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Clausal Analysis of First-order Proof Schemata
[article]
2017
arXiv
pre-print
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Proof schemata are a variant of LK-proofs able to simulate various induction schemes in first-order logic by adding so called proof links to the standard first-order LK-calculus. ...
In "Towards a clausal analysis of cut-elimination", it was shown that reductive cut-elimination transforms a given LK-proof in such a way that a subsumption relation holds between the pre- and post-transformation ...
Note that LKS-proofs have a free parameter, which when instantiated results in an LK-proof. ...
arXiv:1702.02589v1
fatcat:tqdpdh5i6rcepjox4xr5mxcjuq
Page 132 of Phrenological Journal and Science of Health Vol. 77, Issue 3
[page]
1883
Phrenological Journal and Science of Health
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The psycho- logical part of Phrenology might be di-
mh & wee lk ...
by mod- ern scientists. ...
Page 1252 of Mathematical Reviews Vol. , Issue 99b
[page]
1991
Mathematical Reviews
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discovery in LK system by analogy (197- 211); Nobuhiro Inuzuka, Hirohisa Seki and Hidenori Itoh, Effi- cient induction of executable logic programs from examples (212- 224); B. ...
Proceedings of the 3rd Asian Computing Science Conference held in Kathmandu, December 9-11, 1997.
Edited by R. K. Shyamasundar and K. Ueda.
Lecture Notes in Computer Science, 1345. ...
Cut as Consequence
2010
History and Philosophy of Logic
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between a system as a whole and its 'semantics'). ...
The papers where Gerhard Gentzen introduced natural deduction and sequent calculi suggest that his conception of logic differs substantially from now dominant views introduced by Hilbert, Gödel, Tarski ...
Acknowledgments The participants in my spring 2009 proof theory seminar at the University of Notre Dame, with their comments and questions, helped me clarify my reading of Gentzen. ...
doi:10.1080/01445340.2010.522365
fatcat:dnibzkfrlfapjkdfxfpaj4d2bm
The Yangian symmetry of the Hubbard models with variable range hopping
1996
Physics Letters A
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1995 pre-print arXiv:cond-mat/9512071v1 fatcat:pcy27d2xzfdjbmdkml2t3of77y
In both cases the Yangians are mutually commuting, hence can be combined into a Y(sl_2)⊕Y(sl_2) Yangian. Their mutual commutativity is of dynamical origin. ...
This work has been supported by the Japan Society for the ...
In analogy to the spin chain case [13] the generator of its Yangian symmetry might be constructed by adding "potential terms" to the second order Yangian generator K α , eq. (29). ...
doi:10.1016/0375-9601(96)00174-0
fatcat:hlot2dzzbbcifoaxoyujhk7xny
Focalisation and Classical Realisability
[chapter]
2009
Lecture Notes in Computer Science
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The distinction is motivated by the fact that they can be subject to different assumptions during proof-search. ...
In the first part of the paper (Section 2) we give a syntax for LC and LL derived from Curien-Herbelin's calculus, the focalising system L (L foc ). ...
Systems Rules for typing L foc in one-sided MALL, LK pol and LL are given Fig. 1, 2 and 3 . ...
doi:10.1007/978-3-642-04027-6_30
fatcat:lfiecqfw3bezfc7yv2mwy2xmte
σ-Set Theory: Introduction to the concepts of σ-antielement, σ-antiset and Integer Space
[article]
2010
arXiv
pre-print
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In this paper we develop a theory called σ-Set Theory, in which we present an axiom system developed from the study of Set Theories of Zermelo-Fraenkel, Neumann-Bernays-Godel and Morse-Kelley. ...
In σ-Set Theory, we present the proper existence of objects called σ-antielement, σ-antiset, natural numbers, antinatural numbers and generated σ-set by two σ-sets, from which we obtain, among other things ...
For all n ∈ IN ⋆ there exists a unique σ-set m such that {n} ∪ {m} = ∅.Proof. This proof is analogous to the previous one. ...
arXiv:0906.3120v8
fatcat:qojqhtnpezeglpuio3tnqpvr7u
Page 403 of The American Whig Review Vol. 16, Issue 95
[page]
1852
The American Whig Review
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}not have been more numerous and exact in i its orders of material faculties; nor was the | progre ss of their discovery and deification accomplished by less observant and judicious | savi ans than those ...
By the ar gum 1ents of natural useless theology, as de ve loped it Brid lore vater atural & x B Tre atises. and by : aj] the ‘ vathen lk yori cians, tioned. i ; We make only the first step; as it has been ...
A combinatorial computation of the first Pontryagin class of the complex projective plane
1994
Geometriae Dedicata
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but it can be so realized by a star-shaped polytope, and the space of all such realizations is not connected. ...
