Abstract
In this paper we define four systems of modal propositional logic that can be used for Conceptual Graphs. These ‘extensions’ of Conceptual Graphs are based on ideas of C.S. Peirce, who also developed a modal variant of his Existential Graphs. We use his ideas to define a modal context, and extend and modify the logical inference rules of Conceptual Graphs. We then prove that these extensions yield four logical systems, which are (logically) equivalent to the minimal modal logic K, the modal logic T, the modal logic S4, and the modal logic S5, respectively.
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