The basic building block for the Moot-Puite nets is a generalized notion of a link, accommodating connectives of any arity.  A link is determined by its type (tensor or cotensor), its premises (a sequence P1,…,Pn, 0 ≤ n), its conclusions (a sequence C1,…,Cm, 0 ≤ m), and its main formula (which can be empty, in the case of a neutral link, or one of the Pi or Ci). A proof structure is a set of links over a finite set of formulas such that every formula is at most once the premise of a link and at most once the conclusion.  Formulas which are not the conclusion of any link are the hypotheses of the proof structures, whereas the formulas which are not the premise of any link are the conclusions.  An axiom formula is a formula which is not the main formula of any link.  Abstract proof structures are obtained by erasing all formulas on the internal nodes. A proof net is a proof structure for which the abstract proof structure converts to a tensor tree — a rooted tree in the case of the intuitionistic systems, possibly an unrooted tree in the case of symmetric LG.  Proofs nets, so defined, can then be show to be the graphs that correspond to valid derivations.