
Publication details
Publisher: Springer
Place: Berlin
Year: 2006
Pages: 172-188
Series: Lecture Notes in Computer Science
ISBN (Hardback): 9783540358930
Full citation:
, "Some notes on proofs with alpha graphs", in: Conceptual structures: inspiration and application, Berlin, Springer, 2006


Some notes on proofs with alpha graphs
pp. 172-188
in: Pascal Hitzler, Peter Øhrstrøm (eds), Conceptual structures: inspiration and application, Berlin, Springer, 2006Abstract
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.
Cited authors
Publication details
Publisher: Springer
Place: Berlin
Year: 2006
Pages: 172-188
Series: Lecture Notes in Computer Science
ISBN (Hardback): 9783540358930
Full citation:
, "Some notes on proofs with alpha graphs", in: Conceptual structures: inspiration and application, Berlin, Springer, 2006