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- All Subjects: Mathematics
- All Subjects: Logic programming
- Genre: Academic theses
- Genre: Doctoral Dissertation
- Creators: Fainekos, Georgios
Description
Answer Set Programming (ASP) is one of the most prominent and successful knowledge representation paradigms. The success of ASP is due to its expressive non-monotonic modeling language and its efficient computational methods originating from building propositional satisfiability solvers. The wide adoption of ASP has motivated several extensions to its modeling language in order to enhance expressivity, such as incorporating aggregates and interfaces with ontologies. Also, in order to overcome the grounding bottleneck of computation in ASP, there are increasing interests in integrating ASP with other computing paradigms, such as Constraint Programming (CP) and Satisfiability Modulo Theories (SMT). Due to the non-monotonic nature of the ASP semantics, such enhancements turned out to be non-trivial and the existing extensions are not fully satisfactory. We observe that one main reason for the difficulties rooted in the propositional semantics of ASP, which is limited in handling first-order constructs (such as aggregates and ontologies) and functions (such as constraint variables in CP and SMT) in natural ways. This dissertation presents a unifying view on these extensions by viewing them as instances of formulas with generalized quantifiers and intensional functions. We extend the first-order stable model semantics by by Ferraris, Lee, and Lifschitz to allow generalized quantifiers, which cover aggregate, DL-atoms, constraints and SMT theory atoms as special cases. Using this unifying framework, we study and relate different extensions of ASP. We also present a tight integration of ASP with SMT, based on which we enhance action language C+ to handle reasoning about continuous changes. Our framework yields a systematic approach to study and extend non-monotonic languages.
ContributorsMeng, Yunsong (Author) / Lee, Joohyung (Thesis advisor) / Ahn, Gail-Joon (Committee member) / Baral, Chitta (Committee member) / Fainekos, Georgios (Committee member) / Lifschitz, Vladimir (Committee member) / Arizona State University (Publisher)
Created2013
Description
Different logic-based knowledge representation formalisms have different limitations either with respect to expressivity or with respect to computational efficiency. First-order logic, which is the basis of Description Logics (DLs), is not suitable for defeasible reasoning due to its monotonic nature. The nonmonotonic formalisms that extend first-order logic, such as circumscription and default logic, are expressive but lack efficient implementations. The nonmonotonic formalisms that are based on the declarative logic programming approach, such as Answer Set Programming (ASP), have efficient implementations but are not expressive enough for representing and reasoning with open domains. This dissertation uses the first-order stable model semantics, which extends both first-order logic and ASP, to relate circumscription to ASP, and to integrate DLs and ASP, thereby partially overcoming the limitations of the formalisms. By exploiting the relationship between circumscription and ASP, well-known action formalisms, such as the situation calculus, the event calculus, and Temporal Action Logics, are reformulated in ASP. The advantages of these reformulations are shown with respect to the generality of the reasoning tasks that can be handled and with respect to the computational efficiency. The integration of DLs and ASP presented in this dissertation provides a framework for integrating rules and ontologies for the semantic web. This framework enables us to perform nonmonotonic reasoning with DL knowledge bases. Observing the need to integrate action theories and ontologies, the above results are used to reformulate the problem of integrating action theories and ontologies as a problem of integrating rules and ontologies, thus enabling us to use the computational tools developed in the context of the latter for the former.
ContributorsPalla, Ravi (Author) / Lee, Joohyung (Thesis advisor) / Baral, Chitta (Committee member) / Kambhampati, Subbarao (Committee member) / Lifschitz, Vladimir (Committee member) / Arizona State University (Publisher)
Created2012
Description
Robotic technology is advancing to the point where it will soon be feasible to deploy massive populations, or swarms, of low-cost autonomous robots to collectively perform tasks over large domains and time scales. Many of these tasks will require the robots to allocate themselves around the boundaries of regions or features of interest and achieve target objectives that derive from their resulting spatial configurations, such as forming a connected communication network or acquiring sensor data around the entire boundary. We refer to this spatial allocation problem as boundary coverage. Possible swarm tasks that will involve boundary coverage include cooperative load manipulation for applications in construction, manufacturing, and disaster response.
