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Topic: Cut-elimination

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Cut-Elimination for Full Intuitionistic Linear Logic We describe in full detail a solution to the problem of proving the cut elimination theorem for FILL, a variant of (multiplicative and exponential-free) Linear Logic introduced by Hyland and de Paiva. The proof, as usual with cut elimination proofs, is a little involved and we have not seen it published anywhere. The procedure for cut elimination applies to (classical) multiplicative Linear Logic, and we can (with care) restrict our attention to the subsystem FILL. www.brics.dk /RS/96/10

The Role of Quantifier Alternations in Cut Elimination The Role of Quantifier Alternations in Cut Elimination www.brics.dk /RS/03/46/index.html

Operation: Landfill Elimination Cut off the top and use as a gift-wrapping box for t-shirts or other small items. Cut off the top and store cassette tapes (for those of you who still use these) in them. Cut a small section off, clean it, and use as a funky napkin ring. www.geocities.com /RainForest/5002

Elimination theory Elimination of quantifiers is a term used in mathematical logic to explain that in some cases - algebraic geometry of projective space over an algebraically closed field being one - existential quantifiers can be removed. The historical development of commutative algebra, which was initially called ideal theory, is closely linked to concepts in elimination theory: ideas of Kronecker, who wrote a major paper on the subject, were adapted by Hilbert and effectively 'linearised' while dropping the explicit constructive content. In algebraic geometry, elimination theory is the classical name for algorithmic approaches to eliminating between polynomials of several variables. www.freeglossary.com /Elimination_theory

Cut-Elimination and the Subformula Property Actually, since via the Curry-Howard isomorphism cut elimination in intuitionistic implicational logic corresponds to beta-normalization of simply typed lambda terms (see Hindley 1997, Chapter 6), this can also be considered a cut elimination result. (Isn't that clever?) Leivant surveys the cut elimination results in higher-order logic. Andrews also proves weak normalization for simply typed lambda terms. www.andrew.cmu.edu /~cebrown/notes/cutelim.html

Alessio Guglielmi's Research Cut elimination is a still mysterious combinatorial phenomenon. cut elimination, is inadequate to decide the question; I believe that the problem is that this is the only (reasonable) normalisation notion available in the sequent calculus and natural deduction. This `subatomic logic´ would then yield a unique deductive system, a big, weird object where cut elimination, together with many other admissibility phenomena, can be defined and studied once and for all. alessio.guglielmi.name /res

Cut Elimination in Categories Composition elimination, in the form of Gentzen's cut elimination, takes in categories, and techniques inspired by Gentzen are shown to work even better in a purely categorical context than in logic. Here it is shown that these notions, in particular the notion of adjunction, can be formulated in such as way as to be characterised by composition elimination. Proof theory and category theory were first drawn together by Lambek some 30 years ago but, until now, the most fundamental notions of category theory (as opposed to their embodiments in logic) have not been explained systematically in terms of proof theory. www.arkanar.com.by /cut_elimination_in_categories.htm

CATV Lowpass Elimination Filters Cut off (Fc) is available from channels for 2 to 104, or, from 50 to 700 MHz. www.tinlee.com /CATV-ChannelEliminator_Lowpass.htm

House Leadership Elimination of the 15 percent cut is budget neutral and has the overwhelming support of the House and the Senate. www.cahsah.org /sampletters/HouseLeadership3.htm

Foundations of Mathematics Natural deduction, Gentzen's sequent calculi, calculi transformations, cut elimination Propositional logic: natural deduction, normalization, sequents, cut elimination Complete theories, compactness theorem, decidability, closed fields, saturated models, quantifier elimination, prime models sakharov.net /foundation_rt.html

Lógica, Provas e Algoritmos Cut Elimination and the Structure of Proofs (Tutorial) Our main concern will be to analyse proofs during the process of cut-elimination through which we will try to bring to light the strong geometric and dynamical flavor lying inside proofs. We survey classical results due to Statman, Tseitin, Orevkov, Haken and others on the complexity of proofs with and without cuts. www.di.ufpe.br /~lpa98/carbone-talks.html

Papers in elementary proof theory 1998--2002. \\ A reasoned bibliography\\ Sara Negri and Jan von Plato It has been a widespread belief that this is impossible, that ``cut elimination fails in the presence of axioms.'' Unaware of this, we found a way of converting universal axioms into sequent calculus rules and proved that Gentzen's cut elimination extends to these, with no cuts left even on atomic formulas. Gentzen's original proof of cut elimination used a rule of multicut (or ``mix rule'') in which several copies of the cut formula were removed in one step. Barr's theorem, stating that if such an implication is provable in a ``geometric theory'' by classical logic, it is provable by intuitionistic logic, comes out as an immediate corollary to cut elimination: A classical cut-free proof is already an intuitionistic proof. www.helsinki.fi /~negri/ptpub.html

