Decidability of the interval temporal logic ABBar over the natural numbers

In this paper, we focus our attention on the interval temporal logic of the Allen's relations "meets", "begins", and "begun by" (ABBar for short), interpreted over natural numbers. We first introduce the logic and we show that it is expressive enough to model distinctive interval properties,such as accomplishment conditions, to capture basic modalities of point-based temporal logic, such as the until operator, and to encode relevant metric constraints. Then, we prove that the satisfiability problem for ABBar over natural numbers is decidable by providing a small model theorem based on an original contraction method. Finally, we prove the EXPSPACE-completeness of the proble

Decidability and complexity of the fragments of the modal logic of Allen's relations over the rationals

Interval temporal logics provide a natural framework for temporal reasoning about interval structures over linearly ordered domains, where intervals are taken as first-class citizens. Their expressive power and computational behaviour mainly depend on two parameters: the set of modalities they feature and the linear orders over which they are interpreted. In this paper, we consider all fragments of Halpern and Shoham's interval temporal logic hs with a decidable satisfiability problem over the rationals, and we provide a complete classification of them in terms of their expressiveness and computational complexity by solving the last few open problems

Acta Informatica manuscript No. (will be inserted by the editor) A Complete Classification of the Expressiveness of Interval Logics of Allen’s Relations The General and the Dense Cases

Abstract Interval temporal logics take time intervals, instead of time instants, as their primitive temporal entities. One of the most studied interval temporal logics is Halpern and Shoham’s modal logic of time intervals HS, which associates a modal operator with each binary relation between intervals over a linear order (the so-called Allen’s interval relations). In this paper, we compare and classify the expressiveness of all fragments of HS on the class of all linear orders and on the subclass of all dense linear orders. For each of these classes, we identify a complete set of definabilities between HS modalities, valid in that class, thus obtaining a complete classification of the family of all 4096 fragments of HS with respect to their expressiveness. We show that on the class of all linear orders there are exactly 1347 expressively different fragments of HS, while on the class of dense linear orders there are exactly 966 such expressively different fragments

A general tableau method for propositional interval temporal logics: Theory and implementation

In this paper, we focus our attention on tableau methods for propositional interval temporal logics. These logics provide a natural framework for representing and reasoning about temporal properties in several areas of computer science. However, while various tableau methods have been developed for linear and branching time point-based temporal logics, not much work has been done on tableau methods for interval-based ones. We develop a general tableau method for Venema’s CDT logic interpreted over partial orders (BCDT+ for short). It combines features of the classical tableau method for first-order logic with those of explicit tableau methods for modal logics with constraint label management, and it can be easily tailored to most propositional interval temporal logics proposed in the literature. We prove its soundness and completeness, and we show how it has been implemented

Interpretable land cover classification with modal decision trees

ABSTRACTLand cover classification (LCC) refers to the task of classifying each pixel in satellite/aerial imagery by predicting a label carrying information about its nature. Despite the importance of having transparent, symbolic decision models, in the recent literature, LCC has been mainly approached with black-box functional models, that are able to leverage the spatial dimensions within the data. In this article, we argue that standard symbolic decision models can be extended to perform a form of spatial reasoning that is adequate for LCC. We propose a generalization of a classical decision tree learning model, based on replacing propositional logic with a modal spatial logic, and provide a CART-like learning algorithm for it. We evaluate its performance at five different LCC tasks, showing that this technique leads to classification models whose performances are superior to those of their propositional counterpart, and at least comparable with those of non-symbolic ones. Ultimately, we show that spatial decision trees and random forests are able to extract complex, but interpretable spatial patterns

Multiobjective Evolutionary Feature Selection for Fuzzy Classification

The interpretability of classification systems refers to the ability of these to express their behaviour in a way that is easily understandable by a user. Interpretable classification models allow for external validation by an expert and, in certain disciplines such as medicine or business, providing information about decision making is essential for ethical and human reasons. Fuzzy rule-based classification systems are consolidated powerful classification tools based on fuzzy logic and designed to produce interpretable models; however, in presence of a large number of attributes, even rule-based models tend to be too complex to be easily interpreted. In this work, we propose a novel multivariate feature selection method in which both search strategy and classifier are based on multi-objective evolutionary computation. We designed a set of experiments to establish an acceptable setting with respect to the number of evaluations required by the search strategy and by the classifier, and we tested our strategy on a real-life dataset. Then, we compared our results against a wide range of feature selection methods that includes filter, wrapper, multivariate and univariate methods, with deterministic and probabilistic search strategies, and with evaluators of diverse nature. Finally, the fuzzy rule-based classification model obtained with the proposed method has been evaluated with standard performance metrics and compared with other wellknown fuzzy rule-based classifiers. We have used two real-life datasets extracted from a contact center; in one case, with the proposed method we obtained an accuracy of 0.7857 with 8 rules, while the best fuzzy classifier compared obtained 0.7679 with 8 rules, and in the second case, we obtained an accuracy of 0.7403 with 5 rules, while the best fuzzy classifier compared obtained 0.6364 with 4 rules

Mining temporal networks: Results and open problems

none3noThe design of temporal networks typically follows a top-down approach where a designer handcrafts a temporal network to model some concrete plan of interest. Instead, the bottom-up approach of mining is the process of building a temporal network from a set of execution traces of some (typically unknown) underlying process. Recent research showed that, due to the structural properties of temporal networks, such a task can be done in polynomial time. In this paper, we give an overview of the current status of our research and highlight open problems concerning Formal Methods and Artificial Intelligence.noneSciavicco G.; Villa T.; Zavatteri M.Sciavicco, G.; Villa, T.; Zavatteri, M

Definability and decidability of binary predicates for time granularity

In this paper we study the definability and decidability of binary predicates for time granularity in monadic languages interpreted over finitely and infinitely layered structures. We focus our attention on the equi-level (respectively equi-column) predicate constraining two time points to belong to the same layer (respectively column) and on the horizontal (respectively vertical) successor predicate relating a time point to its successor within a given layer (respectively column). We give a number of positive and negative results by reduction to/from a wide spectrum of decidable/undecidable problems