Advances on elementary equivalence in model theory of fuzzy logics

Dellunde and Garca-Cerda~na are supported by EdeTRI (TIN2012-39348-C02-01); Garca-Cerda~na is also supported by the Spanish MICINN project MTM 201125745 and the grant 2009SGR 1433 from the Generalitat de Catalunya;Noguera is supported by the project GA13-14654S of the Czech Science Foundation and by the FP7-PEOPLE-2009-IRSES project MaToMUVI (PIRSES-GA-2009-247584)Peer Reviewe

Back-and-forth systems for fuzzy first-order models

This paper continues the study of model theory for fuzzy logics by addressing the fundamental issue of classifying models according to their first-order theory. Three different definitions of elementary equivalence for fuzzy first-order models are introduced and separated by suitable counterexamples. We propose several back-and-forth conditions, based both on classical two-sorted structures and on non-classical structures, that are useful to obtain elementary equivalence in particular cases as we illustrate with several example

On similarity in fuzzy description logics

This paper is a contribution to the study of similarity relations between objects represented as attribute-value pairs in Fuzzy Description Logics . For this purpose we use concrete domains in the fuzzy description logic IALCEF(D)IALCEF(D) associated either with a left-continuous or with a finite t-norm. We propose to expand this fuzzy description logic by adding a Similarity Box (SBox) including axioms expressing properties of fuzzy equalities. We also define a global similarity between objects from similarities between the values of each object attribute (local similarities) and we prove that the global similarity defined using a t-norm inherits the usual properties of the local similarities (reflexivity, symmetry or transitivity). We also prove a result relative to global similarities expressing that, in the context of the logic MTL∀, similar objects have similar properties, being these properties expressed by predicate formulas evaluated in these object

A logical study of local and global graded similarities

In this work we study the relationship between global and local similarities in the graded framework of fuzzy class theory (FCT), in which there already exists a graded notion of similarity. In FCT we can express the fact that a fuzzy relation is reflexive, symmetric, or transitive up to a certain degree, and similarity is defined as a first-order sentence, which is the fusion of three sentences corresponding to the graded notions of reflexivity, symmetry, and transitivity. This allows us to speak in a natural way of the degree of similarity of a relation. We consider global similarities defined from local similarities using t-norms as aggregation operators, and we obtain some results in the framework of FCT that, adequately interpreted, allow us to say that when we take a t-norm as an aggregation operator, the properties of reflexivity, symmetry, and transitivity of fuzzy binary relations are inherited from the local to the global level, and that the global similarity is a congruence if some of the local similarities are congruence

Discovering abstentionist profiles in 2015 Catalan elections

One of the main democratic act is to elect representers for a country Government. Voters have to choose the representers of political parties that best fit their interests. However, it is also possible to abstain, i.e., to give up choosing the representers. Lastly, the percentage of abstention has increased in many democracies and, consequently, many studies have been carried out in order to discover the causes of the abstention. Causes such as alienation and indifference for politics have been found and characterized, but it is not clear who is abstaining. Some studies in specific countries have related aspects such age, education or wealth with voting. Nevertheless, all these studies are based on questionnaires that could not be completely reliable. In the present paper we use decision trees, an artificial intelligence technique, to extract patterns that characterize the profile of abstentionists. Differently from other studies, we used a data base elaborated from public data bases with both socio-economic and electoral data. In particular, we focused our study in Catalonia and the electoral results to the Catalan Parliament held in 2015. We also propose the use of decision trees to analyze the database and to extract patterns to characterize different profiles of abstentionist people.Peer reviewe

Decision Trees as a Tool for Data Analysis. Elections in Barcelona: A Case Study

Decision trees are inductive learning methods that construct a domain model easy to understand from domain experts. For this reason, we claim that the description of a given data set using decision trees is an easy way to both discover patterns and compare the classes that form the domain at hand. It is also an easy way to compare different models of the same domain. In the current paper, we have used decision trees to analyze the vote of the Barcelona citizens in several electoral convocations. Thus, the comparison of the models we have obtained has let us know that the percentage of people with a university degree is the most important aspect to separe the neighbourhoods of Barcelona according to the most voted party in a neighbourhood. We also show that in some neighbourhoods has always won the same party independently of the kind of convocation (local or general).This research is funded by the project RPREF (CSIC Intramural 201650E044); and the grant 2014-SGR-118 from the Generalitat de Catalunya

Axiomatizing monoidal logic: A correction

The propositional monoidal logic ML of U. Höhle, determined through an algebraic semantics given by the class of all residuated lattices, was (claimed to be) reaxiomatized in the recent monograph [5]. We show that this reaxiomatization is defective and prove the independence of one of U. Höhle's original axioms from the axioms in [5]. Additionally the axiomatization in [5] is completed.The third author is partially supported by Catalan grant 2000FI00100 and by Spanish grant 2000SGR00007.Peer Reviewe

Local and Global Similarities in Fuzzy Class Theory

Similarity is a central issue in many topics from psychology to artificial intelligence. In the present paper we want to contribute to the study of the similarity relation between objects represented as attribute-value pairs in the logical context. Following the idea that similarity is a phenomena essentially fuzzy, we introduce fuzzy similarities and prove some logical properties in the framework of Fuzzy Class Theory based on the logic MTLΛ. We prove that the global similarity inherits the usual properties of the local similarities (reflexivity, symmetry, transitivity). We also show that similar objects have similar properties, being these properties expressed by MTLΛ ∀ formulas evaluated in these objects