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Theorem proving by chain resolution

Patrick Dehornoy, Abderrahim Marzouk
1998 Theoretical Computer Science  
Starting from the intuition given by Wu's algorithm for the resolution of polynomial systems, we construct new efficient resolution strategies for propositional clauses. @ 1998-Elsevier Science B.V.  ...  It is a natural idea to apply such an algorithm in the framework of theorem proving in propositional logic by considering propositional formulas as polynomials over the finite field with 2 elements and  ...  The main theoretical results we establish here are completeness theorems for chain resolution and its variants.  ... 
doi:10.1016/s0304-3975(97)00128-x fatcat:smbgp3pkvrfzjcehs7e4cfhiva

Page 883 of Mathematical Reviews Vol. , Issue 2000b [page]

2000 Mathematical Reviews  
Sauro Tulipani (1-PERG; Perugia) 2000b:03039 03B35 68T15 Dehornoy, Patrick (F-CAEN; Caen); Marzouk, Abderrahim (F-CAEN; Caen) Theorem proving by chain resolution. (English summary) Theoret. Comput.  ...  After a general discussion concerning our viewpoint on theorem proving in first-order theories and a brief comparison with theory resolution, the power and generality of T-resolution are emphasized by  ... 

On minimal projective resolution

M. A. Al Shumrani
2007 International Mathematical Forum  
The aim of this paper is to prove that for any unbounded chain complex Y in the category Ch(R) of chain complexes whose homology modules H i (Y ) are of finite type has a minimal projective resolution  ...  In [1, Theorem 2.4], it is proved that any bounded below chain complex Y in Ch(R) whose homology modules H i (Y ) are of finite type has a minimal projective resolution when R is a commutative noetherian  ...  The following result is important and will play a major role in proving the minimal part of the main theorem of this paper. It is [2, Lemma 4.43]. Lemma 1.4.  ... 
doi:10.12988/imf.2007.07281 fatcat:ald64gz4yfgrpkspqs6xep3rvi

Regular projective resolutions OF SEMIMODULES

Ho Xuan Thang, Nguyen Xuan Tuyen
2017 HUE UNIVERSITY JOURNAL OF SCIENCE NATURAL SCIENCE  
In this paper, we present an approach version of semimodule homologies by regular projective resolutions such as define a concept of a regular projective resolution, prove the comparison theorem for semimodules  ...  by these resolutions and based them provide cohomology monoids of semimodules.  ...  With the same idea, in this paper, we introduce the concept of a projective regular resolution of a semimoduleand prove the comparison theorem for these resolutions (Theorem 2.6).  ... 
doi:10.26459/hueuni-jns.v126i1b.4272 fatcat:fgu3kwfv6jez7obd6lzx5bfr4m

GORENSTEIN AND Sr PATH IDEALS OF CYCLES

DARIUSH KIANI, SARA SAEEDI MADANI, NAOKI TERAI
2014 Glasgow Mathematical Journal  
Finally, we prove that I t (C n ) has a linear resolution if and only if t ≥ n − 2. 2010 Mathematics Subject Classification. 13D02, 13F55, 05C75, 05C38.  ...  The path ideal (of length t ≥ 2) of a directed graph G is the monomial ideal, denoted by I t (G), whose generators correspond to the directed paths of length t in G. Let C n be an n-cycle.  ...  The research of the first author was in part supported by a grant from IPM (No. 93050220).  ... 
doi:10.1017/s0017089514000111 fatcat:pcysbxzfszfahiqzjoctpld42a

Tight closure in F-rational rings

Ian M. Aberbach
1994 Nagoya mathematical journal  
We are now ready to prove Theorem 1.1. Proof (of Theorem 1.1). The equivalence of (1) and (2) We first prove Ό^A).  ...  F 1 ( 1 M P ) and θ£ p = (θ£) P = 0 P = 0 by [AHH, Theorem 8.1].  ... 
doi:10.1017/s0027763000004943 fatcat:yw4oz67lvbgmja4apwnzm4fyim

Page 212 of The Annals of Mathematical Statistics Vol. 29, Issue 1 [page]

1958 The Annals of Mathematical Statistics  
These chains are the subject of papers by Chung and Derman [2], and Breiman [3]. 2. Use of the semi-martirgale theorem. THEOREM 1. Let 29, 2, -°-- be an atomic chain.  ...  This type of chain has been termed atomic by D.  ... 

