Abstract
We present preliminary results for a proof system based on Natural Deduction for intuitionistic Euler-Venn diagrams. These diagrams are our building blocks to visualise intuitionistic arguments, that is, arguments avoiding classical Boolean arguments, for example “proof by contradiction” or the “law of the excluded middle”. We have previously presented semantics for these diagrams and a proof system in the style of Sequent Calculus. Within this proof system, proof search consists of gradually decomposing the diagram to prove. While such a style is easy to automate, it is not very intuitive for human reasoners. Since formalising human reasoning was the main intention behind Natural Deduction, we choose this style for a proof system that is easier to apply and to understand than the existing system.
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Notes
- 1.
The lattice operations reflect the logical operators: the meet \(\sqcap \) is the algebraic equivalent to conjunction \(\wedge \), the join \(\sqcup \) to disjunction \(\vee \), and the algebraic implication \(\mapsto \) corresponds to logical implication \(\rightarrow \). The complement \(- \mathbf {a}\) is defined by \(\mathbf {a} \mapsto 0\) (where \(0\) is the bottom element of the algebra), and corresponds to negation.
- 2.
\(\varGamma \vdash d\) means that using the diagrams in \(\varGamma \) as assumptions, we can prove \(d\).
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Linker, S. (2021). Natural Deduction for Intuitionistic Euler-Venn Diagrams. In: Basu, A., Stapleton, G., Linker, S., Legg, C., Manalo, E., Viana, P. (eds) Diagrammatic Representation and Inference. Diagrams 2021. Lecture Notes in Computer Science(), vol 12909. Springer, Cham. https://doi.org/10.1007/978-3-030-86062-2_54
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