Query Graphs with Cuts: Mathematical Foundations

Query graphs with cuts are inspired by Sowa’s conceptual graphs, which are in turn based on Peirce’s existential graphs. In my thesis ‘The Logic System of Concept Graphs with Negations’, conceptual graphs are elaborated mathematically, and the cuts of existential graphs are added to them. This yields the system of concept graphs with cuts. These graphs correspond to the closed formulas of first order predicate logic. Particularly, concept graphs are propositions which are evaluated to truth-values. In this paper, concept graphs are extended to so-called query graphs, which are evaluated to relations instead. As the truth-values TRUE and FALSE can be understood as the two 0-ary relations, query graphs extend the expressiveness of concept graphs.

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