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Clausal Analysis of First-order Proof Schemata [article]

David M. Cerna, Michael Lettmann
2017 arXiv   pre-print
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  
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  
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

Curtis Franks
2010 History and Philosophy of Logic  
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

Frank Göhmann, Vladimir Inozemtsev
1996 Physics Letters A  
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]

Guillaume Munch-Maccagnoni
2009 Lecture Notes in Computer Science  
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]

Ivan Gatica Araus
2010 arXiv   pre-print
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  
}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

Lazar Milin
1994 Geometriae Dedicata  
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

B. Khesin
2003 Moscow Mathematical Journal  
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]

Cesar Ceballos, Henri Mühle
2021 arXiv   pre-print
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]

Christopher William Davis, Matthias Nagel, Patrick Orson, Mark Powell
2017 arXiv   pre-print
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]

Matthias Nagel, Mark Powell
2018 arXiv   pre-print
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

Celia García-Pareja, Henrik Hult, Timo Koski
2021 Advances in Applied Probability  
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

T.S. Davies
1826 The Philosophical Magazine  
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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