Atlas: A Model Based Cut Elimination Proof by Olivier Hermant This method is proved complete for rewrite systems for which the cut elimination holds. Putting these two results together this leads to a new cut elimination theorem for the cases studied by Stuber [5]. Unfortunately, the cut elimination property doesn't hold and depends on the considered rewrite system. atlas-conferences.com /c/a/j/y/09.htm

Deep Inference and the Calculus of Structures Deep inference severely challenges the usual cut elimination methods, but this is mitigated by atomic cuts being much simpler objects than generic cuts. The systems so obtained cannot be presented in the sequent calculus, but they enjoy the usual properties of locality, decomposition and cut elimination available in the calculus of structures. Several normal propositional modal logics, including S5, are systematically presented in the calculus of structures and cut elimination is proved. alessio.guglielmi.name /res/cos

Business 2.0 :: Online Article :: Tech Investor :: Cutting the Dividend Tax Cut Investors should now be on the lookout for companies using the dividend tax cut elimination as an excuse to not pay dividends, says Joseph Beaulieu, an analyst with Morningstar. But on Wednesday, the Senate surprised nearly everyone -- including, one must assume, president Bush -- when it voted 51 to 48 to effectively cut the White House's proposed tax cut program in half, to $350 billion. Among the first items facing the chopping block if the House approves the Senate version is the president's plan to eliminate dividend taxes. www.business2.com /b2/web/articles/0,17863,515569,00.html

CNN.com - Bush to seek $600 billion economic boost - Jan. 7, 2003 Americans with higher incomes would benefit more from a cut in the tax on dividend income because they invest more in stocks and bonds. President Bush is to unveil an economic stimulus program Tuesday that will call for eliminating taxes on stock dividends as well as providing $3,000 payments to help unemployed people find new jobs, the White House said Monday. About half of that amount will go toward eliminating the tax on dividends -- an idea some congressional Democrats are assailing as a gift to the rich. www.cnn.com /2003/ALLPOLITICS/01/06/economic.stimulus

NDRio 2001 - Invited Lecturer We also detail why the correspondence fails for the v-connective, even if both our normalisation and cut- elimination procedures are strongly normalising. We shall present a cut-elimination procedure which is strongly normalising for all connectives and then show the correspondence with normalisation for the fragment that includes exists, i.e. Since we use term annotations for sequent and natural deduction proofs, our arguments are much simpler in comparison with Zucker's work. www.inf.puc-rio.br /nd/urban.html

Cut-elimination theorem Cut elimination is one of the most powerful tools for proving interpolation theorems. Once a system is shown to have a cut elimination theorem, it is normally immediate that the system is consistent. The cut-elimination theorem states that any judgement that possesses a proof in the sequent calculus that makes use of the cut rule also possesses a cut-free proof, that is, a proof that does not make use of the cut rule. www.mcfly.org /en/Cut-elimination

update_2.htm Cutting the amount of “savings” that is derived from “breakage” -- hiring less experienced teachers in place of those retiring at higher pay rates. Elimination of the Dean of Students at Cameron Middle School, and one Vice Principal at Walsh Middle School, due to declining enrollments The Town will cut $350,000 and look to cash reserves or the stabilization account for the remaining $425,000. pages.framingham.k12.ma.us /news/update_2.htm

GW to cut budget, eliminate newspaper program - GW Hatchet - Campus News The decision to cut the newspaper program was based on the consideration that only 22 to 24 percent of the newspapers are being picked up each day, Johnnie Osborne, associate vice president and chief financial officer for Student and Academic Support Services, wrote in an e-mail Friday. The GW Reads program, which deposits three major newspapers in residence halls on weekdays, is one of several services being eliminated or reduced by cuts for the next fiscal year, which begins July 1. The University's Board of Trustees is slated to meet May 14 to approve the proposed cuts, which officials are still discussing. www.gwhatchet.com /news/2004/04/26/CampusNews/Gw.To.Cut.Budget.Eliminate.Newspaper.Program-671119.shtml

"President Bush's Tax Cut Proposals, 2003: an interview with Alan Orlowsky on Bloomberg Radio, January 7, 2003" Yes, there's more in the plan besides eliminating the tax on dividends, but that is more than half of the tax cut. And particularly with regard to the elimination of taxation on the dividend, it'll put a lot of money into the pockets of the wealthy, the plan being that it will increase the valuation of the stock market, which is good for the overall economy. Now to me, the tax cut on dividends is enormous compared to the income tax cut. www.agoltd.com /bloomberg.htm

