From Existential Graphs to Conceptual Graphs

Existential graphs (EGs) are a simple, readable, and expressive graphic notation for logic. Conceptual graphs (CGs) combine a logical foundation based on EGs with features of the semantic networks used in artificial intelligence and computational linguistics. CG design principles address logical, linguistic, and cognitive requirements: a formal semantics defined by the ISO standard for Common Logic; the flexibility to support the expressiveness, context dependencies, and metalevel commentary of natural language; and cognitively realistic operations for reasoning by induction, deduction, abduction, and analogy. To accommodate the vagueness and ambiguities of natural language, informal heuristics can supplement the formal semantics. With sufficient background knowledge and a clarifying dialog, informal graphs can be refined to any degree of precision. Peirce claimed that the rules for reasoning with EGs generate “a moving picture of the action of the mind in thought.” Some philosophers and psychologists agree: Peirce’s diagrams and rules are a good candidate for a natural logic that reflects the neural processes that support thought and language. They are psychologically realistic and computationally efficient. 1. LANGUAGES AND DIAGRAMS FOR LOGIC Existential graphs and the conceptual graphs based on them are formally defined, but they follow the long tradition of deriving logical patterns from language patterns. For the first formal logic, Aristotle developed a stylized or controlled version of natural language (NL). To clarify the references and reduce ambiguity, he replaced pronouns with letters. For his Elements of Geometry, Euclid followed Aristotle’s conventions as far as he could. When he needed more expressive power, Euclid added diagrams and a broader range of language patterns. Controlled Greek was the first CNL, but logicians and mathematicians translated it to controlled Latin, Arabic, and other languages. Over the centuries, they abbreviated words and phrases with various symbols and organized them in diagrams. The plus sign +, for example, is a simplified ampersand &, which abbreviated a hand-written et in Latin. The oldest surviving type hierarchy is the Tree of Porphyry from the third century AD. John F. Sowa VivoMind Research, LLC, USA