Elimination Of Cuts Research Articles

The Elimination of Maximum Cuts in Linear Logic and BCK Logic

The Elimination of Maximum Cuts in Linear Logic and BCK Logic

Welfare Effects of TTIP in a DSGE Model

Several studies have analyzed the trade and output effects of the Transatlantic Trade and Investment Partnership (TTIP) between the United States and the European Union, but our paper is the first attempt to study its welfare effects. We measure the welfare effect of TTIP as the percentage of initial consumption that households would be willing to pay for TTIP in order to remain as well off with TTIP as without it. The discounted present value of the welfare gain of TTIP, which leads to the elimination of tariffs and cuts in non-tariff measures by 25%, is in the range of 1% to 4% of initial consumption, depending on the parameterization. The welfare gain increases in the elasticity of substitution between domestic and foreign goods. The bulk of the welfare gain is caused by cuts in non-tariff measures.

The fission yeast MTREC complex targets CUTs and unspliced pre-mRNAs to the nuclear exosome.

Cryptic unstable transcripts (CUTs) are rapidly degraded by the nuclear exosome. However, the mechanism by which they are recognized and targeted to the exosome is not fully understood. Here we report that the MTREC complex, which has recently been shown to promote degradation of meiotic mRNAs and regulatory ncRNAs, is also the major nuclear exosome targeting complex for CUTs and unspliced pre-mRNAs in Schizosaccharomyces pombe. The MTREC complex specifically binds to CUTs, meiotic mRNAs and unspliced pre-mRNA transcripts and targets these RNAs for degradation by the nuclear exosome, while the TRAMP complex has only a minor role in this process. The MTREC complex physically interacts with the nuclear exosome and with various RNA-binding and RNA-processing complexes, coupling RNA processing to the RNA degradation machinery. Our study reveals the central role of the evolutionarily conserved MTREC complex in RNA quality control, and in the recognition and elimination of CUTs.

On the elimination of quantifier-free cuts

When investigating the complexity of cut-elimination in first-order logic, a natural subproblem is the elimination of quantifier-free cuts. So far, the problem has only been considered in the context of general cut-elimination, and the upper bounds that have been obtained are essentially double exponential. In this note, we observe that a method due to Dale Miller can be applied to obtain an exponential upper bound.

Corrected upper bounds for free-cut elimination

Free-cut elimination allows cut elimination to be carried out in the presence of non-logical axioms. Formulas in a proof are anchored provided they originate in a non-logical axiom or non-logical inference. This paper corrects and strengthens earlier upper bounds on the size of free-cut elimination. The correction requires that the notion of a free cut be modified so that a cut formula is anchored provided that all of its introductions are anchored, instead of only requiring that one of its introductions is anchored. With the correction, the originally proved size upper bounds remain unchanged. These results also apply to partial cut elimination. We also apply these bounds to elimination of cuts in propositional logic. If the non-logical inferences are closed under cut and infer only atomic formulas, then all cuts can be eliminated. This extends earlier results of Takeuti and of Negri and von Plato.

SN and CR for free-style LKtq: linear decorations and simulation of normalization

AbstractThe present report is a, somewhat lengthy, addendum to [4], where the elimination of cuts from derivations in sequent calculus for classical logic was studied ‘from the point of view of linear logic’. To that purpose a formulation of classical logic was used, that - as in linear logic - distinguishes between multiplicative and additive versions of the binary connectives.The main novelty here is the observation that this type-distinction is not essential: we can allow classical sequent derivations to use any combination of additive and multiplicative introduction rules for each of the connectives, and still have strong normalization and confluence of tq-reductions.We give a detailed description of the simulation of tq-reductions by means of reductions of the interpretation of any given classical proof as a proof net of PN2 (the system of second order proof nets for linear logic), in which moreover all connectives can be taken to be of one type, e.g., multiplicative.We finally observe that dynamically the different logical cuts, as determined by the four possible combinations of introduction rules, are independent: it is not possible to simulate them internally, i.e.. by only one specific combination, and structural rules.

Elimination of branch cuts from the normal-mode solution using gradient half spaces

A method for eliminating the branch cuts and branch line integrals from the normal-mode solution to the range-invariant acoustic wave equation has been developed and implemented. In the usual normal-mode formulation, evaluation of the vertical wave number in the ocean waveguide’s lower half space involves a square root operation and gives rise to a branch point at the critical angle. When the Pekeris cut is chosen, energy steeper than the critical angle is represented by leaky modes, and lateral-wave energy near the critical angle is represented by the branch line integral. When a mode lies near the branch cut, the branch line integral can be significant at all ranges. Branch line integrals are cumbersome to compute, and, for range-dependent problems, cannot be included in adiabatic and coupled-mode algorithms. By inserting small attenuation and sound-speed gradients in the lower half space, the plane-wave solution is replaced by an Airy function solution, the branch point is eliminated, the Pekeris branch cut is replaced by a series of modes, and the leaky modes become bounded at infinite depth. Implementation of and example calculations using this approach using the normal-mode model ORCA are given.