Logic Journal of the IGPL, Volume 8, Issue 6: November 2000. Smullyan maintains that the importance of cut-free proofs does not stem from cut elimination per se but rather from the fact that they satisfy the subformula property. The main advantage of analytic cut trees over tableaux is efficiency: while analytic cut trees can simulate tableaux with an increase in complexity by at most a constant factor, tableaux cannot polynomially simulate analytic cut trees. Like tableaux analytic cut trees are a refutation system but unlike tableaux they have a single inference rule (a form of the analytic cut rule) and several branch closure rules. www3.oup.co.uk /igpl/Volume_08/Issue_06

DSM ECU - Fuel Cut Elimination This limit can be removed so the ecu will never cut fuel or spark. The ECU will cut fuel and spark if the airflow value exceeds a certain limit. www.nsfabrication.com /epromfc.php

Cut Elimination by Resolution differentials, integrals etc. Therefore it is useful to concentrate on cut-elimination procedures which eliminate cuts by analyzing these explicit definitions and reducing cuts from inside out. In Baaz Leitsch 1997, ( FTP97) and Baaz Leitsch 1999, ( JSC) a different cut elimination method has been presented: This method characterizes cuts by sets of clauses obtained from the derivation of the cut formulas. Moreover the cut formulas to be eliminated must be rendered main formulas of inferences by adequate proof transformations. www.logic.at /people/moser/cres.html

Cut-elimination Cut elimination is one of the most powerful tool for proving interpolation theorems. Once a system is shown to have a cut elimination theorem, it is normally immediate that the system is consistent. The theorem is easy to state: it says that for these systems, the cut rule is admissible. pedia.newsfilter.co.uk /wikipedia/c/cu/cut_elimination.html

Structural Cut Elimination - Pfenning (ResearchIndex) Abstract: We present new proofs of cut elimination for intuitionistic, classical, and linear sequent calculi. @inproceedings{ pfenning95structural, author = "Frank Pfenning", title = "Structural Cut Elimination", booktitle = "Proceedings of the Tenth Annual Symposium on Logic in Computer Science", month = "June", publisher = "IEEE Computer Society Press", address = "San Diego, California", editor = "D. Kozen", pages = "156--166", year = "1995", url = "citeseer.ist.psu.edu/article/pfenning95structural.html" } 34.4% : A Structural Proof of Cut Elimination and Its Representation in.. citeseer.ist.psu.edu /81257.html

The Calgary Sun: Call for tax cut follows debt elimination The Calgary Sun: Call for tax cut follows debt elimination As far as where the money freed up goes now the debt's done, the government will send out surveys to find out what the people want -- and that may or may not include tax or health premium cuts, she said. Now that Alberta's books are in order, it's time to give the people who really pay the bills a break, says the Canadian Taxpayers' Federation. www.canoe.ca /NewsStand/CalgarySun/News/2004/07/14/538904.html

Secrets Of Debt Elimination, Consolidation, Negotiation And Management Revealed: Eliminate Credit Card Debt And More. With the average household having 14 credit cards, its no wonder that credit card debt elimination is a big concern for most families. The details of a solid debt elimination plan to eliminate debt once and for all. This is just one of the things you will learn about here that will aid you in your debt elimination plan. www.debt-elimination-guide.com

Thomas Floats Cap. Gains Cut Under the latest plan, Thomas would retain provisions to accelerate the administration’s 2001 cuts in personal income tax rates, eliminate the marriage penalty and boost the child credit — each of which was included in Bush’s original proposal. Ways and Means Chairman Bill Thomas (R-Calif.) is honing a plan to replace the centerpiece of President Bush’s tax package — a $396 billion cut in dividend taxes — with a slimmer plan that would trim the top rate of dividend and capital gains taxes to 18 percent. Ways and Means Committee aides put the total cost of the 8-18 plan at about $234 billion over 10 years, down from the $396 price tag for the total elimination of dividend taxes. qa-rollcall.iproduction.com /issues/48_85/news/1367-1.html

ESSLLI 2001 Programme Natural deduction, classical and constructive logic, Curry-de Bruijn-Howard isomorphism, cut elimination in the empty theory, applications to proof search and to programming in constructive logic. Examples of theories having the cut elimination property. Deduction and computation in proof search, rewriting terms and rewriting propositions. www.helsinki.fi /esslli/courses/PiDM.html

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