scholarly journals The weak extension property and finite axiomatizability for quasivarieties

2009 ◽  
Vol 202 (3) ◽  
pp. 199-223 ◽  
Author(s):  
Wiesław Dziobiak ◽  
Miklós Maróti ◽  
Ralph McKenzie ◽  
Anvar Nurakunov
Keyword(s):  
Extension Property ◽  
Finite Axiomatizability ◽  
Weak Extension

scholarly journals More on Modal Aspects of Default Logic1

1992 ◽  
Vol 17 (1-2) ◽  
pp. 99-116
Author(s):  
V. Wiktor Marek ◽  
Miroslaw Truszczynski
Keyword(s):  
Modal Logic ◽  
Default Logic ◽  
Nonmonotonic Logic ◽  
Default Reasoning ◽  
Default Theory ◽  
Autoepistemic Logic ◽  
The Relationship ◽  
Natural Classes ◽  
Weak Extension

Investigations of default logic have been so far mostly concerned with the notion of an extension of a default theory. It turns out, however, that default logic is much richer. Namely, there are other natural classes of objects that might be associated with default reasoning. We study two such classes of objects with emphasis on their relations with modal nonmonotonic formalisms. First, we introduce the concept of a weak extension and study its properties. It has long been suspected that there are close connections between default and autoepistemic logics. The notion of weak extension allows us to precisely describe the relationship between these two formalisms. In particular, we show that default logic with weak extensions is essentially equivalent to autoepistemic logic, that is, nonmonotonic logic KD45. In the paper we also study the notion of a set of formulas closed under a default theory. These objects are shown to correspond to stable theories and to modal logic S5. In particular, we show that skeptical reasoning with sets closed under default theories is closely related with provability in S5. As an application of our results we determine the complexity of reasoning with weak extensions and sets closed under default theories.

scholarly journals On the c0-extension property for compact lines

2015 ◽  
Vol 428 (1) ◽  
pp. 184-193
Author(s):  
Claudia Correa ◽  
Daniel V. Tausk
Keyword(s):  
Extension Property

scholarly journals Biquasitriangularity and spectral continuity

1985 ◽  
Vol 26 (2) ◽  
pp. 177-180 ◽  
Author(s):  
Ridgley Lange
Keyword(s):  
Hilbert Space ◽  
Sufficient Conditions ◽  
Invariant Subspaces ◽  
Extension Property ◽  
Point Of View ◽  
Single Valued Extension Property ◽  
Continuity Theorem ◽  
Spectral Continuity ◽  
Necessary And Sufficient ◽  
Continuity Of The Spectrum

In [6] Conway and Morrell characterized those operators on Hilbert space that are points of continuity of the spectrum. They also gave necessary and sufficient conditions that a biquasitriangular operator be a point of spectral continuity. Our point of view in this note is slightly different. Given a point T of spectral continuity, we ask what can then be inferred. Several of our results deal with invariant subspaces. We also give some conditions characterizing a biquasitriangular point of spectral continuity (Theorem 3). One of these is that the operator and its adjoint both have the single-valued extension property.

Property (ω) and the Single-valued Extension Property

2021 ◽  
Vol 37 (8) ◽  
pp. 1254-1266
Author(s):  
Lei Dai ◽  
Xiao Hong Cao ◽  
Qi Guo
Keyword(s):  
Extension Property ◽  
Single Valued Extension Property
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