The power set of a finite set is used as the alphabet of a string interpreting a sentence of Monadic Second-Order Logic so that the string can be reduced (in a straightforward way) to the symbols occurring in the sentence. Simple extensions to regular expressions are described matching the succinctness of Monadic Second-Order Logic. A link to Goguen and Burstall’s notion of an institution is forged, and applied to conceptions within natural language semantics of time based on change.
The paper is devoted to correct understanding of the notation for the power set. Often this notation is mistaken with a power of the number 2. The correct definition of the power set is presented as well as several task which an serve for strengthening the understanding of this notion.
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The paper contains some sufficient conditions for Marczewski-Burstin representability of an algebra A of sets which is isomorphic to P(X) for some X. We characterize those algebras of sets which are inner MB-representable and isomorphic to a power set. We consider connections between inner MB-representability and hull property of an algebra isomorphic to P(X) and completeness of an associated quotient algebra. An example of an infinite universally MB-representable algebra is given.