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

Similarity Structure on Scientific Theories

I review and amplify on some of the many uses of representing a scientific theory in a particular context as a collection of models endowed with a similarity structure, which encodes the ways in which those models are similar to one another. This structure, which is related to topological structure, proves fruitful in the analysis of a variety of issues central to the philosophy of science. These include intertheoretic reduction, emergent properties, the epistemic connections between modeling and inference, the semantics of counterfactual conditionals, and laws of nature. The morals are twofold: first, the further adoption of formal methods for describing similarity (and related topological) structure has the potential to aid in decisive progress in philosophy of science; and second, the selection and justification of such structure is not a matter of technical convenience, but rather often involves great conceptual and philosophical subtlety. I conclude with various directions for future research

Similarity Structure on Scientific Theories

I review and amplify on some of the many uses of representing a scientific theory in a particular context as a collection of models endowed with a similarity structure, which encodes the ways in which those models are similar to one another. This structure, which is related to topological structure, proves fruitful in the analysis of a variety of issues central to the philosophy of science. These include intertheoretic reduction, emergent properties, the epistemic connections between modeling and inference, the semantics of counterfactual conditionals, and laws of nature. The morals are twofold: first, the further adoption of formal methods for describing similarity (and related topological) structure has the potential to aid in decisive progress in philosophy of science; and second, the selection and justification of such structure is not a matter of technical convenience, but rather often involves great conceptual and philosophical subtlety. I conclude with various directions for future research

Modal Hybrid Logic

This is an extended version of the lectures given during the 12-th Conference on Applications of Logic in Philosophy and in the Foundations of Mathematics in Szklarska Poręba (7–11 May 2007). It contains a survey of modal hybrid logic, one of the branches of contemporary modal logic. In the first part a variety of hybrid languages and logics is presented with a discussion of expressivity matters. The second part is devoted to thorough exposition of proof methods for hybrid logics. The main point is to show that application of hybrid logics may remarkably improve the situation in modal proof theory

Rasiowa-Sikorski Deduction Systems: a Handy Tool for Computer Science Logics

. A Rasiowa-Sikorski system is a sequence-type formalization of logics based on building decomposition trees of formulae labelled with sequences of formulae. Proofs are nite decomposition trees with leaves having \fundamental", valid labels. The system is dual to the tableau system. The author gives examples of applying the R-S formalism to various C.S and A.I. logic, including a logic for reasoning about relative similarity, a three-valued software specication logic with McCarthy's connectives, and a logic for nondeterministic specications. As a new result, an R-S system for many-sorted rst order logic with possibly empty carriers of some sorts is developed. 1 Introduction An issue in computer science logics that has gained much popularity lately are the so-called labelled deductive systems [5]. The predecessors of this type of deductive systems were Beth's tableau systems [1] and Rasiowa-Sikorski (R-S) deduction systems [12], both developed over thirty years ago. Their important..