Abstract
This paper offers a framework for extending Arnon Avron and Iddo Lev’s non-deterministic semantics to quantified predicate logic with the intent of resolving several problems and limitations of Avron and Anna Zamansky’s approach. By employing a broadly Fregean picture of logic, the framework described in this paper has the benefits of permitting quantifiers more general than Walter Carnielli’s distribution quantifiers and yielding a well-behaved model theory. This approach is purely objectual and yields the semantical equivalence of both α-equivalent formulae and formulae differing only by codenotative terms. Finally, we make a brief excursion into non-deterministic model theory, proving a strong Łoś’ Theorem and compactness for all finitely-valued, non-deterministic logics whose quantifiers have intensions describable in a first order metalanguage.
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Ferguson, T.M. On Non-Deterministic Quantification. Log. Univers. 8, 165–191 (2014). https://doi.org/10.1007/s11787-014-0100-x
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DOI: https://doi.org/10.1007/s11787-014-0100-x