A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Dualization in lattices given by implicational bases
[article]

2020
*
arXiv
*
pre-print

It was recently proved that the

arXiv:1901.07503v5
fatcat:wm7iya77hjdm5mrc4nwd36d4e4
*dualization**in**lattices**given**by**implicational**bases*is impossible*in*output-polynomial time unless P=NP. ...*In*this paper, we~show that this result holds even when the premises*in*the*implicational**base*are of size at most two. ... The*dualization**in**lattices**given**by**implicational**bases*is impossible*in*output-polynomial time unless P=NP, even for*implicational**bases*of dimension two. ...##
###
Dualization in Lattices Given by Ordered Sets of Irreducibles
[article]

2015
*
arXiv
*
pre-print

*In*contrast to usual

*dualization*setting, where a

*lattice*is

*given*

*by*the ordered set of its elements,

*dualization*

*in*this case is shown to be impossible

*in*output polynomial time unless P = NP. ...

*In*this paper we consider finite

*lattices*

*given*

*by*ordered sets of their meet and join irreducibles (i.e., as a concept

*lattice*of a formal context). ... The second author was supported

*by*the Basic Research Program of the National Research University Higher School of Economics (Moscow, Russia) and Russian Foundation for Basic Research. ...

##
###
Translating between the representations of a ranked convex geometry
[article]

2021
*
arXiv
*
pre-print

It is well known that every closure system can be represented

arXiv:1907.09433v2
fatcat:zshldvesr5d6hjoyvdf4dpxb7m
*by*an*implicational**base*, or*by*the set of its meet-irreducible elements. ... Quite surprisingly, we show that the problem*in*this context is already harder than the*dualization**in*distributive*lattices*, a generalization of the well-known hypergraph*dualization*problem for which ... Let us first define the*dualization*problem*in**lattices**given**by**implicational**bases*. ...##
###
Discovery of the D-basis in binary tables based on hypergraph dualization

2017
*
Theoretical Computer Science
*

At the core of the method are the D-relation defined

doi:10.1016/j.tcs.2015.11.031
fatcat:eh2sjwcy5vbmrkuips5vha5mk4
*in*the*lattice*theory framework, and the hypergraph*dualization*algorithm that allows us to effectively produce the set of transversals for a*given*... The latter algorithm, first developed*by*specialists from Rutgers Center for Operations Research, has already found numerous applications*in*solving optimization problems*in*data*base*theory, artificial ... The results of this paper were prompted*by*the discussion of the hypergraph*dualization*algorithm with E. Boros and V. Gurvich, at the RUT-COR seminar during the first author's visit*in*2011. ...##
###
Complement-Topoi and Dual Intuitionistic Logic

2010
*
The Australasian Journal of Logic
*

Mortensen studies dual intuitionistic logic

doi:10.26686/ajl.v9i0.1819
fatcat:x3xmpxk5dfeepnhrbsntoyatda
*by**dualizing*topos internal logic, but he did not study a sequent calculus. ...*In*this paper I present a sequent calculus for complement-topos logic, which throws some light on the problem of giving a*dualization*for LJ. ...*In*order to*dualize*a*given*formula a A b, change the antecedent*by*the consequent and vice versa and then replace A*by*−. ...##
###
On Dualization over Distributive Lattices
[article]

2022
*
arXiv
*
pre-print

As an application, we show that minimal infrequent closed sets of attributes

arXiv:2006.15337v3
fatcat:mcgsvasfsbezpkpiirselgqjoq
*in*a rational database, with respect to a*given**implication**base*of maximum premise size of one, can be enumerated*in*incremental ... and cover (*by*domination) the entire*lattice*. ...*Given*a database D, an*implication**base*Σ, and and an integer t, a maximal t-frequent closed set, is a set X ∈ C(Σ) maximal with the property that | supp D (X)| ≥ t. ...##
###
On the dualization in distributive lattices and related problems
[article]

2020
*
arXiv
*
pre-print

*In*this paper, we study the

*dualization*

*in*distributive

*lattices*, a generalization of the well-known hypergraph

*dualization*problem. ...

*In*this new framework, a poset on vertices is

*given*together with the input (hyper)graph, and minimal "ideal solutions" are to be generated. ...

*In*[DN19] , it was shown that this result holds even when the premises

*in*the

*implicational*

*base*(coding the

*lattice*) are of size at most two. ...

##
###
Dihypergraph Decomposition: Application to Closure System Representations

2020
*
European Conference on Artificial Intelligence
*

Among representations, dihypergraphs (or attribute

dblp:conf/ecai/VilminN20
fatcat:jmogxvplrvcfxc4zl4a42zz2iu
*implications*) and meet-irreducible elements (reduced context) are widely used*in*the literature. ... From this result, we deduce an algorithm which computes meet-irreducible elements*in*a divide-and-conquer way and puts the light on the major role of*dualization**in*closure systems. ...*In*this paper, we suppose that*implicational**bases*are*given*as directed hypergraphs. ...##
###
Computational aspects of monotone dualization: A brief survey

2008
*
Discrete Applied Mathematics
*

*Dualization*of a monotone Boolean function represented

*by*a conjunctive normal form (CNF) is a problem which,

*in*different disguise, is ubiquitous

*in*many areas including Computer Science, Artificial Intelligence ...

