Rasiowa–Sikorski deduction systems in computer science applications

AbstractA Rasiowa-Sikorski system is a sequence-type formalization of logics. The system uses invertible decomposition rules which decompose a formula into sequences of simpler formulae whose validity is equivalent to validity of the original formula. There may also be expansion rules which close indecomposable sequences under certain properties of relations appearing in the formulae, like symmetry or transitivity. Proofs are finite decomposition trees with leaves having “fundamental”, valid labels. The author describes a general method of applying the R-S formalism to develop complete deduction systems for various brands of C.S and A.I. logic, including a logic for reasoning about relative similarity, a three-valued software specification logic with McCarthy's connectives and Kleene quantifiers, a logic for nondeterministic specifications, many-sorted FOL with possibly empty carriers of some sorts, and a three-valued logic for reasoning about concurrency

Discussion of decentralized capacity management and internal pricing

Dutta and Reichelstein (2010) study the role of transfer pricing and organizational choice in providing incentives for efficient decisions on the acquisition and subsequent reallocation of capacity within decentralized firms. Their analysis suggests that transfer prices based on the historical cost of capacity facilitate the efficient allocation of resources. They also find that symmetric responsibility center structures are generally better suited for providing efficient investment incentives than hybrid organizations. An important condition for the derivation of the two results is the linearity of the shadow prices of capacity. If shadow prices are nonlinear, transfer prices should be below (above) the historical cost of capacity in order to counteract the managers’ incentives to underinvest (overinvest). Because profit center organizations can use transfer prices for mitigating the inefficiency caused by nonlinear shadow prices, they offer a natural advantage over pure investment center organizations in implementing efficient capacity decisions. Overall, these observations suggest that the curvature of profit functions is an important factor in determining the suitable instruments for decentralized capacity management