We present variant of simplification logic for reasoning with if-then dependencies that arise in ... more We present variant of simplification logic for reasoning with if-then dependencies that arise in formal concept analysis of data with graded attributes. The dependencies and the proposed logic are parameterized by systems of isotone Galois connections which allows us to handle a large family of possible interpretations of data dependencies. We describe semantics of the rules, axiomatic system of the logic, and prove its soundness and completeness.
Closure system is a fundamental concept appearing in several areas such as databases, formal conc... more Closure system is a fundamental concept appearing in several areas such as databases, formal concept analysis, artificial intelligence, etc. It is well-known that there exists a connection between a closure operator on a set and the lattice of its closed sets. Furthermore, the closure system can be replaced by a set of implications but this set has usually a lot of redundancy inducing non desired properties. In the literature, there is a common interest in the search of the mini- mality of a set of implications because of the importance of bases. The well-known Duquenne-Guigues basis satisfies this minimality condition. However, several authors emphasize the relevance of the optimality in order to reduce the size of implications in the basis. In addition to this, some bases have been defined to improve the computation of closures relying on the directness property. The eciency of computation with the direct basis is achieved due to the fact that the closure is computed in one traver...
En este articulo se presenta una experiencia pedagogica alrededor del tema de las ecuaciones dife... more En este articulo se presenta una experiencia pedagogica alrededor del tema de las ecuaciones diferenciales exactas y no exactas con factor integrante, llamando la atencion sobre procesos de solucion que normalmente no se exploran y que podrian enriquecer la apropiacion de conceptos en este tema en ocasiones problematico para los estudiantes de cursos regulares de ecuaciones diferenciales ordinarias.
We present unified predictions for the crack onset strain, evolution of crack density, and change... more We present unified predictions for the crack onset strain, evolution of crack density, and changes in electrical resistance in indium tin oxide/polymer thin films under tensile loading. We propose a damage mechanics model to quantify and predict such changes as an alternative to fracture mechanics formulations. Our predictions are obtained by assuming that there are no flaws at the onset of loading as opposed to the assumptions of fracture mechanics approaches. We calibrate the crack onset strain and the damage model based on experimental data reported in the literature. We predict crack density and changes in electrical resistance as a function of the damage induced in the films. We implement our model in the commercial finite element software ABAQUS using a user subroutine UMAT. We obtain fair to good agreement with experiments.
Due to its solid mathematical foundations, Formal Concept Analysis (FCA) has become an emergent t... more Due to its solid mathematical foundations, Formal Concept Analysis (FCA) has become an emergent topic in the area of data analysis and knowledge discovering. Information is represented in a binary table defining a relation between a set o f objects and a set of attributes—the formal context. The knowledge extracted from the formal context allows to identify useful patterns in data in different forms. One very useful knowledge representation in FCA are implications among attributes which are validated over the objects. The most outstanding feature of implications is that they can be managed by means of inference systems. Equivalent sets of implications can be obtained using different logic-based t ransformations. The aim of these transformations is to turn the original set of implications into an equivalent one fulfilling some desir ed properties. Among them, the directness and optimality are very popular targets because getting a direct-optimal basis ensures tha t the closure of a set of attributes may be computed with lower cost (time and resources). In this work, we introduce a new method to compute the direct-optimal basis which improves the existing ones. The new method reduces the input in a first stage and is guided by the id ea of limiting the growth of the intermediate sets of implications as a way to improve the performance. We illustrate the good features of the new method with both a detailed example and by experimental evaluation.
Advances in Intelligent Systems and Computing, 2014
A deterministic tableau decision procedure via reductions, TK, for verification of validity of mo... more A deterministic tableau decision procedure via reductions, TK, for verification of validity of modal logic K is presented. The system TK is a deterministic tableau decision procedure defined in the original methodology of tableau systems which does not use any additional kind of branching (apart from the required branching for disjunctions) nor any external techniques such as backtracking, backjumping, loop-checking, etc. A nice feature of system TK is its uniqueness; given a formula it generates in a deterministic way only one tableau tree for it.
