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On the Commutative Diagrams Among Galois Connections Involved in Closure Structures
In previous works we proved that fuzzy closure structures such as closure systems, fuzzy closure systems, fuzzy closure operators and fuzzy closure...
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Galois theory for analogical classifiers
Analogical proportions are 4-ary relations that read “A is to B as C is to D”. Recent works have highlighted the fact that such relations can support...
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Transport via Partial Galois Connections and Equivalences
Multiple types can represent the same concept. For example, lists and trees can both represent sets. Unfortunately, this easily leads to incomplete...
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Domain Precision in Galois Connection-Less Abstract Interpretation
The ever growing pervasiveness of software systems in modern days technology results in an increasing need of software/program correctness proofs....
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The algebraic structure of the densification and the sparsification tasks for CSPs
The tractability of certain CSPs for dense or sparse instances is known from the 90s. Recently, the densification and the sparsification of CSPs were...
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Study on the Necessity Operator to Factorize Formal Contexts in a Multi-adjoint Framework
Dubois and Prade have already shown that the necessity operator is helpful in the decomposition of Boolean data tables into independent sub-tables....
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A modal approach to conscious social agents
An agent’s awareness has previously been modelled as a modal operator in such a way that awareness can be iterated, and consciousness formalised as...
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Right Adjoint Algebras Versus Operator Left Residuated Posets
Algebraic structures are essential in fuzzy frameworks such as fuzzy formal concept analysis and fuzzy rough set theory. This paper studies two...
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Galois Connections for Patterns: An Algebra of Labelled Graphs
A pattern is a generic instance of a binary constraint satisfaction problem (CSP) in which the compatibility of certain pairs of variable-value...
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Formal Choreographic Languages
We introduce a meta-model based on formal languages, dubbed formal choreographic languages, to study message-passing systems. Our main motivation is...
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Polynomial Analysis of Modular Arithmetic
The modular polynomial abstract domain, MPAD, is proposed, whose invariants are systems of polynomial equations that hold modulo a power of 2. Its...
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Solving decomposable sparse systems
Améndola et al. proposed a method for solving systems of polynomial equations lying in a family which exploits a recursive decomposition into smaller...
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On Categories of L-Fuzzifying Approximation Spaces, L-Fuzzifying Pretopological Spaces and L-Fuzzifying Closure Spaces
This paper investigates the essential connections among several categories with a weaker structure than that of L-fuzzifying topology, namely...
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A New Kind of Implication to Reason with Unknown Information
Formal Concept Analysis (FCA) extracts knowledge from an object-attribute relation. In the classical case, it focuses on positive information, i.e....
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A Relational Extension of Galois Connections
In this paper, we focus on a twofold relational generalization of the notion of Galois connection. It is twofold because it is defined between sets...
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Graph-FCA Meets Pattern Structures
A number of extensions have been proposed for Formal Concept Analysis (FCA). Among them, Pattern Structures (PS) bring complex descriptions on...
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Representative Set of Objects in Rough Sets Based on Galois Connections
This paper introduces a novel definition, called representative set of objects of a decision class, in the framework of decision systems based on...
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Attribute Reduction Using Functional Dependency Relations in Rough Set Theory
This paper presents some functional dependency relations defined on the attribute set of an information system. We establish some basic relationships...
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An energy efficient encryption technique for the Internet of Things sensor nodes
Securing data at the back end in Internet of Things (IoT) applications, such as a cloud server, is easy due to the ample computational resources at...
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Symbolic dynamics and rotation symmetric Boolean functions
We identify the weights w t ( f n ) of a family { f n } of rotation symmetric Boolean functions with the cardinalities of the sets of n -periodic points of a...
