Комбинированные логики В. А. Смирнова и логика с операторами истинности и ложности.

Аннотация

There are two stages in V.A.Smirnov's constructing o f combined calculi o f propositions and events. In [5] a number o f two-level combined calculi are constructed where external level o f propositions corresponding to an abstract part o f logic is varied as well as their internal level corresponding to ontological presuppositions. At the same time the event terms p differ from propositions $\varTheta p$ and acts o f assertion are not iterated.

In his later work [6] V. A.Smirnov points out that an act o f assertion itself is an event and the question o f iteration arises. Referring to ideas laying in the grounds o f von Wright's logic TL in [7] V.A.Smirnov proposes the generalized combined logic o f propositions and events.

V.A.Smirnov compares the language o f combined logic o f propositions and events OCM with the language o f von Wrights logic o f truth TL and shows that for each T-sentence corresponding formula o f OCM can be constructed and vice versa.

Since von Wright's logics o f truth are similar to the logic with operators o f truth and falsehood [3.4] (these are compared in [4]) it is interesting to compare the last one with combined logic o f prepositions and events.

V.A.Smirnov formulates a number o f combined calculi and logic o f truth TL in sequent form. It is formulating the logic with operators o f truth and falsehood FL4 also in sequent form.