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The problem Of Quantificational Completeness and the Characterization of All Perfect Quantifiers in 3‐Valued Logics
Author(s) -
Carnielli Walter A.
Publication year - 1987
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19870330104
Subject(s) - completeness (order theory) , mathematics , characterization (materials science) , classical logic , calculus (dental) , discrete mathematics , algebra over a field , pure mathematics , medicine , mathematical analysis , materials science , dentistry , nanotechnology
Consider a formal language L, adequate to the formalization of an m-valued predicate logic (i.e., a formal language with symbols for variables, predicates, quantifiers, and unary and binary connectives); then the interpretations for the unary and binary connectives of L, are functions f , : m m and g j : (m x m) + m, where m = = (0, 1 , . . . , m l} is the set of truth values of L,. The logic L, is said to be functionally complete when the interpretation of its connectives are such that they can define, by algebraic composition, all the functions from m to m and from (m x m) to m. When all those functions can be defined by a single function, we say that this single function is a complete connective.