In this work, I address the challenges of controlling a swarm of resource-constrained robots to achieve boundary coverage, which I refer to as the problem of stochastic boundary coverage. I first examined an instance of this behavior in the biological phenomenon of group food retrieval by desert ants, and developed a hybrid dynamical system model of this process from experimental data. Subsequently, with the aid of collaborators, I used a continuum abstraction of swarm population dynamics, adapted from a modeling framework used in chemical kinetics, to derive stochastic robot control policies that drive a swarm to target steady-state allocations around multiple boundaries in a way that is robust to environmental variations.
Next, I determined the statistical properties of the random graph that is formed by a group of robots, each with the same capabilities, that have attached to a boundary at random locations. I also computed the probability density functions (pdfs) of the robot positions and inter-robot distances for this case.
I then extended this analysis to cases in which the robots have heterogeneous communication/sensing radii and attach to a boundary according to non-uniform, non-identical pdfs. I proved that these more general coverage strategies generate random graphs whose probability of connectivity is Sharp-P Hard to compute. Finally, I investigated possible approaches to validating our boundary coverage strategies in multi-robot simulations with realistic Wi-fi communication.
In this work, I address the challenges of controlling a swarm of resource-constrained robots to achieve boundary coverage, which I refer to as the problem of stochastic boundary coverage. I first examined an instance of this behavior in the biological phenomenon of group food retrieval by desert ants, and developed a hybrid dynamical system model of this process from experimental data. Subsequently, with the aid of collaborators, I used a continuum abstraction of swarm population dynamics, adapted from a modeling framework used in chemical kinetics, to derive stochastic robot control policies that drive a swarm to target steady-state allocations around multiple boundaries in a way that is robust to environmental variations.
Next, I determined the statistical properties of the random graph that is formed by a group of robots, each with the same capabilities, that have attached to a boundary at random locations. I also computed the probability density functions (pdfs) of the robot positions and inter-robot distances for this case.
I then extended this analysis to cases in which the robots have heterogeneous communication/sensing radii and attach to a boundary according to non-uniform, non-identical pdfs. I proved that these more general coverage strategies generate random graphs whose probability of connectivity is Sharp-P Hard to compute. Finally, I investigated possible approaches to validating our boundary coverage strategies in multi-robot simulations with realistic Wi-fi communication.
ContributorsPeruvemba Kumar, Ganesh (Author) / Berman, Spring M (Thesis advisor) / Fainekos, Georgios (Thesis advisor) / Bazzi, Rida (Committee member) / Syrotiuk, Violet (Committee member) / Taylor, Thomas (Committee member) / Arizona State University (Publisher)
Created2016
Description
Knowledge representation and reasoning is a prominent subject of study within the field of artificial intelligence that is concerned with the symbolic representation of knowledge in such a way to facilitate automated reasoning about this knowledge. Often in real-world domains, it is necessary to perform defeasible reasoning when representing default behaviors of systems. Answer Set Programming is a widely-used knowledge representation framework that is well-suited for such reasoning tasks and has been successfully applied to practical domains due to efficient computation through grounding--a process that replaces variables with variable-free terms--and propositional solvers similar to SAT solvers. However, some domains provide a challenge for grounding-based methods such as domains requiring reasoning about continuous time or resources.
To address these domains, there have been several proposals to achieve efficiency through loose integrations with efficient declarative solvers such as constraint solvers or satisfiability modulo theories solvers. While these approaches successfully avoid substantial grounding, due to the loose integration, they are not suitable for performing defeasible reasoning on functions. As a result, this expressive reasoning on functions must either be performed using predicates to simulate the functions or in a way that is not elaboration tolerant. Neither compromise is reasonable; the former suffers from the grounding bottleneck when domains are large as is often the case in real-world domains while the latter necessitates encodings to be non-trivially modified for elaborations.
