Four weak positional calculi are constructed and examined. They refer to the use of the connective of negation within the scope of the positional connective “R” of realization. The connective of negation may be fully classical, partially analogical or independent from the classical, truth-functional negation. It has been also proved that the strongest system, containing fully classical connective of negation, is deductively equivalent to the system MR from Jarmużek and Pietruszczak.

The purpose of this paper is to present a very versatile family of logical systems ofpositionalortopologicallogic. These systems—obtained by generalizing the existing systems of chronological logic—are to have a very general nature, capable of reflecting the characteristics of a wide range of logical systems, including not only chronological (alsotemporalortense) logic, but also what we may call locative or place logic, and even a logic of “possible worlds”.

The book examines the Master Argument of Diodorus Cronus in the context of the Sea-Battle Tomorrow of Aristotle. The author investigates problems of sentences about the future, time and determinism. He shows that certain reconstructions of the MA do not assume a linear time structure. Thus, the MA is not an argument in favour of determinism.

A formal language is positional if it involves a positional connecitve, i.e. a connective of realization to relate formulas to points of a kind, like points of realization or points of relativization. The connective in focus in this paper is the connective “R”, first introduced by Jerzy Łoś. Formulas [Rαφ] involve a singular name α and a formula φ to the effect that φ is satisfied relative to the position designated by α. In weak positional calculi no nested occurences of (...) the connective “R” are allowed. The distribution problem in weak positional logics is actually the problem of distributivity of the connective “R” over classical connectives, viz. the problem of relation between the occurences of classical connectives inside and outside the scope of the positional connective “R”. (shrink)