We present variant of simplification logic for reasoning with if-then dependencies that arise in ... more We present variant of simplification logic for reasoning with if-then dependencies that arise in formal concept analysis of data with graded attributes. The dependencies and the proposed logic are parameterized by systems of isotone Galois connections which allows us to handle a large family of possible interpretations of data dependencies. We describe semantics of the rules, axiomatic system of the logic, and prove its soundness and completeness.
Closure system is a fundamental concept appearing in several areas such as databases, formal conc... more Closure system is a fundamental concept appearing in several areas such as databases, formal concept analysis, artificial intelligence, etc. It is well-known that there exists a connection between a closure operator on a set and the lattice of its closed sets. Furthermore, the closure system can be replaced by a set of implications but this set has usually a lot of redundancy inducing non desired properties. In the literature, there is a common interest in the search of the mini- mality of a set of implications because of the importance of bases. The well-known Duquenne-Guigues basis satisfies this minimality condition. However, several authors emphasize the relevance of the optimality in order to reduce the size of implications in the basis. In addition to this, some bases have been defined to improve the computation of closures relying on the directness property. The eciency of computation with the direct basis is achieved due to the fact that the closure is computed in one traver...
En este articulo se presenta una experiencia pedagogica alrededor del tema de las ecuaciones dife... more En este articulo se presenta una experiencia pedagogica alrededor del tema de las ecuaciones diferenciales exactas y no exactas con factor integrante, llamando la atencion sobre procesos de solucion que normalmente no se exploran y que podrian enriquecer la apropiacion de conceptos en este tema en ocasiones problematico para los estudiantes de cursos regulares de ecuaciones diferenciales ordinarias.
We present unified predictions for the crack onset strain, evolution of crack density, and change... more We present unified predictions for the crack onset strain, evolution of crack density, and changes in electrical resistance in indium tin oxide/polymer thin films under tensile loading. We propose a damage mechanics model to quantify and predict such changes as an alternative to fracture mechanics formulations. Our predictions are obtained by assuming that there are no flaws at the onset of loading as opposed to the assumptions of fracture mechanics approaches. We calibrate the crack onset strain and the damage model based on experimental data reported in the literature. We predict crack density and changes in electrical resistance as a function of the damage induced in the films. We implement our model in the commercial finite element software ABAQUS using a user subroutine UMAT. We obtain fair to good agreement with experiments.
Due to its solid mathematical foundations, Formal Concept Analysis (FCA) has become an emergent t... more Due to its solid mathematical foundations, Formal Concept Analysis (FCA) has become an emergent topic in the area of data analysis and knowledge discovering. Information is represented in a binary table defining a relation between a set o f objects and a set of attributes—the formal context. The knowledge extracted from the formal context allows to identify useful patterns in data in different forms. One very useful knowledge representation in FCA are implications among attributes which are validated over the objects. The most outstanding feature of implications is that they can be managed by means of inference systems. Equivalent sets of implications can be obtained using different logic-based t ransformations. The aim of these transformations is to turn the original set of implications into an equivalent one fulfilling some desir ed properties. Among them, the directness and optimality are very popular targets because getting a direct-optimal basis ensures tha t the closure of a set of attributes may be computed with lower cost (time and resources). In this work, we introduce a new method to compute the direct-optimal basis which improves the existing ones. The new method reduces the input in a first stage and is guided by the id ea of limiting the growth of the intermediate sets of implications as a way to improve the performance. We illustrate the good features of the new method with both a detailed example and by experimental evaluation.
Advances in Intelligent Systems and Computing, 2014
A deterministic tableau decision procedure via reductions, TK, for verification of validity of mo... more A deterministic tableau decision procedure via reductions, TK, for verification of validity of modal logic K is presented. The system TK is a deterministic tableau decision procedure defined in the original methodology of tableau systems which does not use any additional kind of branching (apart from the required branching for disjunctions) nor any external techniques such as backtracking, backjumping, loop-checking, etc. A nice feature of system TK is its uniqueness; given a formula it generates in a deterministic way only one tableau tree for it.
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Papers by Angel Mora