Calculus CL as a Formal System

In Ahti Veikko Pietarinen, Peter Chapman, Leonie Bosveld-de Smet, Valeria Giardino, James Corter & Sven Linker, Diagrammatic Representation and Inference. Diagrams 2020. Lecture Notes in Computer Science, vol 12169. 2020. pp. 445-460 (2020)
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Abstract

In recent years CL diagrams inspired by Lange’s Cubus Logicus have been used in various contexts of diagrammatic reasoning. However, whether CL diagrams can also be used as a formal system seemed questionable. We present a CL diagram as a formal system, which is a fragment of propositional logic. Syntax and semantics are presented separately and a variant of bitstring semantics is applied to prove soundness and completeness of the system.

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Author Profiles

Jens Lemanski
University of Münster
Ludger Jansen
PTH Brixen College

Citations of this work

A Bitstring Semantics for Calculus CL.Fabien Schang & Jens Lemanski - 2022 - In Jean-Yves Beziau & Ioannis Vandoulakis, The Exoteric Square of Opposition. Birkhauser. pp. 171–193.
Extended Syllogistics in Calculus CL.Jens Lemanski - 2020 - Journal of Applied Logics 8 (2):557-577.

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References found in this work

Euler-type Diagrams and the Quantification of the Predicate.Jens Lemanski - 2020 - Journal of Philosophical Logic 49 (2):401-416.
Oppositional Geometry in the Diagrammatic Calculus CL.Jens Lemanski - 2017 - South American Journal of Logic 3 (2):517-531.

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