On the Gorenstein and 픉-cohomological dimensions

Simon St. John-Green
2014 Bulletin of the London Mathematical Society  
As a corollary we improve upon a theorem of Degrijse concerning subadditivity of the F-cohomological dimension under group extensions.  ...  We prove that for any discrete group G with finite F-cohomological dimension, the Gorenstein cohomological dimension equals the F-cohomological dimension.  ...  In general we have the following chain of inequalities. Gcd G ≤ Fcd G ≤ n G ≤ cd G We prove the following: Theorem 3.6] .  ... 
doi:10.1112/blms/bdu030 fatcat:vggx4jyrurhjxilzvhyq7gyyqm

Experiments on Supporting Interactive Proof Using Resolution [chapter]

Jia Meng, Lawrence C. Paulson
2004 Lecture Notes in Computer Science  
Interactive theorem provers can model complex systems, but require much effort to prove theorems.  ...  Resolution theorem provers are automatic and powerful, but they are designed to be used for very different applications.  ...  Research was funded by the epsrc grant GR/S57198/01 Automation for Interactive Proof.  ... 
doi:10.1007/978-3-540-25984-8_28 fatcat:cih6ysuuvvb6zj2jbemcqhz75a

FI-hyperhomology and ordered configuration spaces [article]

Jeremy Miller, Jennifer C. H. Wilson
2019 arXiv   pre-print
Our bounds on generation degree improve the best known stability slope by a factor of 5/2 in the most general case.  ...  Using a result of Gan and Li on FI-hyperhomology and a semi-simplicial resolution of configuration spaces due to Randal-Williams, we establish an improved representation stability stable range for configuration  ...  Randal-Williams proved the following [RW13, Section 9.4]. We now use Theorem 3.2 to prove the following. In this section, we prove the main theorem.  ... 
arXiv:1903.02722v2 fatcat:ywv66rfo2zdvzbebqslfc4rj7i

Butler groups of infinite rank

L Fuchs
1995 Journal of Pure and Applied Algebra  
In attacking these problems, a new approach is used by utilizing X0-prebalanced chains and relative balanced-projective resolutions introduced by Bican and Fuchs [S].  ...  One definition requires that all the balanced extensions of torsion groups by them are splitting, while the other stipulates that they admit continuous transfinite chains (with finite rank factors) of  ...  If H is a &group, then by Corollary 2.4 G admits an K,,-prebalanced chain, so by Theorem 4.1 G is a B,-group.  ... 
doi:10.1016/0022-4049(94)00016-c fatcat:l7ue66denjbhvne2pzqjwwyccm

The projective dimension of valuated vector spaces

Paul Hill, Errin White
1982 Journal of Algebra  
More precisely, we prove that proj. dim.(V) < n if and only if V is the union of a smooth ascending chain of EC,_,-separable subspaces, 0 = V" c V, G ... E V, L ... such that dim(V,+ ,/V,) ,< p(,.  ...  After it is obtained, we are able to prove the existence of valuated vector spaces having projective dimension exactly n for each positive integer n.  ...  The backward indexing in (3.1) will prove more convenient for proofs of theorems that are established by induction on n.  ... 
doi:10.1016/0021-8693(82)90031-x fatcat:rzlzpbk2yzgjhfzy5nqg5eo5dq

Multiplicative structure in equivariant cohomology [article]

Kathryn Hess
2011 arXiv   pre-print
We introduce the notion of a strongly homotopy-comultiplicative resolution of a module coalgebra over a chain Hopf algebra, which we apply to proving a comultiplicative enrichment of a well-known theorem  ...  The importance of our enriched version of Moore's theorem lies in its application to the construction of useful cochain algebra models for computing multiplicative structure in equivariant cohomology.  ...  In particular, if ϕ ′ is a DCSH-resolution of N ′ , then ω is a DCSH-resolution of N over H. The proof of Theorem 3.4 The following technical lemma from [6] is the key to proving Theorem 3.4.  ... 
arXiv:1011.6092v2 fatcat:ki2y2tgo7bakxdgpabquvle4pq

Butler groups of infinite rank

L. Fuchs
1995 Journal of Pure and Applied Algebra  
In attacking these problems, a new approach is used by utilizing X0-prebalanced chains and relative balanced-projective resolutions introduced by Bican and Fuchs [S].  ...  One definition requires that all the balanced extensions of torsion groups by them are splitting, while the other stipulates that they admit continuous transfinite chains (with finite rank factors) of  ...  If H is a &group, then by Corollary 2.4 G admits an K,,-prebalanced chain, so by Theorem 4.1 G is a B,-group.  ... 
doi:10.1016/0022-4049(95)90015-2 fatcat:ftt752juyffnxmhi2gxmlryn3y

Relative measure homology and continuous bounded cohomology of topological pairs [article]

Roberto Frigerio, Cristina Pagliantini
2011 arXiv   pre-print
Zastrow and Hansen independently proved that there exists a canonical isomorphism between measure homology and singular homology (on the category of CW-complexes), and it was then shown by Loeh that, in  ...  We prove that relative singular homology and relative measure homology are isometrically isomorphic for a wide class of topological pairs.  ...  In the absolute case, i.e. when W = ∅, Theorem 1.7 is proved in [Fri11, Theorem 1.2].  ... 
arXiv:1105.4851v1 fatcat:bz3h4stie5hz3gvcushgwtbugy
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