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  1. Gamma Graph Calculi for Modal Logics.Minghui Ma & Ahti-Veikko Pietarinen - 2018 - Synthese 195 (8):3621-3650.
    We describe Peirce’s 1903 system of modal gamma graphs, its transformation rules of inference, and the interpretation of the broken-cut modal operator. We show that Peirce proposed the normality rule in his gamma system. We then show how various normal modal logics arise from Peirce’s assumptions concerning the broken-cut notation. By developing an algebraic semantics we establish the completeness of fifteen modal logics of gamma graphs. We show that, besides logical necessity and possibility, Peirce proposed an epistemic interpretation of the (...)
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  • The Sheet of Indication: A Diagrammatic Semantics for Peirce’s EG-Alpha.Gianluca Caterina & Rocco Gangle - 2015 - Synthese 192 (4):923-940.
    Following the guiding thread of Peirce’s use of diagrammatic syntax in his system of existential graphs , which depends crucially on the role of the Sheet of Assertion, we introduce the notion of Sheet of Indication as the basis for a general diagrammatic semantics applicable to a wide range of diagrams. We then show how Peirce’s EG-alpha graphs may be understood as instances of SIs and how logically coherent models of the graphs are represented in the SI semantics.
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  • Instante y momento oportuno en los grafos existenciales de Charles S. Peirce. Por una dimensión kairológica de la creatividad.José Romero Tenorio - 2017 - Pensamiento 73 (276):301-318.
    Para la estética, la creatividad es la emergencia del instante que la vuelve irrepetible o un transitar pendular que la hace resurgir como reminiscencia cegada por un ocaso repetitivo. Haciendo coincidir proceso y teleología, Peirce aglutina estas dos dimensiones, sin atisbar realmente un atisbo de humanidad para disfrutar de lo ínfimo. De ahí que propongamos un momento oportuno que nos dirija hacia una temporalidad más humana.
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  • Signs Systematically Studied: Invitation to Peirce’s Theory.Ahti-Veikko Pietarinen - 2015 - Sign Systems Studies 43 (4):372-398.
    This introductory presentation reviews noteworthy topics and concepts in Peirce’s interrelated kingdoms of the theory of signs, their classification, categories, logic and semeiotic.
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  • Exploring the Beta Quadrant.Ahti-Veikko Pietarinen - 2015 - Synthese 192 (4):941-970.
    The theory of existential graphs, which Peirce ultimately divided into four quadrants , is a rich method of analysis in the philosophy of logic. Its $$\upbeta $$ β -part boasts a diagrammatic theory of quantification, which by 1902 Peirce had used in the logical analysis of natural-language expressions such as complex donkey-type anaphora, quantificational patterns describing new mathematical concepts, and cognitive information processing. In the $$\upbeta $$ β -quadrant, he came close to inventing independence-friendly logic, the idea of which he (...)
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  • Peirce and Diagrams: Two Contributors to an Actual Discussion Review Each Other.Frederik Stjernfelt & Ahti-Veikko Pietarinen - 2015 - Synthese 192 (4):1073-1088.
    The following two review papers have a common origin. Pietarinen’s book Signs of Logic and Stjernfelt’s book Diagrammatology were both published in the same Synthese Library Series being published by Springer. The two books also share the common topic of diagrammatic reasoning in Charles Peirce’s work. Beginning in a conference Applying Peirce held in Helsinki in conjunction with the World Congress of Semiotics in June 2007, two authors have commented upon these books under the headline of Synthese Library Book Session (...)
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  • Reprint Of: Assertion and Denial: A Contribution From Logical Notations.Ahti-Veikko Pietarinen & Francesco Bellucci - 2017 - Journal of Applied Logic 25:S3-S24.
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