The conditions of the original formula must be modified since the 8-vertex triangulation of the 3-sphere link of each vertex cannot be realized as the complex of faces of a convex polytope in 4-space, ...
The proof that (ngt~6)g and nj~; belong to the same component of CFo (Lk(i j ) ) is analogous. ...
doi:10.1007/bf01264030
fatcat:ofcmuujyevgjxgazs7ef4xfgby
Geometry of Higher Helicities
2003
Moscow Mathematical Journal
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results related to Arnold's theorem on the asymptotic Hopf invariant on three-dimensional manifolds and recent work on linking of a vector field with a foliation, the asymptotic crossing number, short path systems ...
The author is grateful for kind hospitality to the ESI in Vienna, the IHES in Bures-sur-Yvette, and Ecole Polytechnique in Paris, where this paper was written. Special thanks go to V. Kaimanovich, M. ...
Proof. lk ξ (F) = M lk ξ (x, F) µ = M lim T →∞ 1 T lk(Γ T (x), F) µ = M lim T →∞ 1 T lk(g [0,T ] x , F) µ = M lim T →∞ 1 T g [0,T ] x d −1 β µ = M lim T →∞ 1 T T 0 i ξ (d −1 β)dt µ. ...
doi:10.17323/1609-4514-2003-3-3-989-1011
fatcat:bmsexkstubd5znxlsktd5ibpry
Revisiting Generalizations of the Dehn–Sommerville Relations
[article]
2021
arXiv
pre-print
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2021 pre-print arXiv:2108.13145v1 fatcat:45moscfrrbcmhcehrvzi4f4oxe
Our proofs are uniform, and are based on two simple evaluations of the h̃-polynomial: one that recovers the f̃-polynomial, and one that counts faces according to certain multiplicities. ...
In addition, we present Dehn–Sommerville relations for reciprocal complexes and general balanced simplicial complexes; which slightly generalize some of the previous results. ...
ACKNOWLEDGEMENTS Part of the results in this manuscript were initially included in a preliminary preprint available at [3] , which was split in two papers afterwards. ...
arXiv:2108.13145v2
fatcat:b2y6rbrairfebcgmwxmnzbmoyi
Triple linking numbers and surface systems
[article]
2017
arXiv
pre-print
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We give a refined value group for the collection of triple linking numbers of links in the 3-sphere. ...
Given two links with the same pairwise linking numbers we show that they have the same refined triple linking number collection if and only if the links admit homeomorphic surface systems. ...
MN and PO were supported by CIRGET postdoctoral fellowships. MP was supported by an NSERC Discovery grant.
Surface systems Definition 2.1. ...
arXiv:1709.08478v1
fatcat:y5ntoxfe4rawvgokpwiswewvnm
Concordance invariance of Levine-Tristram signatures of links
[article]
2018
arXiv
pre-print
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In particular [GL15] inspired the question that led to this paper. We also thank the referee for helpful feedback. M. Powell is supported by an NSERC Discovery grant. M. ...
Nagel is supported by a CIRGET Postdoctoral Fellowship. ...
That is, the sum of the entries in each row and in each column of the matrix Lk L is zero. We will use this observation in the proof below. Lemma 5.4. ...
arXiv:1608.02037v3
fatcat:lpr43moodff27p6bwjdx4qodlq
Exact simulation of coupled Wright–Fisher diffusions
2021
Advances in Applied Probability
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Finally, the algorithm's complexity is derived and its performance demonstrated in a simulation study. ...
Once a candidate is accepted, the remainder of the path can be recovered by sampling from neutral multivariate Wright–Fisher bridges, for which an exact sampling strategy is also provided. ...
summands in (7.2).
2 ( 1 21 + |θ |) z j x j .The proof for the general (d − 1)-dimensional case follows analogously. ...
doi:10.1017/apr.2021.9
fatcat:txaiwpqrpva7lmbl4ycf2xconu
XVI. Properties of the trapezium
1826
The Philosophical Magazine
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LK : EL. LD. :: CB.BK: EB.BD. PROP. IV. (Fig. 1.) Let the points E C KD lie in the circumference of a circle; then AE:AK:: (~L: LK:: EL: LD::AC: CD. Dem.--By cireleAE. AD : AC. AK : : CL. LD: EL. ...
In like manner is the second analogy demonstrated. Q.E.D. Cot. Hence also CE 2 : KD 2 : : CL. LE : KL. LD, : : CA. AE : KA. AD, and CK ~ : ED ~ : : CL. LK : EL. LD :: BC.BK: EB. BD. PROP. ...
doi:10.1080/14786442608674096
fatcat:jwdbjz7jgna7ph6vy2aooxtgn4
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