Are any terms of BCI combinator calculus eligible for copyright? In logic, a combinatory calculus is a system for expressing proofs whose conclusions are combinations of their premises. Such proofs are called combinators. Premises can be proofs, and a combinator can apply one of its premises to another. Today, I'm curious about the BCI combinator calculus. This calculus has three axioms, called B, C, and I: B: (y → z) → (x → y) → (x → z) C: (x → (y → z)) → (y → (x → z)) I: x → x The reader may recognize these; B is modus ponens, C swaps two premises, and I is a tautology. Now, it is well-known folklore in computer science that BCI is a complete basis for simple linear logic (e.g. see nLab). In more familiar language, this means that for any proof which only uses each premise exactly once (&quot;linear logic&quot;), there is a term which only uses B, C, and I as its ingredients and faithfully represents that proof. For a demonstration, consider Algorithm B at this interactive Web page; if the input only uses each letter once, then the output will only use B, C, and I. Which terms, if any, are eligible for copyright? In particular, is there a smallest copyrightable term of BCI? I know that this is a jurisdiction-dependent question. If this question seems silly, note that for the BI calculus (just containing B and I) the answer is hopefully &quot;none&quot; and for the SK calculus (which is equivalent to typical programming languages in expressive power) the answer is hopefully &quot;some&quot;; I figure that asking about a non-trivial intermediate calculus is interesting.
Short Answer No meaningful intellectual property protection is available for BCI calculus, BI calculus, or SK calculus. Long Answer Copyright Protection There are several categories of things that can’t be copyrighted. A common thread to most of them is that they lack the necessary creativity to be eligible for copyright. Ideas This includes procedures, processes, systems, methods of operation, concepts, principles, or discoveries. Plans, methods, and devices, are also not protectable. However the particular manner in which they are expressed or described in a writing can be copyrighted. (Source) Copyright can protect a particular expression of an idea (e.g. the layout and exact language of a page in a textbook about BCI calculus that is not the only possible way to present it), but not a concept or system like BCI calculus. The same reasoning means that it is probably not possible to copyright BI calculus or SK calculus, even though a particular textbook expressing them in a particular way might be possible to protect with copyright. Also, since BCI calculus is derived from publications in mathematics journals made in 1924 and 1930 by its two lead creators, anything derived from the original publications would probably be in the public domain by now. In the United States: every book and tale published before 1927 is in the public domain; American copyrights last for 95 years for books originally published between 1927 and 1978 if the copyright was properly registered and maintained. It is likely that the copyright for the 1930 journal article in question was not registered and maintained, as it was not routine practice for mathematical journals to do so at the time. Even if it was, the copyright for the 1930 paper would be almost spent and would expire in the year 2025. The Alternative Of Patent Protection Patents can protect ideas of ways to implement something, but also has limitations that probably exclude BCI calculus as something that could be patented: Certain things can never be patented, regardless of how well they meet these four standards. They include the elements, theoretical plans, laws of nature, physical phenomena, and abstract ideas. So patenting fire or the wheel is out, though some people have tried. (Source) Any patent received for BCI calculus prior to the year 2002 would also have expired bringing the subject matter of the patent into the public domain. Also, since BCI calculus is something that has already been disclosed to the public, it is barred from patentability as a form of existing prior art. The existence of prior art would also prevent BI calculus and SK calculus from being patented. Trade Secret Protection Considered It also probably isn't possible to protect BCI calculus (or BI calculus or SK calculus) as a trade secret, because it has been disclosed to the public and hence isn't secret. (Source) Trade Mark Protection Considered It might be possible to protect the name &quot;BCI calculus&quot; as a trademark under which services teaching people to use it are marketed, but that wouldn't protect the underlying system or concepts. But there is a strong argument that this would not even qualify as a trademark because it is merely descriptive and does not have a &quot;secondary meaning&quot; particular to a particular user of the label for the system.