*In*this paper, we briefly survey computational results for this problem, where we focus on the famous paper

*by*Fredman and Khachiyan (J. ... Furthermore, all prime

*implicants*and prime

*implicates*of a monotone f are monotone, and it has a unique prime CNF, denoted CNF(f ), which is

*given*

*by*the conjunction of all its prime

*implicates*. ...

##
###
Dualizing Clones as Models of Lawvere Theories

2014
*
Electronical Notes in Theoretical Computer Science
*

be beneficial for the classical problem of studying the

doi:10.1016/j.entcs.2014.02.005
fatcat:d7eyy7ksevckhjt6sfajempv3m
*lattice*of clones on a*given*set. ...*In*this paper, we argue that the possibility of applying duality theory might be such a reason, and we support this claim*by*outlining how treating and*dualizing*clones as models of Lawvere theories can ... Vice versa, a Priestley space*dualizes*to the bounded distributive*lattice**given**by*its clopen increasing subsets. ...##
###
Disjunctive and conjunctive normal forms of pseudo-Boolean functions

2000
*
Discrete Applied Mathematics
*

*In*a similar way the concepts of conjunctive normal form,

*implicates*and prime

*implicates*, as well as the resolution method are examined

*in*the case of pseudo-Boolean functions. ? ... ), the concepts of

*implicants*and of prime

*implicants*are analyzed

*in*the pseudo-Boolean context, and a consensus-type method is presented for ÿnding all the prime

*implicants*of a pseudo-Boolean function ... Acknowledgements This work was partially supported

*by*NSF grant DMS-9806389 and ONR grant N00014-92-J-1375. ...

##
###
The Involutive Quantaloid of Completely Distributive Lattices
[article]

2020
*
arXiv
*
pre-print

If this is the case, then the dual tensor operation corresponds, via Raney's transforms, to composition

arXiv:1911.01085v3
fatcat:rk6ewzmn3jc7rlnb3ua6sdk7ui
*in*the (dual) quantale of meet-continuous endo-functions of L. ... Let sLatt be the category of sup-*lattices*and join-continuous functions and let cdLatt be the full subcategory of sLatt whose objects are the completely distributive*lattices*. ... Recalling that involutive quantale structures on a*given*quantale are determined*by*the cyclic*dualizing*elements and that complete chains are completely distributive, the following statement from the ...##
###
Dualizability and graph algebras

2000
*
Discrete Mathematics
*

We characterize the finite graph algebras which are

doi:10.1016/s0012-365x(99)00225-3
fatcat:aevgi4zhd5fatggww5p2cmes5y
*dualizable*. ... Indeed, a finite graph algebra is*dualizable*if and only if each connected component of the underlying graph is either complete or bipartite complete (or a single point). ... This method, which is used implicitly*in*Davey and Werner [9] to prove that the 2-element*implication*algebra is not*dualizable*and more plainly*in*the proof*by*Davey, Heindorf, and McKenzie of the Big ...##
###
Fake rings, fake modules, and duality

1977
*
Journal of Algebra
*

A duality theory for modules over a commutative ring is developed using

doi:10.1016/0021-8693(77)90233-2
fatcat:gz2nhberyfeqzko6doesa7gmtu
*lattice*modules. Using this duality theory several classical results for Noetherian modules are*dualized*to Artinian modules. ... F or a multiplicative*lattice*L, we define a fake L-module N to be a complete*lattice*N satisfying Our duality construction*given**in*Section 2 carries over to fake L-modules (where L is now a multiplicative ...*By*proving theorems about modules for the larger class of fake modules, we are able to*dualize*the results.*In*Section 2 we introduce fake modules and give our basic duality construction. ...##
###
Measuring the Implications of the D-Basis in Analysis of Data in Biomedical Studies
[chapter]

2015
*
Lecture Notes in Computer Science
*

This enables a ranking of all attributes,

doi:10.1007/978-3-319-19545-2_3
fatcat:meyn5g3qe5c4ziycbyd7aqutzu
*by*relevance parameter to the same fixed attribute, and, as a consequence, reveals the*implications*of the basis most relevant to this attribute. ... Each test case requires a specialized approach*in*converting the real-valued data into binary data and careful analysis of the transformed data*in*a multi-disciplinary environment of cross-field collaboration ... We received the permission of Takeaki Uno, from the National Institute of Informatics*in*Tokyo, to implement the call to his subroutine performing the hypergraph*dualization*, within the structure of our ...
« Previous

*Showing results 1 — 15 out of 1,867 results*