This dissertation presents a novel framework called Answer Set Programming Modulo Theories (ASPMT) that is a tight integration of the stable model semantics and satisfiability modulo theories. This framework both supports defeasible reasoning about functions and alleviates the grounding bottleneck. Combining the strengths of Answer Set Programming and satisfiability modulo theories enables efficient continuous reasoning while still supporting rich reasoning features such as reasoning about defaults and reasoning in domains with incomplete knowledge. This framework is realized in two prototype implementations called MVSM and ASPMT2SMT, and the latter was recently incorporated into a non-monotonic spatial reasoning system. To define the semantics of this framework, we extend the first-order stable model semantics by Ferraris, Lee and Lifschitz to allow "intensional functions" and provide analyses of the theoretical properties of this new formalism and on the relationships between this and existing approaches.
To address these domains, there have been several proposals to achieve efficiency through loose integrations with efficient declarative solvers such as constraint solvers or satisfiability modulo theories solvers. While these approaches successfully avoid substantial grounding, due to the loose integration, they are not suitable for performing defeasible reasoning on functions. As a result, this expressive reasoning on functions must either be performed using predicates to simulate the functions or in a way that is not elaboration tolerant. Neither compromise is reasonable; the former suffers from the grounding bottleneck when domains are large as is often the case in real-world domains while the latter necessitates encodings to be non-trivially modified for elaborations.
This dissertation presents a novel framework called Answer Set Programming Modulo Theories (ASPMT) that is a tight integration of the stable model semantics and satisfiability modulo theories. This framework both supports defeasible reasoning about functions and alleviates the grounding bottleneck. Combining the strengths of Answer Set Programming and satisfiability modulo theories enables efficient continuous reasoning while still supporting rich reasoning features such as reasoning about defaults and reasoning in domains with incomplete knowledge. This framework is realized in two prototype implementations called MVSM and ASPMT2SMT, and the latter was recently incorporated into a non-monotonic spatial reasoning system. To define the semantics of this framework, we extend the first-order stable model semantics by Ferraris, Lee and Lifschitz to allow "intensional functions" and provide analyses of the theoretical properties of this new formalism and on the relationships between this and existing approaches.
ContributorsBartholomew, Michael James (Author) / Lee, Joohyung (Thesis advisor) / Bazzi, Rida (Committee member) / Colbourn, Charles (Committee member) / Fainekos, Georgios (Committee member) / Lifschitz, Vladimir (Committee member) / Arizona State University (Publisher)
Created2016
Description
A storage system requiring file redundancy and on-line repairability can be represented as a Steiner system, a combinatorial design with the property that every $t$-subset of its points occurs in exactly one of its blocks. Under this representation, files are the points and storage units are the blocks of the Steiner system, or vice-versa. Often, the popularities of the files of such storage systems run the gamut, with some files receiving hardly any attention, and others receiving most of it. For such systems, minimizing the difference in the collective popularity between any two storage units is nontrivial; this is the access balancing problem. With regard to the representative Steiner system, the access balancing problem in its simplest form amounts to constructing either a point or block labelling: an assignment of a set of integer labels (popularity ranks) to the Steiner system's point set or block set, respectively, requiring of the former assignment that the sums of the labelled points of any two blocks differ as little as possible and of the latter that the sums of the labels assigned to the containing blocks of any two distinct points differ as little as possible. The central aim of this dissertation is to supply point and block labellings for Steiner systems of block size greater than three, for which up to this point no attempt has been made. Four major results are given in this connection. First, motivated by the close connection between the size of the independent sets of a Steiner system and the quality of its labellings, a Steiner triple system of any admissible order is constructed with a pair of disjoint independent sets of maximum cardinality. Second, the spectrum of resolvable Bose triple systems is determined in order to label some Steiner 2-designs with block size four. Third, several kinds of independent sets are used to point-label Steiner 2-designs with block size four. Finally, optimal and close to optimal block labellings are given for an infinite class of 1-rotational resolvable Steiner 2-designs with arbitrarily large block size by exploiting their underlying group-theoretic properties.
