Conceptual Graphs (CG, www.conceptualgraphs.org) are one of the semantic textmodels 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 insuch areas as mathematical linguistics, bioinformatics, mathematical logic andartificial intelligence. CG model was considered as a compromise between aformal language and a graphical language.

HistoryGraph-based semantic depiction was extremelypopular in both computational and theoretical linguistics during the 1960s. Inthe early 1960s a semantic network including a lattice of concept types wasintroduced by Margaret Masterman. A bit later, Silvio Ceccato came up withcorrelational nets based on 56 different relations with subtypes, instances andmany kinds of attributes. David Hays followed with his presentation of dependencygraphs. Although all these graph notations represented the relational structuresemantics, none of them could express full first-order logic.

In 1970s many graph notations were introduced torepresent first-order logic or a formally defined subset. In 1976 John F. Sowadeveloped his version of conceptual graphs (CGs). He emphasized by CG syntaxthe features of natural language and based their logical structure on existentialgraphs (EG) of Charles Sanders Peirce (1909).The difference between the EG and CG notationsPierce used three operators tovisualize the first-order logic (FOL) using existential graphs (EG). Theseoperators are:· an existential quantifier expressed by a bar orlinked structure of bars called a line of identity; · negation expressed by an oval context delimiter; · conjunction expressed by the occurrence of two ormore graphs in the same context.

Sowa in his CGs has usedrectangles, which are called concepts and linked concepts with ovals, which arecalled conceptual relations.Conceptual graphs are usually presentedin the following form, also called a displayform:Figure 1. CG Display FormThis display form is read as “ConceptBrepresents the relation of ConceptA”, where arrows direction points out thedirection of the display form reading. The display form shown on the figure 1can be translated into text based form, also known as linear form:The full stop in this linearform indicates the end of the certain graph. Admittedly, concepts can havereferents referring to an instance or person of the concept. As an example, tocreate 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”, whereLaura is a conformity to the type label Student in the given concept. In otherwords, Laura conforms to the label Student.

Figure 2 visualizes the differencebetween the EG and CG. Both kinds of graphs describe the sentence ” If a personowns a dog then he pets it”.Figure 2. Existential and Conceptual GraphsIn EG an oval enclosure showsscope and the default operator for oval with no other marking is negation, butany metalevel relation can be linked to the oval.

For CGs, Sowa used rectanglesinstead 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 anoval and identifies the first argument of the relation. An arrow that isdirected away from an oval marks the last argument. The sentence “if a person owns adog then he pets it” can also be represented by the following linear formula:All the model-theoreticsemantics 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 isknown as the Conceptual GraphInterchange Format (CGIF). Twoversions of the CGIF exist:· Core CGIF, which represents a type of logicwithout a type and expresses the full Common Logic semantics. This mostly correspondsto Peirce’s EGs: its only primitives are conjunction, negation, and theexistential quantifier.

It does permit quantifiers to range over relations, butPeirce also experimented with that option for EGs.· Extended CGIF, which represents an upward compatibleextension of the core and adds a universal quantifier; type labels forrestricting the range of quantifiers; Boolean contexts with type labels If, Then, Either, Or, Equivalence, and Iff; and the option of importingexternal text into any CGIF text.