Some syntactical properties of intermediate predicate logics.
Nobu-Yuki Suzuki · Notre Dame Journal of Formal Logic · 1990
In a previous paper the author introduced a syntactical property, which he calls the pseudo-relevance property, for the sake of studying a certain semantical aspect.An intermediate predicate logic L is said to have the pseudo-relevance property if for all formulas A and B which contain no predicate variable in common, either not-^4 or B is provable in L whenever A implies B is provable in L. The pseudo-relevance property can be regarded as a weak version of Craig's interpolation property.From the same point of view, one can see the similarity between Hallden-completeness and the disjunction property.We treat these syntactical properties and their weak versions, and study the relationships between them.