ContributorsLusi, Dylan (Author) / Colbourn, Charles J (Thesis advisor) / Czygrinow, Andrzej (Committee member) / Fainekos, Georgios (Committee member) / Richa, Andrea (Committee member) / Arizona State University (Publisher)
Created2021
Description
The notion of the safety of a system when placed in an environment with humans and other machines has been one of the primary concerns of practitioners while deploying any cyber-physical system (CPS). Such systems, also called safety-critical systems, need to be exhaustively tested for erroneous behavior. This generates the need for coming up with algorithms that can help ascertain the behavior and safety of the system by generating tests for the system where they are likely to falsify. In this work, three algorithms have been presented that aim at finding falsifying behaviors in cyber-physical Systems. PART-X intelligently partitions while sampling the input space to provide probabilistic point and region estimates of falsification. PYSOAR-C and LS-EMIBO aims at finding falsifying behaviors in gray-box systems when some information about the system is available. Specifically, PYSOAR-C aims to find falsification while maximizing coverage using a two-phase optimization process, while LS-EMIBO aims at exploiting the structure of a requirement to find falsifications with lower computational cost compared to the state-of-the-art. This work also shows the efficacy of the algorithms on a wide range of complex cyber-physical systems. The algorithms presented in this thesis are available as python toolboxes.
ContributorsKhandait, Tanmay Bhaskar (Author) / Pedrielli, Giulia (Thesis advisor) / Fainekos, Georgios (Thesis advisor) / Gopalan, Nakul (Committee member) / Arizona State University (Publisher)
Created2022
Description
In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a trade off between accuracy and complexity. In particular, we develop a sequence of tractable optimization problems - in the form of Linear Programs (LPs) and/or Semi-Definite Programs (SDPs) - whose solutions converge to the exact solution of the NP-hard problem. However, the computational and memory complexity of these LPs and SDPs grow exponentially with the progress of the sequence - meaning that improving the accuracy of the solutions requires solving SDPs with tens of thousands of decision variables and constraints. Setting up and solving such problems is a significant challenge. The existing optimization algorithms and software are only designed to use desktop computers or small cluster computers - machines which do not have sufficient memory for solving such large SDPs. Moreover, the speed-up of these algorithms does not scale beyond dozens of processors. This in fact is the reason we seek parallel algorithms for setting-up and solving large SDPs on large cluster- and/or super-computers.
We propose parallel algorithms for stability analysis of two classes of systems: 1) Linear systems with a large number of uncertain parameters; 2) Nonlinear systems defined by polynomial vector fields. First, we develop a distributed parallel algorithm which applies Polya's and/or Handelman's theorems to some variants of parameter-dependent Lyapunov inequalities with parameters defined over the standard simplex. The result is a sequence of SDPs which possess a block-diagonal structure. We then develop a parallel SDP solver which exploits this structure in order to map the computation, memory and communication to a distributed parallel environment. Numerical tests on a supercomputer demonstrate the ability of the algorithm to efficiently utilize hundreds and potentially thousands of processors, and analyze systems with 100+ dimensional state-space. Furthermore, we extend our algorithms to analyze robust stability over more complicated geometries such as hypercubes and arbitrary convex polytopes. Our algorithms can be readily extended to address a wide variety of problems in control such as Hinfinity synthesis for systems with parametric uncertainty and computing control Lyapunov functions.
We propose parallel algorithms for stability analysis of two classes of systems: 1) Linear systems with a large number of uncertain parameters; 2) Nonlinear systems defined by polynomial vector fields. First, we develop a distributed parallel algorithm which applies Polya's and/or Handelman's theorems to some variants of parameter-dependent Lyapunov inequalities with parameters defined over the standard simplex. The result is a sequence of SDPs which possess a block-diagonal structure. We then develop a parallel SDP solver which exploits this structure in order to map the computation, memory and communication to a distributed parallel environment. Numerical tests on a supercomputer demonstrate the ability of the algorithm to efficiently utilize hundreds and potentially thousands of processors, and analyze systems with 100+ dimensional state-space. Furthermore, we extend our algorithms to analyze robust stability over more complicated geometries such as hypercubes and arbitrary convex polytopes. Our algorithms can be readily extended to address a wide variety of problems in control such as Hinfinity synthesis for systems with parametric uncertainty and computing control Lyapunov functions.
ContributorsKamyar, Reza (Author) / Peet, Matthew (Thesis advisor) / Berman, Spring (Committee member) / Rivera, Daniel (Committee member) / Artemiadis, Panagiotis (Committee member) / Fainekos, Georgios (Committee member) / Arizona State University (Publisher)
Created2016