Geodesic
A~matrix notation for the nets of marks
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part VI, Tome 40 (1974), pp. 4-9

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The author's method [1] of establishing deducibility is intuitionistie propositional calculus (JPC) is clarified in this note. A tested formula is first transformed into a conjunction of $\pi$-chains [1]. Then each $\pi$-chain is rewritten as a matrix. After that some occurences of atomic formulas are marked by “+” or “-” according to so called “rule of marks”. A notion of completed matrix is introduced. The main result is the following theorem: The deducibility of a $\pi$-chain in JPC is equivalent to the possibility to construct a completed matrix for that $\pi$-chain. 
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     author = {Ya. Ya. Golota},
     title = {A~matrix notation for the nets of marks},
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     volume = {40},
     year = {1974},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_1974_40_a1/}
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Ya. Ya. Golota. A~matrix notation for the nets of marks. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part VI, Tome 40 (1974), pp. 4-9. http://geodesic.mathdoc.fr/item/ZNSL_1974_40_a1/