Machines must be wrong

Making mistakes is an intrinsic human feature. But far to be an unwelcome feature, it is useful. For instance it bears us to learn, to review our beliefs and to support our decisions among others. This capability of using mistakes in our reasonings is already represented by Logic by means of the inference rule of “reduction ad absurdum”, which can be seen as a “supervised kind of mistake”. However in Computer Sciences, apart from the theoretical tools of “reductio ad absurdum” and methods obtained from it (as SLD resolution [1]), contradictions and mistakes are considered features that must be avoided. In some situations this behavior is understandable (e.g. the control of a train or a medical device) but in others, it represents a considerable limitation (e.g. in learning or optimization). Thus, considering knowledge systems involved in wrong information is not only an option for the scientific community, but a necessity. In this talk we explain how wrongness can be represented as a fuzzy notion and why con- tradictory information must be considered as an important piece of information nowadays. Moreover, the consideration of inconsistent knowledge systems is motivated to show how we can retrieve informations from wrongness. We refer to readers interested in more information to [2, 3].Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

On the Use of F-transform on the Reduction of Concept Lattices

In this paper, we show that F-transform can be used to re- duce relational databases. Subsequently, we show that the respective concept lattice is reduced significantly as well. Moreover, we present a clarifying example of the procedure.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. The research was supported by the European Regional Development Fund by projects (CZ.1.05/1.1.00/02.0070) and (TIN12-39353- C04-04)

Toward the use of the contraposition law in multi-adjoint lattices

A study of the contraposition rule in fuzzy logic by means of adjoint triples.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Scalar field dynamics in a BTZ background with generic boundary conditions

The revisit the dynamics of a massive scalar field in a BTZ background taking into account the lack of global hyperbolicity of the spacetime. We approach this issue using the strategy of Ishibashi and Wald which finds a unique smooth solution as the causal evolution of initial data, each possible evolution corresponding to a positive self-adjoint extension of certain operator in a Hilbert space on the initial surface. Moreover, solutions obtained this way are the most general ones satisfying a few physically-sensible requirements. This procedure is intimately related to the choice of boundary conditions and the existence of bound states. We find that the scalar field dynamics in the (effective) mass window −3/4≤m2eℓ2<0 can be well-defined within a one-parametric family of distinct boundary conditions (−3/4 being the conformally-coupled case), while for m2eℓ2≥0 the boundary condition is unique (only one self-adjoint extension is possible). It is argued that there is no sensible evolution possible for m2eℓ2<−1, and also shown that in the range m2eℓ2∈[−1,−3/4) there is a U(1) family of allowed boundary conditions, however, the positivity of the self-adjoint extensions is only motivated but not proven. We focus mainly in describing the dynamics of such evolutions given the initial data and all possible boundary conditions, and in particular we show the energy is always positive and conserved.Fil: Garbarz, Alan Nicolás. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: La Madrid, Joan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Leston, Mauricio. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentin

Definición de particiones difusas condicionadas usando transformadas difusas

Las particiones difusas pueden definirse de diferentes formas, pero casi siempre, la definición se efectúa atendiendo a las características generales de la totalidad del universo. En este trabajo se presenta un método para definir particiones difusas condicionadas a la satisfacción de cierto atributo difuso. En concreto, se muestra cómo definir diferentes particiones difusas atendiendo a las características de diferentes subconjuntos difusos del universo

Kitainik axioms do not characterize the class of inclusion measures based on contrapositive fuzzy implications

In this short communication, we refute the conjecture by Fodor and Yager from [5] that the class of inclusion measures proposed by Kitainik coincides with that of inclusion measures based on contrapositive fuzzy implications. In particular, we show that the conjecture only holds when the considered universe of discourse is finite.The research reported in this paper was conducted with the financial support of the Odysseus programme of the Research Foundation – Flanders (FWO) (grant number G0H9118N) and partially supported by the Spanish Ministry of Science, Innovation and Universities (MCIU), State Agency of Research (AEI), Junta de Andalucía (JA), Universidad de Málaga (UMA) and European Regional Development Fund (FEDER) through the projects PGC2018-095869-B- I00 (MCIU/AEI/FEDER) and UMA2018-FEDERJA-001 (JA/UMA/FEDER). Funding for open access charge: Universidad de Málaga / CBU

Approaching the square of opposition in terms of the f-indexes of inclusion and contradiction

We continue our research line on the analysis of the properties of the f-indexes of inclusion and contradiction; in this paper, specifically, we show that both notions can be related by means of the, conveniently reformulated, Aristotelian square of opposition. We firstly show that the extreme cases of the f-indexes of inclusion and contradiction coincide with the vertexes of the Aristotelian square of opposition in the crisp case; then, we allocate the rest of f-indexes in the diagonals of the extreme cases and we prove that the Contradiction, Contrariety, Subcontrariety, Subalternation and Superalternation relations also hold between the f-indexes of inclusion and contradiction.Funding for open Access charge: Universidad de Málaga / CBUA. Partially supported by the Ministry of Science, Innovation, and Universities (MCIU), the State Agency of Research (AEI) and the European Social Fund (FEDER) through the research projects PGC2018-095869-B-I00 (MCIU/AEI/FEDER, UE) and VALID (PID2022-140630NB-I00 MCIN/AEI/10.13039/501100011033), and by Junta de Andalucía, Universidad de Málaga and the European Social Fund (FEDER) through the research project UMA2018-FEDERJA-001

Rough sets based on Galois connections

Rough set theory is an important tool to extract knowledge from relational databases. The original definitions of approximation operators are based on an indiscernibility relation, which is an equivalence one. Lately. different papers have motivated the possibility of considering arbitrary relations. Nevertheless, when those are taken into account, the original definitions given by Pawlak may lose fundamental properties. This paper proposes a possible solution to the arising problems by presenting an alternative definition of approximation operators based on the closure and interior operators obtained from an isotone Galois connection. We prove that the proposed definition satisfies interesting properties and that it also improves object classification tasks

Generalized antisymmetric filters for edge detection

A large number of filters has been proposed to compute local gradients in grayscale images, usually having as goal the adequate characterization of edges. A significant portion of such filters are antisymmetric with respect to the origin. In this work we propose to generalize those filters by incorporating an explicit evaluation of the tonal difference. More specifically, we propose to apply restricted dissimilarity functions to appropriately measure the tonal differences. We present the mathematical developments, as well as quantitative experiments that indicate that our proposal offers a clear option to improve the performance of classical edge detection filters