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单词 finite model property
释义
finite model property

Logic
  • With respect to a modal logic L, a property satisfied by L when for any formula φ in the language of L, if there is a Kripke model with a possible world at which φ is true, then there exists a finite Kripke model (i.e., whose set of possible worlds is finite) with a world at which φ is true. When L is a sound and complete modal logic that extends classical logic, this condition may be equivalently stated as the property that if Lφ (i.e., φ is not an L-theorem), there exists a finite Kripke model with a possible world at which φ is true. That a modal logic has the finite model property is frequently an important ingredient in proving it to be decidable.


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