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Which structural rules admit cut elimination? An algebraic criterion

Kazushige Terui
2007 Journal of Symbolic Logic (JSL)  
Hence it is natural to ask under which condition cut elimination is preserved when a set of structural rules is added to a structure-free logic.  ...  As an application, we show that any set ℛ of structural rules can be "completed" into another set ℛ*, so that the cut elimination theorem holds for FL enriched with ℛ*. while the provability remains the  ...  We are indebted to Jean-Yves Girard, who suggested to the author a possible linkage between his test and cut elimination in 1999, and thus motivated the current work.  ... 
doi:10.2178/jsl/1191333839 fatcat:yajavswp6veihfktlsk47ely7e

Semantic A-translation and Super-consistency entail Classical Cut Elimination [article]

Lisa Allali
2014 arXiv   pre-print
We show that if a theory R defined by a rewrite system is super-consistent, the classical sequent calculus modulo R enjoys the cut elimination property, which was an open question.  ...  This allows to show the stability of the super-consistency criterion and the cut elimination theorem.  ...  Since the reducibility candidates model of [10] is an instance of pseudo-Heyting algebra, this criterion implies that of [10] , and all of its normalization / cut elimination corollaries.  ... 
arXiv:1401.0998v1 fatcat:npcwlc3fbvflpa7hgc7oghy4ly

Semantic A-translations and Super-Consistency Entail Classical Cut Elimination [chapter]

Lisa Allali, Olivier Hermant
2013 Lecture Notes in Computer Science  
We show that if a theory R defined by a rewrite system is super-consistent, the classical sequent calculus modulo R enjoys the cut elimination property, which was an open question.  ...  This allows to show the stability of the super-consistency criterion and the cut elimination theorem.  ...  Since the reducibility candidates model of [10] is an instance of pseudo-Heyting algebra, this criterion implies that of [10] , and all of its normalization / cut elimination corollaries.  ... 
doi:10.1007/978-3-642-45221-5_28 fatcat:nm25kwa6cncejoy6l7szv76siu

Towards a Semantic Characterization of Cut-Elimination

Agata Ciabattoni, Kazushige Terui
2006 Studia Logica: An International Journal for Symbolic Logic  
We introduce necessary and sufficient conditions for a (single-conclusion) sequent calculus to admit (reductive) cut-elimination. Our conditions are formulated both syntactically and semantically.  ...  If L admits reductive cut-elimination, then its structural rules are weakly substitutive. Proof.  ...  On the other hand, the equivalence between (i) and (iii) shows an algebraic perspective of reductive cut-elimination.  ... 
doi:10.1007/s11225-006-6607-2 fatcat:soygnhdryba7jikhisajkq6iwy

Cut elimination in coalgebraic logics

Dirk Pattinson, Lutz Schröder
2010 Information and Computation  
We then independently isolate a purely syntactic property of the set of modal rules that guarantees cut elimination.  ...  We give two generic proofs for cut elimination in propositional modal logics, interpreted over coalgebras.  ...  to the syntactic requirement which is needed for cut elimination.  ... 
doi:10.1016/j.ic.2009.11.008 fatcat:um5uutkui5fvhpd7vmgylgpopm

Towards an algorithmic construction of cut-elimination procedures

2008 Mathematical Structures in Computer Science  
We investigate cut-elimination in propositional substructural logics. The problem is to decide whether a given calculus admits (reductive) cut-elimination.  ...  We show that, for commutative single-conclusion sequent calculi containing generalized knotted structural rules and arbitrary logical rules, the problem can be decided by resolution-based methods.  ...  Theorem 5.1 (Cut Elimination). Any knotted commutative calculus K in which (a) logical rules are reductive and (b) structural rules are weakly substitutive, admits cut-elimination. Proof.  ... 
doi:10.1017/s0960129507006573 fatcat:lgvaxbrkjrgk3mztjxikao7tbq

A Simple Proof that Super-Consistency Implies Cut Elimination

Gilles Dowek, Olivier Hermant
2012 Notre Dame Journal of Formal Logic  
As an application, we compare our work with the cut elimination theorems in higher-order logic that involve V-complexes.  ...  It also takes ideas from the semantic proofs of cut elimination that proceed by proving the completeness of the cut-free calculus.  ...  Cut Elimination The Algebra Of Sequents Definition 3.1 (Neutral proof) A proof is said to be neutral if its last rule is the axiom rule or an elimination rule, but not an introduction rule.  ... 
doi:10.1215/00294527-1722692 fatcat:b645m56r3vedlonbk5vk75rtsy

An effectful way to eliminate addiction to dependence

Pierre-Marie Pedrot, Nicolas Tabareau
2017 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)  
Crucially, the construction requires that the universe of algebras of the monad forms itself an algebra.  ...  The weaning translation applies to a version of the Calculus of Inductive Constructions (CIC) with a restricted version of dependent elimination.  ...  For recursive datatypes, recursive calls are turned into the free algebra itself, which raises an issue in CIC. Namely, datatype constructors must satisfy the positivity criterion.  ... 
doi:10.1109/lics.2017.8005113 dblp:conf/lics/PedrotT17 fatcat:n6zg5i4anfgkje44g5ntcltkpq

