Interval-based Synthesis

We introduce the synthesis problem for Halpern and Shoham's modal logic of intervals extended with an equivalence relation over time points, abbreviated HSeq. In analogy to the case of monadic second-order logic of one successor, the considered synthesis problem receives as input an HSeq formula phi and a finite set Sigma of propositional variables and temporal requests, and it establishes whether or not, for all possible evaluations of elements in Sigma in every interval structure, there exists an evaluation of the remaining propositional variables and temporal requests such that the resulting structure is a model for phi. We focus our attention on decidability of the synthesis problem for some meaningful fragments of HSeq, whose modalities are drawn from the set A (meets), Abar (met by), B (begins), Bbar (begun by), interpreted over finite linear orders and natural numbers. We prove that the fragment ABBbareq is decidable (non-primitive recursive hard), while the fragment AAbarBBbar turns out to be undecidable. In addition, we show that even the synthesis problem for ABBbar becomes undecidable if we replace finite linear orders by natural numbers.Comment: In Proceedings GandALF 2014, arXiv:1408.556

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

Probabilistic Interval Temporal Logic and Duration Calculus with Infinite Intervals: Complete Proof Systems

The paper presents probabilistic extensions of interval temporal logic (ITL) and duration calculus (DC) with infinite intervals and complete Hilbert-style proof systems for them. The completeness results are a strong completeness theorem for the system of probabilistic ITL with respect to an abstract semantics and a relative completeness theorem for the system of probabilistic DC with respect to real-time semantics. The proposed systems subsume probabilistic real-time DC as known from the literature. A correspondence between the proposed systems and a system of probabilistic interval temporal logic with finite intervals and expanding modalities is established too.Comment: 43 page

Complexity of ITL model checking: some well-behaved fragments of the interval logic HS

Model checking has been successfully used in many computer science fields, including artificial intelligence, theoretical computer science, and databases. Most of the proposed solutions make use of classical, point-based temporal logics, while little work has been done in the interval temporal logic setting. Recently, a non-elementary model checking algorithm for Halpern and Shoham's modal logic of time intervals HS over finite Kripke structures (under the homogeneity assumption) and an EXPSPACE model checking procedure for two meaningful fragments of it have been proposed. In this paper, we show that more efficient model checking procedures can be developed for some expressive enough fragments of HS

Semantic-based decision support for remote care of dementia patients

This paper investigates the challenges in developing a semantic-based Dementia Care Decision Support System based on the non-intrusive monitoring of the patient's behaviour. Semantic-based approaches are well suited for modelling context-aware scenarios similar to Dementia care systems, where the patient's dynamic behaviour observations (occupants movement, equipment use) need to be analysed against the semantic knowledge about the patient's condition (illness history, medical advice, known symptoms) in an integrated knowledgebase. However, our research findings establish that the ability of semantic technologies to reason upon the complex interrelated events emanating from the behaviour monitoring sensors to infer knowledge assisting medical advice represents a major challenge. We attempt to address this problem by introducing a new approach that relies on propositional calculus modelling to segregate complex events that are amenable for semantic reasoning from events that require pre-processing outside the semantic engine before they can be reasoned upon. The event pre-processing activity also controls the timing of triggering the reasoning process in order to further improve the efficiency of the inference process. Using regression analysis, we evaluate the response-time as the number of monitored patients increases and conclude that the incurred overhead on the response time of the prototype decision support systems remains tolerable