Completeness of Minimal Positional Calculus

Tomasz Jarmużek, Andrzej Pietruszczak



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).


Minimal Positional Calculus; Jerzy Łoś

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Garson, J., and N. Rescher, “Topologicallogic”, Journalof Symbolic Logic, 33 (1968): 537–548.

Łoś, J., “Podstawy analizy metodologicznej kanonów Milla”, Annales Universitatis Maria Curie-Skłodowska, 2 (1948): 269–301.

Rasiowa, H., and R. Sikorski, Mathematics of Metamathematics, Warszawa, second edition, PWN, 1968.

Rescher, N., “On the logic of chronological propositions”, Mind, 77 (1966): 75–96.

Rescher, N., and Urquhart A., Temporal Logic, Vienna, Springer-Verlag, 1971.

ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

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