Strong normalization proofs for cut elimination in Gentzen's sequent calculi

Elias Bittar
1999 Banach Center Publications  
This modification allows us to interpret a symmetrical system of mix elimination rules E LKsp by a finite rewriting system; the termination of this rewriting system can be machine checked.  ...  We give also a self-contained strong normalization proof by structural induction.  ...  Non-structural mix elimination rules of E LK are obtained by replacing in the non-structural mix elimination rules of E LKsp the use of parallel structural rules by several applications of structural rules  ... 
doi:10.4064/-46-1-179-225 fatcat:s63qp5afl5bbrkz4xnkeokhzua

On the elimination of imaginaries from certain valued fields

Philip Scowcroft, Angus Macintyre
1993 Annals of Pure and Applied Logic  
The criterion on p. 242 of the Introduction implies that any structure with a definable well-ordering eliminates imaginaries, and so the proof is complete if h exists.  ...  If we do not insist on structures that admit definable Skolem functions, we may eliminate imaginaries in K by expanding it to a model of Shelah's Th(K)eq.  ... 
doi:10.1016/0168-0072(93)90222-y fatcat:2zg7ogbb25hdvfni7gv7evibnm

The fire triangle: how to mix substitution, dependent elimination, and effects

Pierre-Marie Pédrot, Nicolas Tabareau
2019 Proceedings of the ACM on Programming Languages (PACMPL)  
There is a critical tension between substitution, dependent elimination and effects in type theory.  ...  To release this tension, we propose ∂CBPV, an extension of call-by-push-value (CBPV) Ða general calculus of effectsÐto dependent types.  ...  The current paper solves this limitation straightforwardly by equipping computation types, seen as terms, with an algebra structure.  ... 
doi:10.1145/3371126 fatcat:qkx25phwpfe37nabscmj7vgnga

Primary-Market Auctions for Event Tickets: Eliminating the Rents of 'Bob the Broker'

Aditya Bhave, Eric B. Budish
2013 Social Science Research Network  
We have proprietary data from TM, which indicate the price at which each ticket was sold in TM's primary-market auction, for all 2007 concert tours that used auctions (we will describe the auction rules  ...  Relative to fixed prices, an appropriately designed auction should improve price discovery, increase revenue, and reduce or eliminate the scope for speculator rent seeking.  ...  sets. rule (k − 1) times yields lim npro→∞ (n pro + n f an − 1) k−1 (k − 1)!  ... 
doi:10.2139/ssrn.2237451 fatcat:snb6r5cuijcrneevqiy7umbqqe

Polynomially scaling spin dynamics II: Further state-space compression using Krylov subspace techniques and zero track elimination

Ilya Kuprov
2008 Journal of magnetic resonance (San Diego, Calif. 1997 : Print)  
Reson. 189 (2007) 241-250] to include on-the-fly detection and elimination of unpopulated dimensions from the system density matrix.  ...  The proposed zero track elimination (ZTE) procedure is computationally inexpensive, reversible, numerically stable and easy to add to any existing simulation code.  ...  A much larger class will stay approximately zero and we need a robust pruning criterion for those, as well as an error estimate.  ... 
doi:10.1016/j.jmr.2008.08.008 pmid:18789735 fatcat:xhjiye5ehrgudeathxipdhiydq

Non-Wellfounded Proof Theory For (Kleene+Action)(Algebras+Lattices)

Anupam Das, Damien Pous, Michael Wagner
2018 Annual Conference for Computer Science Logic  
We prove cut-elimination for a sequent-style proof system which is sound and complete for the equational theory of Kleene algebra, and where proofs are (potentially) non-wellfounded infinite trees.  ...  We recover the equational theory of all action lattices by restricting to regular proofs (with cut) -those proofs that are unfoldings of finite graphs.  ...  Cut reduction Our cut-elimination argument is driven by a standard set of cut reduction rules, which we do not have space to present in the main text.  ... 
doi:10.4230/lipics.csl.2018.19 dblp:conf/csl/DasP18 fatcat:5hg67ddwr5hu7fkiuryt4rl4ru

Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media

Haijian Yang, Chao Yang, Shuyu Sun
2016 SIAM Journal on Scientific Computing  
The active-set reduced-space method consists of two major steps: (a) in the first phase, an index set with respect to the computational domain is decomposed into active and inactive parts, based on a criterion  ...  The proposed active-set reduced-space method with nonlinear elimination consists of two major ingredients: (a) a global update based on an active-set reduced-space method as an outer nonlinear solve and  ...  In this paper, we have proposed an active-set reduced-space method with nonlinear elimination for the fully implicit simulation of two-phase flows.  ... 
doi:10.1137/15m1041882 fatcat:pl3lckfyifdmbnaxzhcpnjq3ie
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