The axiom system of propositional provability logic. From Wordnik.com. [Provability Logic] Reference
Finally, one can of course study predicate provability logic. From Wordnik.com. [Provability Logic] Reference
Of course, this result concerns provability relative to a system. From Wordnik.com. [Epistemic Paradoxes] Reference
Two strands of research have led to the birth of provability logic. From Wordnik.com. [Provability Logic] Reference
That doesn ` t necessarily go to guilt or innocence; it goes to provability. From Wordnik.com. [CNN Transcript Aug 21, 2007] Reference
A denotes provability of a modal formula A in propositional provability logic. From Wordnik.com. [Provability Logic] Reference
Propositional provability logic is often called GL, after Gödel and Löb. From Wordnik.com. [Provability Logic] Reference
For example, it is still an open question whether GL is the provability logic of. From Wordnik.com. [Provability Logic] Reference
In this section, some recent trends in research on provability logic are discussed. From Wordnik.com. [Provability Logic] Reference
By 'rigorous justification' von Neumann here means provability by a finite machine. From Wordnik.com. [Backing Into an Evidentiary Standard for ID] Reference
Furthermore, provability logic provides tools to study the notion of self-reference. From Wordnik.com. [Provability Logic] Reference
Let Prov be the formalized provability predicate for Peano Arithmetic, which is of the form. From Wordnik.com. [Provability Logic] Reference
Let us repeat only the most interesting clause, the one for the provability operator –¡. From Wordnik.com. [Provability Logic] Reference
The veracity/provability of Terri's wishes has been the main issue driving the whole debate. From Wordnik.com. [Inside Story on Schiavo Case] Reference
It is not clear yet whether condition 1 gives a lower bound on the scope of provability logic. From Wordnik.com. [Provability Logic] Reference
These rely on different formalizations of the provability predicate PrT than the standard ones. From Wordnik.com. [Hilbert's Program] Reference
Is the purpose of a trial to test for guilt, to test for innocence, or to test for provability?. From Wordnik.com. [False Allegation Worse Than Rape?] Reference
The result is the same: finitary provability turns out to be coextensive with provability in PA. From Wordnik.com. [Hilbert's Program] Reference
ProvT, a natural provability predicate with respect to a sufficiently simple axiomatization of T. From Wordnik.com. [Provability Logic] Reference
Here, the situation becomes much more complex than in the case of propositional provability logic. From Wordnik.com. [Provability Logic] Reference
Now as far as provability that really is a moot point as the 'Russell's teapot' argument has shown. From Wordnik.com. [Early Buzz: The First Review of Bruno | /Film] Reference
Strong completeness does not hold for provability logic, however, because semantic compactness fails. From Wordnik.com. [Provability Logic] Reference
All in all, formal provability is a precisely defined concept, much more so than truth and knowledge. From Wordnik.com. [Provability Logic] Reference
Thus, self-reference within the scope of provability does not lead to semantic paradoxes like the Liar. From Wordnik.com. [Provability Logic] Reference
But the gap between provability and truth has nevertheless taken on a larger metaphorical significance. From Wordnik.com. [The Dream of Mind and Machine] Reference
It turns our that the new axiom (GL) of provability logic corresponds to a condition on frames, as follows. From Wordnik.com. [Provability Logic] Reference
Gödel then noticed that such paradoxes would not necessarily arise if truth were replaced by provability. From Wordnik.com. [Kurt Gödel] Reference
Next, we discuss some generalizations of propositional provability logic in more expressive modal languages. From Wordnik.com. [Provability Logic] Reference
Modus ponens is the only deduction rule; this gives the usual notion of proof and provability of the logic BL. From Wordnik.com. [Fuzzy Logic] Reference
Left out in the above discussion are many other important strands of research in provability logic and its extensions. From Wordnik.com. [Provability Logic] Reference
In fact, provability logic embodies all the desiderata that Quine (1953) set out for syntactic treatments of modality. From Wordnik.com. [Provability Logic] Reference
PA indeed proves realizations of propositional tautologies, and provability of the Distribution Axiom of GL translates to. From Wordnik.com. [Provability Logic] Reference
And by defining the realm of meta-mathematics, Hilbert explicitly raised questions about truth and provability in mathematics. From Wordnik.com. [The Dream of Mind and Machine] Reference
Is there a nicely axiomatized predicate provability logic that is adequate, proving exactly the valid principles of provability?. From Wordnik.com. [Provability Logic] Reference
At least according to the scientific method, a theory approximates correctness if it has provability and helps to explain reality. From Wordnik.com. [Think Progress » McCain and Lieberman Express Support For Sending More Troops to Iraq] Reference
Unless explicitly stated otherwise, in the sequel “provability logic” stands for the system GL of propositional provability logic. From Wordnik.com. [Provability Logic] Reference
The main "modal" result about provability logic is the fixed point theorem, which D. de Jongh and G. Sambin independently proved in 1975. From Wordnik.com. [Provability Logic] Reference
I am not talking about the provability of logical systems but the incompleteness of formal systems containing a certain part of arithmetic. From Wordnik.com. [Please Tell Me What “God” Means] Reference
It is unsound in the least, arguably so, and provability is going to be a very long time coming. From Wordnik.com. [TrinidadExpress Today's News] Reference
LearnThatWord and the Open Dictionary of English are programs by LearnThat Foundation, a 501(c)3 nonprofit.
Questions? Feedback? We want to hear from you!
Email us
or click here for instant support.
Copyright © 2005 and after - LearnThat Foundation. Patents pending.