On interval dynamic logic: Introducing quasi-action lattices

In this paper we discuss the incompatibility between the notions of validity and impreciseness in the context of Dynamic Logics. To achieve that we consider the Łukasiewicz action lattice and its interval counterpart, we show how some validities fail in the context of intervals. In order to capture the properties of action lattices that remain valid for intervals we propose a new structure called Quasi-action Lattices which generalizes action lattices and is able to model both: The Łukasiewicz action lattice, Ł, and its interval counterpart, Łˆ. The notion of graded satisfaction relation is extended to quasi-action lattices. We demonstrate that, in the case of intervals, the relation of graded satisfaction is correct (cf. Theorem 3) with respect to the graded satisfaction relation on the Łukasiewicz action lattice. Although this theorem guarantees that satisfiability is preserved on intervals, we show that validity is not. We propose, then, to weaken the notion of validity on action lattices to designated validity on quasi-action lattices. In this context, Theorem 4 guarantees that the dynamic formulæ which are valid with respect to Ł will be designated valid with respect to Łˆpublishe

Reasoning about real-time systems with temporal interval logic constraints on multi-state automata

Models of real-time systems using a single paradigm often turn out to be inadequate, whether the paradigm is based on states, rules, event sequences, or logic. A model-based approach to reasoning about real-time systems is presented in which a temporal interval logic called TIL is employed to define constraints on a new type of high level automata. The combination, called hierarchical multi-state (HMS) machines, can be used to model formally a real-time system, a dynamic set of requirements, the environment, heuristic knowledge about planning-related problem solving, and the computational states of the reasoning mechanism. In this framework, mathematical techniques were developed for: (1) proving the correctness of a representation; (2) planning of concurrent tasks to achieve goals; and (3) scheduling of plans to satisfy complex temporal constraints. HMS machines allow reasoning about a real-time system from a model of how truth arises instead of merely depending of what is true in a system

Block-Matching Optical Flow for Dynamic Vision Sensor- Algorithm and FPGA Implementation

Rapid and low power computation of optical flow (OF) is potentially useful in robotics. The dynamic vision sensor (DVS) event camera produces quick and sparse output, and has high dynamic range, but conventional OF algorithms are frame-based and cannot be directly used with event-based cameras. Previous DVS OF methods do not work well with dense textured input and are designed for implementation in logic circuits. This paper proposes a new block-matching based DVS OF algorithm which is inspired by motion estimation methods used for MPEG video compression. The algorithm was implemented both in software and on FPGA. For each event, it computes the motion direction as one of 9 directions. The speed of the motion is set by the sample interval. Results show that the Average Angular Error can be improved by 30\% compared with previous methods. The OF can be calculated on FPGA with 50\,MHz clock in 0.2\,us per event (11 clock cycles), 20 times faster than a Java software implementation running on a desktop PC. Sample data is shown that the method works on scenes dominated by edges, sparse features, and dense texture.Comment: Published in ISCAS 201

Optimal External Memory Interval Management

AMS subject classifications. 68P05, 68P10, 68P15 DOI. 10.1137/S009753970240481XIn this paper we present the external interval tree, an optimal external memory data structure for answering stabbing queries on a set of dynamically maintained intervals. The external interval tree can be usedin an optimal solution to the dynamic interval management problem, which is a central problem for object-orientedandtemp oral databases andfor constraint logic programming.Part of the structure uses a weight-balancing technique for efficient worst-case manipulation of balanced trees, which is of independent interest. The external interval tree, as well as our new balancing technique, have recently been used to develop several efficient external data structures

Adaptive Non-singleton Type-2 Fuzzy Logic Systems: A Way Forward for Handling Numerical Uncertainties in Real World Applications

