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N N N N Cf. On the Idea of Logical Truth 11, p. 21. 56 COMBINED MODALITIES Note. - There are various extensions of the Systems VE, E V , and V E + E V . One type of extensions are those, in which E-sentences are added to the systems. Thus we get three new Systems V E + E, and E V + E, and VE + E V + E. The expressions in these new systems have a greater number of constituents than expressions in the old systems with the same number of atomic predicates. The solution of the decision problem, however, is essentially the same for the old and the new systems.

V DEONTIC MODALITIES The deontic modalities are about the mode or way in which we are permitted or not to perform an act. They are used in phrases such as “it is obligatory to . ”, “it is permitted to . . ”, or “it is forbidden to . ”. I n ordinary language the word “act” is ambiguously applied to properties of a certain kind and to individual instances of such properties. , theft as such, without regard to concrete cases, an act. But we also call the theft committed by Jones on a certain occasion an act.

The same symbols as before will be used for those concepts. As variable names of acts we shall use variable names of properties A , B, . . As an undefined deontic modality we introduce the concept of There is a more elaborate account of this topic in my article Deontic Logic in Mind 60, 1951. The concept of an act-individual presents some complications. The description of the individual involves the mention both of an agent by which and of an occasion on which the act is performed. The occasion, moreover, need not be spatio-temporally continuous.

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