Completeness of Minimal Positional Calculus

Abstract

In the article "Podstawy analizy metodologicznej kanonów Milla" [2] Jerzy Łoś proposed an operator that refered sentences to temporal moments. Let us look, for example, at a sentence ‘It is raining in Toruń’. From a logical point of view it is a propositional function, which does not have any logical value, unless we point at a temporal context from a fixed set of such contexts. If the sentence was considered today as a description of a state of affairs, it could be true. If it was considered yesterday, it could be false. 1 The operator enables us to connect any sentence p with any temporal context t. Such a complex sentence we read as: a sentence p is realized at a temporal context t (a point of time, an interval of some kind, etc).