Tamil The Unsound

So would it be correct to summarize unsoundness as: An implementation detail which allows for potential use of an abstraction in such a way that it could lead to a security or safety vulnerabilities under certain circumstances but in itself it does not represent one?

That sounds correct, but overly complicated. I'm trying to figure out if I leaves anything uncovered though.

Regardless: I wouldn't use the words "implementation detail", because soundness is not a detail, it's a fundamental, and critical, aspect of the design, just like "correctness".

I understand you mean the jargon-version of "detail" that means "the way it is implemented, which could be changed", but that downplays the importance, and ignores the fact that some APIs can be unsound in their public interface, which is not a concealed "implementation detail" in the normal sense.

E.g. the original, unsound, API for scoped threads, which caused a bit of a (professionally-handled) meltdown when it was discovered at the time.

Tamil The Unsound

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For getting a quick and punchy but still accurate dictionary definition of "unsound", I'd point at the UCG glossary: -lang/unsafe-code-guidelines/blob/636d140ce9c74ffc4d1fc082bef0771f238f64c9/reference/src/glossary.md#soundness-of-code--of-a-library

we say that a library (or an individual function) is sound if it is impossible for safe code to cause Undefined Behavior using its public API. Conversely, the library/function is unsound if safe code can cause Undefined Behavior.

For OCaml type system, it is impossible to distinguish non-returning expressions and expressions with unsound types. This is why it cannot rule out unsound things as errors. Tracking the definitions to tell a statement has an unsound type or not is generally impossible either and costs a lot even when possible.

That is, an unsound proof system produces proofs for inferences that are not actually valid. Of course, this makes the proof system rather useless, since you want a proof system as a device to show that an inference holds, but in an unsound proof system the situation is precisely that you do not have the guarantee that the proved inference actually holds.

Since unsound proof systems are not very useful, you won't commonly run into them when studying logic. I don't know off the top of my mind of any real-life example, but of course, it can well happen (and most likely has happend throughout history) that the developer of the proof system had the intention of a sound proof system but made a mistake in the design of the rules and had them not adequately reflect the semantics, so that it later turned out to actually be unsound (and didn't make it to popularity for that reason).

And unsoundness doesn't automatically make the proof system inconsistent: A proof system is insoncistent iff it proves both A and A for some formula A, that is, if it proves a contradiction. Suppose A is valid (hence A is contradictory), and the proof system proves A but not A. Then the proof system is unsound, because with A it proves a formula that not actually valid, but it is not inconsistent, because it doesn't prove A which would be necessary to derive a contradiction.

I am writing to ask the members of chess.com (my future opponents) to suggest some unsound openings that I can try out. I play chess entirely for fun, and I don't mind losing sometimes. That said, I usually win with my current set of unsound openings.

My goal is not to simply play bad moves, but to play unsound moves where I am objectively worse, but I nonetheless have a chance to get good counterplay. Even if it's not unsound, I still might play something if it's highly unorthodox and aggressive.

When reading about formal systems one is often warned that, even assuming the system is consistent, one can't be sure that any theorem proved in the system is actually true. For instance, if one can prove $\neg G$ where $G$ is the Gdel sentence in some formal system $S$, then that doesn't immediately make $S$ inconsistent. $G$ might not be provable despite the fact that that's exactly what $\neg G$ asserts. $S$ would have proven a falsehood, making it unsound, yet it might still be consistent.

What bugs me is: if one has arrived at a falsehood, doesn't that imply that either one of the axioms was false or that one of the rules of inference was invalid (capable of deducing a falsehood from truths)? But if either of those were the case that would make the interpretation under consideration no longer be an interpretation at all. And that would annul the charge that $S$ was unsound.

So according to Franzn ZFC + "ZFC is inconsistent" is unsound because it proves the falsehood "ZFC is inconsistent". But that's not how I see it. To me any structure where "ZFC is inconsistent" is a false statement can't serve as an interpretation of this system to begin with. After all, one of the axioms is false.

