation expressed by an oval context delimiter;

·

conjunction expressed by the occurrence of two or

more graphs in the same context.

Sowa in his CGs has used

rectangles, which are called concepts and linked concepts with ovals, which are

called conceptual relations.

Conceptual graphs are usually presented

in the following form, also called a display

form:

Figure 1. CG Display Form

This display form is read as “ConceptB

represents the relation of ConceptA”, where arrows direction points out the

direction of the display form reading. The display form shown on the figure 1

can be translated into text based form, also known as linear form:

The full stop in this linear

form indicates the end of the certain graph. Admittedly, concepts can have

referents referring to an instance or person of the concept. As an example, to

create the type label ‘Student’ and assign referent to it, let’s say, Laura,

the concept would look like:

This concept is read as “The Student known as Laura”, where

Laura is a conformity to the type label Student in the given concept. In other

words, Laura conforms to the label Student.

Figure 2 visualizes the difference

between the EG and CG. Both kinds of graphs describe the sentence ” If a person

owns a dog then he pets it”.

Figure 2. Existential and Conceptual Graphs

In EG an oval enclosure shows

scope and the default operator for oval with no other marking is negation, but

any metalevel relation can be linked to the oval. For CGs, Sowa used rectangles

instead of ovals as rectangles nest better than ovals; and more importantly,

each context box can be interpreted as a concept box that contains a nested CG.

In the given example, there is an arrow or an arc that is directed toward an

oval and identifies the first argument of the relation. An arrow that is

directed away from an oval marks the last argument.

The sentence “if a person owns a

dog then he pets it” can also be represented by the following linear formula:

All the model-theoretic

semantics in the CGs and EGs are specified in the ISO standard for Common Logic

(CL). Each semantic feature of graphs that is represented by a linear notation is

known as the Conceptual Graph

Interchange Format (CGIF). Two

versions of the CGIF exist:

·

Core CGIF, which represents a type of logic

without a type and expresses the full Common Logic semantics. This mostly corresponds

to Peirce’s EGs: its only primitives are conjunction, negation, and the

existential quantifier. It does permit quantifiers to range over relations, but

Peirce also experimented with that option for EGs.

·

Extended CGIF, which represents an upward compatible

extension of the core and adds a universal quantifier; type labels for

restricting the range of quantifiers; Boolean contexts with type labels If, Then, Either, Or, Equivalence, and Iff; and the option of importing

external text into any CGIF text.