scholarly journals Uniform Lyndon interpolation property in propositional modal logics

2020 ◽  
Vol 59 (5-6) ◽  
pp. 659-678
Author(s):  
Taishi Kurahashi
Keyword(s):  
Interpolation Property ◽  
Modal Logics

scholarly journals Constructive interpolation in hybrid logic

2003 ◽  
Vol 68 (2) ◽  
pp. 463-480 ◽  
Author(s):  
Patrick Blackburn ◽  
Maarten Marx
Keyword(s):  
Modal Logic ◽  
Strong Evidence ◽  
Interpolation Property ◽  
Modal Logics ◽  
Hybrid Logic ◽  
Basic Algorithm ◽  
Technical Problems ◽  
First Order ◽  
Elementary Class ◽  
Interpolation Algorithms

AbstractCraig's interpolation lemma (if φ → ψ is valid, then φ → θ and θ → ψ are valid, for θ a formula constructed using only primitive symbols which occur both in φ and ψ) fails for many propositional and first order modal logics. The interpolation property is often regarded as a sign of well-matched syntax and semantics. Hybrid logicians claim that modal logic is missing important syntactic machinery, namely tools for referring to worlds, and that adding such machinery solves many technical problems. The paper presents strong evidence for this claim by defining interpolation algorithms for both propositional and first order hybrid logic. These algorithms produce interpolants for the hybrid logic of every elementary class of frames satisfying the property that a frame is in the class if and only if all its point-generated subframes are in the class. In addition, on the class of all frames, the basic algorithm is conservative: on purely modal input it computes interpolants in which the hybrid syntactic machinery does not occur.

scholarly journals A Modified Subformula Property for the Modal Logic S4.2

2019 ◽  
Vol 48 (1) ◽  
Author(s):  
Mitio Takano
Keyword(s):  
Modal Logic ◽  
Sequent Calculus ◽  
Interpolation Property ◽  
Modal Logics ◽  
Finite Model ◽  
Model Property ◽  
Cut Rule ◽  
Finite Model Property ◽  
Axiom A ◽  
Subformula Property

The modal logic S4.2 is S4 with the additional axiom ◊□A ⊃ □◊A. In this article, the sequent calculus GS4.2 for this logic is presented, and by imposing an appropriate restriction on the application of the cut-rule, it is shown that, every GS4.2-provable sequent S has a GS4.2-proof such that every formula occurring in it is either a subformula of some formula in S, or the formula □¬□B or ¬□B, where □B occurs in the scope of some occurrence of □ in some formula of S. These are just the K5-subformulas of some formula in S which were introduced by us to show the modied subformula property for the modal logics K5 and K5D (Bull Sect Logic 30(2): 115–122, 2001). Some corollaries including the interpolation property for S4.2 follow from this. By slightly modifying the proof, the finite model property also follows.

Modal logics with Belnapian truth values

2010 ◽  
Vol 20 (3) ◽  
pp. 279-304 ◽  
Author(s):  
Serge P Odintsov ◽  
Heinrich Wansing
Keyword(s):  
Modal Logics ◽  
Truth Values

scholarly journals On modal logics arising from scattered locally compact Hausdorff spaces

2019 ◽  
Vol 170 (5) ◽  
pp. 558-577
Author(s):  
Guram Bezhanishvili ◽  
Nick Bezhanishvili ◽  
Joel Lucero-Bryan ◽  
Jan van Mill
Keyword(s):  
Modal Logics ◽  
Hausdorff Spaces ◽  
Locally Compact

Modal logics of domains on the real plane

Studia Logica ◽  
1983 ◽  
Vol 42 (1) ◽  
pp. 63-80 ◽  
Author(s):  
V. B. Shehtman
Keyword(s):  
Modal Logics ◽  
Real Plane ◽  
The Real
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