Diagrammatic Logic of Existential Graphs: A Case Study of Commands Ahti-Veikko Pietarinen Department of Philosophy P.O. Box 9, FI-00014 University of Helsinki ahti-veikko.pietarinen@helsinki.fi Abstract. Diagrammatic logics have advantages over symbolic cousins. Peirce thought that logical diagrams (Existential Graphs, EG) are capa- ble of “expression of all assertions”, as our reason is no longer limited to the “line of speech” (MS 654). This paper points out one such value: the economy resulting from combining multi-dimensional diagrams with multi-modal features. In particular, EGs are well-suited for represent- ing and reasoning about non-declarative assertions, such as questions (interrogatives, vert), commands (e.g., imperatives, vair) and the com- pelled (potent). An advantage over symbolic-logical counterparts is multi- dimensionality that entitles recognition of non-declarative moods in an instantaneous fashion: there is no need to attune to the phonetics of expressions. The paper suggest an application of diagrammatic logic of commands to the cases where (i) minimal reaction time to commands is of essence, (ii) a full comprehension of the meaning of imperatives (‘search for their objects’) is needed, and (iii) an effective discrimination of commands from other non-declarative moods is critical. Keywords: diagrammatic logic, existential graphs, multi-dimensionality, multi-modality, tinctures, commands. 1 Diagrammatic Logic of Existential Graphs Peirce’s diagrammatic logic of Existential Graphs (EGs, [1,5]) is both visual (iconic) and formally rigorous. The expressive power goes up to higher-order modal logics. EGs can represent any assertion that has propositional content. 1.1 Multi-dimensionality EGs are scribed on a multi-dimansional manifold, the Sheet of Assertion. For example, in the theory of Beta graphs, which corresponds to the theory of predicate logic with identity, the sheet is 4-dimensional. 1.2 Modality EGs capture modalities in terms of a broken cut [3,5]. A broken cut does not compel the interpreter to admit that the graph P within its enclosure is true: G. Stapleton, J. Howse, and J. Lee (Eds.): Diagrams 2008, LNAI 5223, pp. 404–407, 2008. c  Springer-Verlag Berlin Heidelberg 2008