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Theorem proving by chain resolution

1998
*
Theoretical Computer Science
*

Starting from the intuition given

doi:10.1016/s0304-3975(97)00128-x
fatcat:smbgp3pkvrfzjcehs7e4cfhiva
*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. ...##
###
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

2007
*
International Mathematical Forum
*

The aim of this paper is to

doi:10.12988/imf.2007.07281
fatcat:ald64gz4yfgrpkspqs6xep3rvi
*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. ...##
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Regular projective resolutions OF SEMIMODULES

2017
*
HUE UNIVERSITY JOURNAL OF SCIENCE NATURAL SCIENCE
*

In this paper, we present an approach version of semimodule homologies

doi:10.26459/hueuni-jns.v126i1b.4272
fatcat:fgu3kwfv6jez7obd6lzx5bfr4m
*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). ...##
###
GORENSTEIN AND Sr PATH IDEALS OF CYCLES

2014
*
Glasgow Mathematical Journal
*

Finally, we

doi:10.1017/s0017089514000111
fatcat:pcysbxzfszfahiqzjoctpld42a
*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). ...##
###
Tight closure in F-rational rings

1994
*
Nagoya mathematical journal
*

We are now ready to

doi:10.1017/s0027763000004943
fatcat:yw4oz67lvbgmja4apwnzm4fyim
*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]. ...##
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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

2014
*
Bulletin of the London Mathematical Society
*

As a corollary we improve upon a

doi:10.1112/blms/bdu030
fatcat:vggx4jyrurhjxilzvhyq7gyyqm
*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] . ...##
###
Experiments on Supporting Interactive Proof Using Resolution
[chapter]

2004
*
Lecture Notes in Computer Science
*

Interactive

doi:10.1007/978-3-540-25984-8_28
fatcat:cih6ysuuvvb6zj2jbemcqhz75a
*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. ...##
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FI-hyperhomology and ordered configuration spaces
[article]

2019
*
arXiv
*
pre-print

Our bounds on generation degree improve the best known stability slope

arXiv:1903.02722v2
fatcat:ywv66rfo2zdvzbebqslfc4rj7i
*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*. ...##
###
Butler groups of infinite rank

1995
*
Journal of Pure and Applied Algebra
*

In attacking these problems, a new approach is used

doi:10.1016/0022-4049(94)00016-c
fatcat:l7ue66denjbhvne2pzqjwwyccm
*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. ...##
###
The projective dimension of valuated vector spaces

1982
*
Journal of Algebra
*

More precisely, we

doi:10.1016/0021-8693(82)90031-x
fatcat:rzlzpbk2yzgjhfzy5nqg5eo5dq
*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. ...##
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Multiplicative structure in equivariant cohomology
[article]

2011
*
arXiv
*
pre-print

We introduce the notion of a strongly homotopy-comultiplicative

arXiv:1011.6092v2
fatcat:ki2y2tgo7bakxdgpabquvle4pq
*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. ...##
###
Butler groups of infinite rank

1995
*
Journal of Pure and Applied Algebra
*

In attacking these problems, a new approach is used

doi:10.1016/0022-4049(95)90015-2
fatcat:ftt752juyffnxmhi2gxmlryn3y
*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. ...##
###
Relative measure homology and continuous bounded cohomology of topological pairs
[article]

2011
*
arXiv
*
pre-print

Zastrow and Hansen independently

arXiv:1105.4851v1
fatcat:bz3h4stie5hz3gvcushgwtbugy
*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]. ...
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