Rasiowa-Sikorski deduction systems in computer science applications

A 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 /nite 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 speci/cation logic with McCarthy’s connectives and Kleene quanti/ers, a logic for nondeterministic speci/cations, many-sorted FOL with possibly empty carriers of some sorts, and a three-valued logic for reasoning about concurrency. c © 2002 Elsevier Science B.V. All rights reserved.