Ruth Barcan Marcus and quantified modal logic

2021 ◽  
pp. 1-31
Author(s):  
Frederique Janssen-Lauret
Keyword(s):  
Modal Logic ◽  
Quantified Modal Logic ◽  
Barcan Marcus

Quantified Modal Logic With Rigid Terms

1988 ◽  
Vol 34 (3) ◽  
pp. 251-259 ◽  
Author(s):  
Giovanna Corsi
Keyword(s):  
Modal Logic ◽  
Quantified Modal Logic

QUANTIFIED MODAL LOGIC ON THE RATIONAL LINE

2014 ◽  
Vol 7 (3) ◽  
pp. 439-454 ◽  
Author(s):  
PHILIP KREMER
Keyword(s):  
Modal Logic ◽  
Real Line ◽  
Topological Spaces ◽  
Topological Semantics ◽  
Cantor Space ◽  
Quantified Modal Logic ◽  
Propositional Modal Logic ◽  
The Family ◽  
Modal Logic S4 ◽  
Rational Line

AbstractIn the topological semantics for propositional modal logic, S4 is known to be complete for the class of all topological spaces, for the rational line, for Cantor space, and for the real line. In the topological semantics for quantified modal logic, QS4 is known to be complete for the class of all topological spaces, and for the family of subspaces of the irrational line. The main result of the current paper is that QS4 is complete, indeed strongly complete, for the rational line.

scholarly journals REALIZABILITY SEMANTICS FOR QUANTIFIED MODAL LOGIC: GENERALIZING FLAGG’S 1985 CONSTRUCTION

2016 ◽  
Vol 9 (4) ◽  
pp. 752-809 ◽  
Author(s):  
BENJAMIN G. RIN ◽  
SEAN WALSH
Keyword(s):  
Modal Logic ◽  
Graph Model ◽  
Church’S Thesis ◽  
Quantified Modal Logic ◽  
First Order ◽  
Continuity Principle ◽  
Generalized Continuity ◽  
Church's Thesis ◽  
Order Arithmetic ◽  
The Stability

AbstractA semantics for quantified modal logic is presented that is based on Kleene’s notion of realizability. This semantics generalizes Flagg’s 1985 construction of a model of a modal version of Church’s Thesis and first-order arithmetic. While the bulk of the paper is devoted to developing the details of the semantics, to illustrate the scope of this approach, we show that the construction produces (i) a model of a modal version of Church’s Thesis and a variant of a modal set theory due to Goodman and Scedrov, (ii) a model of a modal version of Troelstra’s generalized continuity principle together with a fragment of second-order arithmetic, and (iii) a model based on Scott’s graph model (for the untyped lambda calculus) which witnesses the failure of the stability of nonidentity.

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