Conceptual structures: information processing in mind and machine
Conceptual structures: information processing in mind and machine
Logic and Visual Information
An Embedding of Existential Graphs into Concept Graphs with Negations
ICCS '02 Proceedings of the 10th International Conference on Conceptual Structures: Integration and Interfaces
Short Proofs of Tautologies Using the Schema of Equivalence
CSL '93 Selected Papers from the 7th Workshop on Computer Science Logic
A diagrammatic reasoning system for the description logic ALC
Journal of Visual Languages and Computing
Constants and Functions in Peirce's Existential Graphs
ICCS '07 Proceedings of the 15th international conference on Conceptual Structures: Knowledge Architectures for Smart Applications
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It is well-known that Peirce's Alpha graphs correspond to propositional logic (PL). Nonetheless, Peirce's calculus for Alpha graphs differs to a large extent to the common calculi for PL. In this paper, some aspects of Peirce's calculus are exploited. First of all, it is shown that the erasure-rule of Peirce's calculus, which is the only rule which does not enjoy the finite choice property, is admissible. Then it is shown that this calculus is faster than the common cut-free calculi for propositional logic by providing formal derivations with polynomial lengths of Statman's formulas. Finally a natural generalization of Peirce's calculus (including the erasure-rule) is provided such that we can find proofs linear in the number of propositional variables used in the formular, depending on the number of propositional variables in the formula.