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....into the form of the axiom and so need not be taken as a reduction operator. Note that this point of view also makes sense substructurally. Consider, for example, the endsequent ; 0 in multiplicative intuitionistic linear logic [9] a similar example can be formulated in BI [21,23,24]) A sketch of a Kripke model generated by a search 6 We use ; as the antecedent constructor for intuitionistic logic to distinguish it from the , used in a later example based on linear logic. 7 Our use of just atoms to form axioms should be considered analogous to the use of atoms in a ....
.... system, there is no possiblity of generating v using the operators corresponding to Contraction or Weakening, C ; W: 8 If the monoid is also preordered, then it might also provide the worlds for a forcing semantics of the intuitionistic connectives (see [24,21,23]) 9 w 1 w 2 w 3 w 4 w 1 : w 2 : w 3 : w 4 : Fig. 5. Substructural Search Semantics as Kripke Semantics It follows that we might expect to interpret reductive logic in models based on families of polynomial categories indexed by Kripke worlds [27] Note that ....
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