Copyright protection is about certain acts, and not about relationships between products. Copyright law says that the creator of an original work hold the exclusive right to copy and to authorize creation of derivative works. Copyright law does not say that anybody can freely create derivative works as long as they are different to a certain extent. So if you take an original Mario and modify it a teeny bit, that is a violation of copyright; if you take an original Mario and modify it hugely, that is a violation of copyright. Degree of similarity is relevant on some cases when the factual question arises whether the allegedly-infringing work is based on some protected original. This is most obvious in music cases, where all baroque music has some similarity to all other baroque music, all death metal has some similarity to all other death metal, and so on. There is not a legal quasi-statutory standard for measuring substantial similarity in music. The scientific underpinning of such a standard would be based on (weighted) combinatorics and the idea that there are only so many tunes possible (that would be a huge number, until you get to the "within a genre" condition). It seems obvious (by your "admission") that the derived works are based on protected works, so Nintendo's permission is required to legally create such works. However, you do or would hold copyright in your unauthorized derived work. Without a trail of evidence such as a SE question pointing to the connection, the derived images might be hard to connect to the originals. In addition, you may be able to avail yourself of a "fair use" defense, in case you get sued by the original creator. Factors favoring such a defense are the insubstantiality of the copying (a small portion) and the "transformativeness" of your creation.
The lack of a copyright notice is irrelevant, what matters is whether permission is granted. The material cannot be copied, except if the copyright holder grants you permission to copy. However, you might be able to create something legal and satisfactory on your own, because the underlying ideas are not protected. By way of analogy, you cannot copy the Turbo Pascal Numeric Methods library without permission, but you can study the logic of a module and write your own FFT routine. The status of something as &quot;declaring code&quot; is entirely irrelevant to the court's decision in Google v. Oracle. What is relevant to the court's finding of fair use is that the content constituted 0.4 percent of the entire API, and the fact that the copied lines of code are inextricably bound to other lines of code that are accessed by programmers, allowing programmers to bring their skills to a new environment. The court found that he amount of copying was tethered to a valid, and transformative, purpose.
This question has been addressed directly, with very similar facts, by the federal courts, and the answer, based on those decisions, is: Maybe. The most famous case in this area is Mirage Editions v. Albuquerque A.R.T. Co., 856 F.2d 1341 (9th Cir. 1988). In that case, the defendant had bought a copy of plaintiff's art book, cut out the pages, and affixed them to ceramic tiles, which it sold. The defendant relied on the first sale doctrine, codified in 17 U.S.C. 109. The first sale doctrine says that if you own a copy of a copyrighted work, you can resell it without the copyright holder's permission. The plaintiff argued that, by altering the original artwork, the defendant had created a new derivative work. The first sale doctrine gives you the right to sell the book to someone else, but not the right to create derivative works, whether by writing and publishing an unauthorized sequel or, they argued, cutting and pasting and tiling and kilning the physical pages. The Mirage Editions court agreed with the plaintiff that the tiles were a derivative work outside the scope of the first sale doctrine, and therefore the defendants had infringed the plaintiffs' copyrights. However, other courts faced with similar facts have disagreed, and to date I'm not aware of any Supreme Court decision resolving the issue. The bottom line is: you are allowed to sell what you bought; you aren't allowed to transform it into something new and sell that. Where the line gets drawn is muddy and likely to remain so at least until the Supreme Court addresses the issue.
A fundamental principle of copyright law is that protection is only afforded to the concrete expression, and not the abstract idea. Therefore, if you write a sort program, what is protected is &quot;that specific program&quot;, and not the general idea of a sort program. There are many kinds of sort algorithms: if you write a bubble sort program, you don't &quot;own&quot; all bubble sort programs, you only own the one that you wrote. If you sell your right to a particular bubble sort program, you don't thereby prevent yourself from writing another bubble sort program. But, technically, you do prevent yourself from copying that program, changing some variable names or maybe manually recoding a couple of lines, and re-licensing the code (assuming that you fully transferred copyright, or gave the customer exclusive rights to the code). The basic question that the courts will ask is &quot;did you copy that program&quot;, which they answer by looking at the similarity between the two programs. All bubble sorts have a necessary similarity. To prove infringement, the plaintiff would (ultimately) have to prove that the similarity had to have come from copying rather than independent coincidental re-creation. Functional considerations and general programmer practice would tend to weigh against an allegation of infringement in certain cases, where &quot;counter&quot; is a common name for a counter variable, and bubble sort is a well known algorithm with limited practical differences in lines of code. The hard part is establishing that it would be natural for such similarities to exist even when independently coded by a single person. It may be common practice to take a program that you've sold and tweak it in some fashion, but that is copyright infringement, whereas &quot;applying the lessons that you learned in writing X to a new program&quot; is not infringement, it is using the same ideas, and the ideas are not what is protected.
