Logica Universalis 8 (2):165-191 (2014)

Authors
Thomas Ferguson
City University of New York
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
Keywords Non-deterministic logic  Łoś’ theorem  nonclassical model theory
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DOI 10.1007/s11787-014-0100-x
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References found in this work BETA

Philosophy of Logics.Susan Haack - 1978 - Cambridge University Press.
Philosophy of Logics.Susan Haack - 1982 - Critica 14 (42):112-119.
Model Theory: An Introduction.David Marker - 2003 - Bulletin of Symbolic Logic 9 (3):408-409.

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Citations of this work BETA

Dunn–Priest Quotients of Many-Valued Structures.Thomas Macaulay Ferguson - 2017 - Notre Dame Journal of Formal Logic 58 (2):221-239.

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