Steven Orey. Model theory for the higher order predicate calculus. Transactions of the American Mathematical Society, vol. 92 (1959), pp. 72–84.

1962 ◽  
Vol 27 (1) ◽  
pp. 96-96
Author(s):  
Kurt Schütte
Keyword(s):  
Model Theory ◽  
American Mathematical Society ◽  
Higher Order ◽  
Predicate Calculus ◽  
Mathematical Society ◽  
Order Predicate Calculus

S. S. Goncharov. Autostability and computable families of constructivizations. Algebra and Logic, vol. 14 (1975), no. 6, pp. 392–409. - S. S. Goncharov. The quantity of nonautoequivalent constructivizations. Algebra and Logic, vol. 16 (1977), no. 3, pp. 169–185. - S. S. Goncharov and V. D. Dzgoev. Autostability of models. Algebra and Logic, vol. 19 (1980), no. 1, pp. 28–37. - J. B. Remmel. Recursively categorical linear orderings. Proceedings of the American Mathematical Society, vol. 83 (1981), no. 2, pp. 387–391. - Terrence Millar. Recursive categoricity and persistence. The Journal of Symbolic Logic, vol. 51 (1986), no. 2, pp. 430–434. - Peter Cholak, Segey Goncharov, Bakhadyr Khoussainov and Richard A. Shore. Computably categorical structures and expansions by constants. The Journal of Symbolic Logic, vol. 64 (1999), no. 1, pp. 13–137. - Peter Cholak, Richard A. Shore and Reed Solomon. A computably stable structure with no Scott family of finitary formulas. Archive for Mathematical Logic, vol. 45 (2006), no. 5, pp. 519–538. - Chris Ash, Julia Knight, Mark Manasse and Theodore Slaman. Generic copies of countable structures. Annals of Pure and Applied Logic, vol. 42 (1989), no. 3, pp. 195–205. - John Chisholm. Effective model theory vs. recursive model theory. The Journal of Symbolic Logic, vol. 55 (1990), no. 3, pp. 1168–1191.

2012 ◽  
Vol 18 (1) ◽  
pp. 131-134
Author(s):  
Daniel Turetsky
Keyword(s):  
Mathematical Logic ◽  
Model Theory ◽  
American Mathematical Society ◽  
Effective Model ◽  
Mathematical Society ◽  
Symbolic Logic ◽  
Applied Logic ◽  
Recursive Model ◽  
Linear Orderings ◽  
Scott Family

A THREE-VALUED QUANTIFIED ARGUMENT CALCULUS: DOMAIN-FREE MODEL-THEORY, COMPLETENESS, AND EMBEDDING OF FOL

2017 ◽  
Vol 10 (3) ◽  
pp. 549-582 ◽  
Author(s):  
RAN LANZET
Keyword(s):  
Natural Language ◽  
Model Theory ◽  
Predicate Calculus ◽  
Extended Version ◽  
First Order ◽  
Completeness Result ◽  
Free Model ◽  
Simplifying Assumptions ◽  
Syntactic Restrictions ◽  
Order Predicate Calculus

AbstractThis paper presents an extended version of the Quantified Argument Calculus (Quarc). Quarc is a logic comparable to the first-order predicate calculus. It employs several nonstandard syntactic and semantic devices, which bring it closer to natural language in several respects. Most notably, quantifiers in this logic are attached to one-place predicates; the resulting quantified constructions are then allowed to occupy the argument places of predicates. The version presented here is capable of straightforwardly translating natural-language sentences involving defining clauses. A three-valued, model-theoretic semantics for Quarc is presented. Interpretations in this semantics are not equipped with domains of quantification: they are just interpretation functions. This reflects the analysis of natural-language quantification on which Quarc is based. A proof system is presented, and a completeness result is obtained. The logic presented here is capable of straightforward translation of the classical first-order predicate calculus, the translation preserving truth values as well as entailment. The first-order predicate calculus and its devices of quantification can be seen as resulting from Quarc on certain semantic and syntactic restrictions, akin to simplifying assumptions. An analogous, straightforward translation of Quarc into the first-order predicate calculus is impossible.

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