The GPL does require you to keep any existing copyright notices: You may copy and distribute verbatim copies of the Program's source code as you receive it, in any medium, provided that you [...] keep intact all the notices that refer to this License and to the absence of any warranty [...] The GPL also recommends adding a notice to each file: Copyright (C) yyyy name of author - This program is free software[...] From my reading of the GPL, if the software you modify contains such notices, which is likely, you must preserve them. This effectively attributes the original author. However, as far as I can see, there is no requirement to have a list of acknowledgements (as is customary in scientific papers), which lists all the software you used. How to attribute parts that are integrated in source form? (Where licence information is given in the file header) If you keep the original file header (and possibly add to it), that should be enough. How to attribute parts that are integrated in binary form? As far as I can see, there is no additional attribution required for distribution in binary form. The GPL requires you to supply the source code along with the binary form, so the attribution in the source code will be available.
Before the AIA in 2012 both companies could apply for a patent and if one of the applicants thought they were both trying to patent the same thing they could initiate an interference proceeding. In that proceeding before the board, they each present their evidence as to date of conception and diligent effort from that point to the date of the first filing. The board decided which application went forward. Now the U.S. is with the rest of the world in first-to-file. It doesn’t matter who conceived first unless one actually stole the idea from the other. There is a new derivation procedure to try to prove that. I don’t think it has ever yet happened. One of the &quot;simultaneous&quot; inventors could publish the invention, putting into the public domain. If published before the other's filing date, it would theoretically prevent the other from getting a patent. In any case a patent owner can stop the other from making their product or charge a royalty. There is a narrow case under the AIA where one company has been using a process that another later patents and can retain a limited right to keep using that process but can’t move or expand operations. This is called Prior User Rights.
The trivial answer is yes, at least under certain circumstances, as the example you give shows. First, the concept of substrings is not particularly useful in trademark law. IF that were the case, then we wouldn't be able to have a company called "Gaudiest Clothing Brand" because it contains the substring audi. But, you might say, what about looking at words instead of characters, as with the example of "Linux" and "The Linux Foundation." In that case, I offer the example of "Target," which is a word found in literally thousands of US trademarks. You'll notice that the first item on this list where word mark is simply target, rather than a phrase containing that word, doesn't even belong to the well known chain of stores. This brings us to another important aspect of trademark protection, which is that the mark's purpose is to identify a producer of goods, a provider of services, or particular goods or services themselves. You could probably start a bookstore called McDonald's, unless you're near Redmond, Washington, but you certainly would not be able to use that name for a chain of hamburger-based fast food restaurants. Back to the subject of Linux, one possible explanation here is therefore that Linux is a trademark for an operating system, while The Linux Foundation is a trademark for a non-profit foundation that is concerned with the operating system. The trademarks don't represent competing entities. Consider, for example, the disclaimer on volkswagenownersclub.com: VolkswagenOwnersClub.com is an independent media publication. VolkswagenOwnersClub.com and its owners are not affiliated with or endorsed by Volkswagen AG or Volkswagen of America, Inc. Volkswagen is a registered trademark of Volkswagen AG. All rights reserved. All information Copyright 2006-2010 (Also consider, for example, the case of Apple Corps, Ltd. and Apple Computer, Inc..) As far as I can tell, however, "Volkswagen Owners' Club" is not directly relevant to this question, because it is not a registered trademark, and the question concerns two registered trademarks. I am not sure whether two such trademarks could coexist if there were an adversarial relationship between their owners. In this case, hwoever, the trademarks are used together because the owners have a collegial relationship. They work for a common goal, the promotion of the product identified by one of the trademarks. The foundation's use of the trademark is therefore undoubtedly with permission. In fact, the Linux foundation is Linus Torvalds' employer, and one of the foundation's purposes is to manage the Linux trademark that Torvalds owns. Now the question of derivative trademarks, such as My Linux is clouded by the fact that Linux is an open source operating system. In principle, you can't modify a product and then sell it using its original trademark unless you have permission. For example, I don't suppose I could rebottle Coca-Cola with some added salt and pepper and sell it as *Phoog's Coca-Cola" unless I had permission from the owner of the trademark. With Linux being an open-source project, however, the terms of the open source license probably explicitly permit people to use the trademark under certain restrictions if they offer, for example, a customized distribution of Linux