Cut normal forms and proof complexity

Statman and Orevkov independently proved that cut-elimination is of nonelementary complexity. Although their worst-case sequences are mathematically different the syntax of the corresponding cut formulas is of striking similarity. This leads to the main question of this paper: to what extent is it possible to restrict the syntax of formulas and — at the same time— keep their power as cut formulas in a proof? We give a detailed analysis of this problem for negation normal form (NNF), prenex normal form (PNF) and monotone formulas. We show that proof reduction to NNF is quadratic, while PNF behaves differently: although there exists a quadratic transformation into a proof in PNF too, additional cuts are needed; the elimination of these cuts requires nonelementary expense in general. By restricting the logical operators to {⋀,⋁,∀,∃}, we obtain the type of monotone formulas. We prove that the elimination of monotone cuts can be of nonelementary complexity (here generalized disjunctions in the antecedents of sequents play a central role). On the other hand, we define a large class of problems (including all Horn theories) where cut-elimination of monotone cuts is only exponential and show that this bound is tight. This implies that the elimination of monotone cuts in equational theories is at most exponential. Particularly, there are no short proofs of Statman's sequence with monotone cuts.

Elimination of branch cuts from the normal mode solution using gradient half‐spaces

Elimination of branch cuts from the normal mode solution using gradient half‐spaces

Elimination of cuts in first-order finite-valued logics

A uniform construction for sequent calculi for finite-valued first-order logics with dis- tribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand's theorem for the four-valued knowledge- representation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information.

The Farm Crisis and the Future of Rural Local Governments

America's farmers are facing difficult financial times, and their problems are spilling over to rural local governments. Declining farm incomes and farm property values erode the local tax base. At the same time, demand for publicly provided services may increase, creating a squeeze between falling revenues and higher costs. This article documents the impact the farm crisis has had on local government tax bases in eight multi-county regions in the Midwest. The impacts found, while severe, would generally be manageable in the absence of other shocks. However, when changes in the intergovernmental aid system–such as the elimination of General Revenue Sharing and other cuts in federal aid—are factored in, local governments in agriculturally dependent areas can encounter financial stress. Higher taxes and lower service levels may permanently change the quality of life in rural America.

A new reduction sequence for arithmetic

The main type of result in proof theory having external applications is normalization theorems: any derivation can be reduced to normal form with the help of a finite number of standard transformations (reductions). An estimate for the convergence of the process of normalization gives an estimate for the growth of provable recursive functions, which recently found application to finitary combinatorics [J. Paris and L. Harrington, “A mathematical incompleteness in Peano arithmetic,” in: Handbook of Mathematical Logic (1978), pp. 1133–1142]. The definition of reduction for the predicate calculus and arithmetic is due to Gentzen, who proved a normalization theorem for derivations of atomic formulas and gave an estimate for convergence with the help of an assignment to derivations d of ordinals O(d)<ε0 such that O(d)>O(d) for reductions ¯d of the derivation d. Later convergence was proved for arbitrary derivations; however, the slight clarity in the choice of ¯d and the proof of decrease of ordinals impede understanding and exposition: both Takeuti (G. Takeuti, Proof Theory, North-Holland, 1975) and Schütte (Ref. Zh. Mat., 1978, 7A48K) restrict themselves to derivations of atomic formulas. In the presentpaper there is given a shorter and clearer construction of reduction ¯d and assignment of ordinals, allowing one also to simplify the proof of decrease of ordinals. The source of all the simplifications is the connection with the continuous operator of cut elimination from infinite derivations proposed by the author. In particular, the symbol Ok(d), in terms of which O(d) is defined, can be read as “ordinal height of the derivation, obtained after elimination of cuts of degree ≥ k from an infinite derivation in which d is represented in a standard way.” We consider the L-formulation, where there are rules of introduction of connectives in the antecedent and succedent. Extension to the natural formulation is obtained with the help of Prawitz translation.

A modal sequent calculus for a fragment of arithmetic

Global properties of canonical derivability predicates (the standard example is Pr() in Peano Arithmetic) are studied here by means of a suitable propositional modal logic GL. A whole book [1] has appeared on GL and we refer to it for more information and a bibliography on GL. Here we propose a sequent calculus for GL and, by exhibiting a good proof procedure, prove that such calculus admits the elimination of cuts. Most of standard results on GL are then easy consequences: completeness, decidability, finite model property, interpolation and the fixed point theorem.

Analytic cut

The real importance of cut-free proofs is not the elimination of cuts per se, but rather that such proofs obey the subformula principle. In this paper we accomplish this latter objective in a different manner.In the usual formulations of Gentzen systems, there is only one axiom scheme; all the other postulates are inference rules. By contrast, we consider here some Gentzen type axiom systems for propositional logic and Quantification Theory in which there is only one inference rule; all the other postulates are axiom schemes. This admits of an unusually elegant axiomatization of logic.