The above reminds me of Saccheri's famous "the hypothesis of the acute angle is absolutely false; because it is repugnant to the nature of straight lines". Non Euclidean geometry isn't unsound just because some of its theorems are false according to the straight line interpretation. By the same token ZFC + "ZFC is inconsistent" isn't unsound just because one of its theorems is false in the standard ZFC structure.

But then this raises the larger question how any formal system could ever be unsound. It would seem that any structure that might hope to serve as a witness for the systems unsoundness would immediately disqualify from being an interpretation at all.

When we say that a theory (like ZFC+"ZFC is inconsistent") is unsound, we are (at least naively) speaking with respect to a specific "intended model." So - under the usual hypotheses - there are models of ZFC+"ZFC is inconsistent" (because it's consistent), but $V$ isn't one of them.

For a more concrete example, insofar as $\mathbb{R}^2$ is our "intended model" non-Euclidean geometry is indeed unsound, since it doesn't hold in $\mathbb{R}^2$. That is, your claim "non-Euclidean geometry isn't unsound just because some of its theorems are false according to the straight line interpretation" is exactly wrong. What is true is that non-Euclidean geometry isn't inconsistent just because some of its theorems are false in the "intended model," and this is exactly the difference between inconsistency and unsoundness.

First read this post on the incompleteness theorems and pay attention to the section of "Soundness versus consistency". If a formal system can talk about finite binary strings (via an appropriate translation), then its soundness for finite binary strings is strictly stronger than its soundness for program halting, which in turn is strictly stronger than consistency. This should adequately explain why systems such as ZFC+Con(ZFC) is consistent but unsound for program halting.

For the past ten years the AUDINT group has been researching these peripheries of sonic perception (unsound) and the portals they open to new dimensions, activating a continual intersection between fiction and fact, and pressuring thought to become something other than what it has been. The 64 short essays in this volume probe how unsound serves to activate the undead.

merge_type Version note:Dart 3 and later does not support code withoutnull safety or with unsound null safety.All code must be soundly null safe.To learn more, check out the Dart 3 sound null safety tracking issue.

This page describes the differences between sound and unsound null safety,with the goal of helping you decide when to migrate to null safety.After the conceptual discussion are instructions for migrating incrementally,followed by details on testing and running mixed-version programs.

Sound null safety is what you want if possible.Dart tools automatically run your program in sound mode ifthe main entrypoint library of your program has opted into null safety.If you import a null-unsafe library,the tools print a warning to let you know thatthey can only run with unsound null safety.

It should be noted that both invalid, as well as valid but unsound, arguments can nevertheless have true conclusions. One cannot reject the conclusion of an argument simply by discovering a given argument for that conclusion to be flawed.

All arguments with this form are valid. Because they have this form, the examples above are valid. However, the first example is sound while the second is unsound, because its premises are false. Now consider:

For the past seven years the AUDINT group has been researching peripheral sonic perception (unsound) and the ways in which frequencies are utilized to modulate our understanding of presence/non-presence, entertainment/torture, and ultimately life/death. Concurrently, themes of hauntology have inflected the musical zeitgeist, resonating with the notion of a general cultural malaise and a reinvestment in traces of lost futures inhabiting the present.

The contributions to this volume reveal how the sonic nurtures new dimensions in which the real and the imagined (fictional, hyperstitional, speculative) bleed into one another, where actual sonic events collide with spatiotemporal anomalies and time-travelling entities, and where the unsound serves to summon the undead.

A sound analyzer is correct with respect to a class of defects it can detect in a safe and exhaustive way. It offers the guarantee that it will detect any such vulnerability occurring during run-time. This is in contrast with an unsound analyzer, which might not flag faulty code lines (in order to limit the number of warnings returned to the user).

This difference between sound and unsound tools is shown in Figure 1. The green space represents the programs that are correct, the red part those that have a defect. In each illustration, a circle represents the answers provided by a tool, with the programs inside the circle being reported as correct and the programs outside the circle reported as potentially buggy. be457b7860