Abstract
We say that an n-argument predicate P ⊂ Ω n is finite, if P is a finite set. Note that the set of individuals Ω is infinite! Finite predicates are useful in data bases and in finite mathematics. The logic DBL proposed here operates on finite predicates only. We construct an imbedding for DBL in a special modal logic MPL. We prove that if a finite predicate is expressible in the classical logic, it is also expressible in DBL. Quantifiers are not necessary in DBL. Some simple algebraic properties of DBL are indicated.
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Dishkant, H. About finite predicate logic. Stud Logica 45, 405–414 (1986). https://doi.org/10.1007/BF00370273
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DOI: https://doi.org/10.1007/BF00370273