Real world environments are characterized by high levels of linguistic and numerical uncertainties. A Fuzzy Logic System (FLS) is recognized as an adequate methodology to handle the uncertainties and imprecision available in real world environments and applications. Since the invention of fuzzy logic, it has been applied with great success to numerous real world applications such as washing machines, food processors, battery chargers, electrical vehicles, and several other domestic and industrial appliances. The first generation of FLSs were type-1 FLSs in which type-1 fuzzy sets were employed. Later, it was found that using type-2 FLSs can enable the handling of higher levels of uncertainties. Recent works have shown that interval type-2 FLSs can outperform type-1 FLSs in the applications which encompass high uncertainty levels. However, the majority of interval type-2 FLSs handle the linguistic and input numerical uncertainties using singleton interval type-2 FLSs that mix the numerical and linguistic uncertainties to be handled only by the linguistic labels type-2 fuzzy sets. This ignores the fact that if input numerical uncertainties were present, they should affect the incoming inputs to the FLS. Even in the papers that employed non-singleton type-2 FLSs, the input signals were assumed to have a predefined shape (mostly Gaussian or triangular) which might not reflect the real uncertainty distribution which can vary with the associated measurement. In this paper, we will present a new approach which is based on an adaptive non-singleton interval type-2 FLS where the numerical uncertainties will be modeled and handled by non-singleton type-2 fuzzy inputs and the linguistic uncertainties will be handled by interval type-2 fuzzy sets to represent the antecedents’ linguistic labels. The non-singleton type-2 fuzzy inputs are dynamic and they are automatically generated from data and they do not assume a specific shape about the distribution associated with the given sensor. We will present several real world experiments using a real world robot which will show how the proposed type-2 non-singleton type-2 FLS will produce a superior performance to its singleton type-1 and type-2 counterparts when encountering high levels of uncertainties.</jats:p

Optimal External Memory Interval Management

This is the published version. Copyright © 2003 Society for Industrial and Applied MathematicsIn this paper we present the external interval tree, an optimal external memory data structure for answering stabbing queries on a set of dynamically maintained intervals. The external interval tree can be used in an optimal solution to the dynamic interval management problem, which is a central problem for object-oriented and temporal databases and for constraint logic programming. Part of the structure uses a weight-balancing technique for efficient worst-case manipulation of balanced trees, which is of independent interest. The external interval tree, as well as our new balancing technique, have recently been used to develop several efficient external data structures

Optimal External Memory Interval Management

This is the publisher's version, which is being shared on KU Scholarworks with permission. The original version may be found at the following link: http://dx.doi.org/10.1137/S009753970240481XIn this paper we present the external interval tree, an optimal external memory data structure for answering stabbing queries on a set of dynamically maintained intervals. The external interval tree can be usedin an optimal solution to the dynamic interval management problem, which is a central problem for object-orientedandtemp oral databases andfor constraint logic programming. Part of the structure uses a weight-balancing technique for efficient worst-case manipulation of balanced trees, which is of independent interest. The external interval tree, as well as our new balancing technique, have recently been used to develop several efficient external data structures

Real-time and Probabilistic Temporal Logics: An Overview

Over the last two decades, there has been an extensive study on logical formalisms for specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have been introduced for the formal specification of real-time and complex systems, an up to date comprehensive analysis of these logics does not exist in the literature. In this paper we analyse real-time and probabilistic temporal logics which have been widely used in this field. We extrapolate the notions of decidability, axiomatizability, expressiveness, model checking, etc. for each logic analysed. We also provide a comparison of features of the temporal logics discussed

Grounding the Lexical Semantics of Verbs in Visual Perception using Force Dynamics and Event Logic

This paper presents an implemented system for recognizing the occurrence of events described by simple spatial-motion verbs in short image sequences. The semantics of these verbs is specified with event-logic expressions that describe changes in the state of force-dynamic relations between the participants of the event. An efficient finite representation is introduced for the infinite sets of intervals that occur when describing liquid and semi-liquid events. Additionally, an efficient procedure using this representation is presented for inferring occurrences of compound events, described with event-logic expressions, from occurrences of primitive events. Using force dynamics and event logic to specify the lexical semantics of events allows the system to be more robust than prior systems based on motion profile