Global Numerical Constraints on Trees

We introduce a logical foundation to reason on tree structures with constraints on the number of node occurrences. Related formalisms are limited to express occurrence constraints on particular tree regions, as for instance the children of a given node. By contrast, the logic introduced in the present work can concisely express numerical bounds on any region, descendants or ancestors for instance. We prove that the logic is decidable in single exponential time even if the numerical constraints are in binary form. We also illustrate the usage of the logic in the description of numerical constraints on multi-directional path queries on XML documents. Furthermore, numerical restrictions on regular languages (XML schemas) can also be concisely described by the logic. This implies a characterization of decidable counting extensions of XPath queries and XML schemas. Moreover, as the logic is closed under negation, it can thus be used as an optimal reasoning framework for testing emptiness, containment and equivalence

Fidel Semantics for Propositional and First-Order Version of the Logic of CG’3

Paraconsistent extensions of 3-valued Gödel logic are studied as tools for knowledge representation and nonmonotonic reasoning. Particularly, Osorio and his collaborators showed that some of these logics can be used to express interesting nonmonotonic semantics. CG’3 is one of these 3-valued logics. In this paper, we introduce Fidel semantics for a certain calculus of CG’3 by means of Fidel structures, named CG’3-structures. These structures are constructed from enriched Boolean algebras with a special family of sets. Moreover, we also show that the most basic CG’3-structures coincide with da Costa–Alves’ bi-valuation semantics; this connection is displayed through a Representation Theorem for CG’3-structures. By contrast, we show that for other paraconsistent logics that allow us to present semantics through Fidel structures, this connection is not held. Finally, Fidel semantics for the first-order version of the logic of CG’3 are presented by means of adapting algebraic tools

Analysis of Academic Achievement in Higher-Middle Education in Mexico through Data Clustering Methods

In recent years, there is a natural need to look for new ways to analyze and process data from different sources. One of these ways is through data analysis methods. Thus, given the importance of making academic diagnoses, this paper presents the academic achievement analysis, in Language and Communication and Mathematics, of students from autonomous, public and private schools of Higher-Middle Education in Mexico through data analysis methods. Data analyzed were registers of the National Plan for the Evaluation of Learning, which puts into operation the National Institute for the Evaluation of Education in coordination with the Secretariat of Public Education, Mexico. A variety of academic achievements was observed, highlighting Insufficient and Elementary in the evaluated population, while a small number reached acceptable achievements, that is, Satisfactory and Outstanding. This contrasts a notable difference between the levels reached by students, which leads them to delay or stop their university studies because they obtain a completion certificate of studies without having the necessary knowledge to pass the entrance examination in the universities

Author manuscript, published in "22nd International Joint Conference on Artificial Intelligence IJCAI'2011 (2011)" Query Reasoning on Trees with Types, Interleaving, and Counting

A major challenge of query language design is the combination of expressivity with effective static analyses such as query containment. In the setting of XML, documents are seen as finite trees, whose structure may additionally be constrained by type constraints such as those described by an XML schema. We consider the problem of query containment in the presence of type constraints for a class of regular path queries extended with counting and interleaving operators. The counting operator restricts the number of occurrences of children nodes satisfying a given logical property. The interleaving operator provides a succinct notation for describing the absence of order between nodes satisfying a logical property. We provide a logic-based framework supporting these operators, which can be used to solve common query reasoning problems such as satisfiability and containment of queries in exponential time.

Counting in Trees along Multidirectional Regular Paths

We propose a tree logic capable of expressing simple cardinality constraints on the number of nodes selected by an arbitrarily deep regular path with backward navigation. Specifically, a sublogic of the alternation-free µ−calculus with converse for finite trees is extended with a counting operator in order to reason on the cardinality of node sets. Also, we developed a bottom-up tableau-based satisfiability-checking algorithm, which resulted to have the same complexity than the logic without the counting operator: a simple exponential in the size of a formula. This result can be seen as an extension of the so-called graded-modalities introduced in [18], which allows counting constraints only on immediate successors, with conditions on the number of nodes accessible by an arbitrary recursive and multidirectional path. This work generalizes the optimal complexity bound: 2 O(n) where n is the length of the formula, shown in [11], for satisfiability of the logic extended with such counting constraints. Finally, we identify a decidable XPath fragment featuring cardinality constraints on paths with upward/downward recursive navigation, in the presence of XML types

Towards a Reasoning Model for Context-aware Systems: Modal Logic and the Tree Model Property

Abstract. Modal logics forms a family of formalisms widely used as reasoning frameworks in diverse areas of computer science. Description logics and their application to the web semantic is a notable example. Also, description logics have been recently used as a reasoning model for context-aware systems. Most reasoning algorithms for modal (description) logics are based on tableau constructions. In this work, we propose a reasoning (satisfiability) algorithm for the multi-modal Km with converse. The algorithm is based on the finite tree model property and a Fischer-Ladner construction. We show the algorithm is sound and complete, and we provide the corresponding complexity analysis. We also present some exploratory results of a preliminary implementation of the algorithm