Matching Items (10)
Description
Research on combinatorics education is sparse when compared with other fields in mathematics education. This research attempted to contribute to the dearth of literature by examining students' reasoning about enumerative combinatorics problems and how students conceptualize the set of elements being counted in such problems, called the solution set. In particular, the focus was on the stable patterns of reasoning, known as ways of thinking, which students applied in a variety of combinatorial situations and tasks. This study catalogued students' ways of thinking about solution sets as they progressed through an instructional sequence. In addition, the relationships between the catalogued ways of thinking were explored. Further, the study investigated the challenges students experienced as they interacted with the tasks and instructional interventions, and how students' ways of thinking evolved as these challenges were overcome. Finally, it examined the role of instruction in guiding students to develop and extend their ways of thinking. Two pairs of undergraduate students with no formal experience with combinatorics participated in one of the two consecutive teaching experiments conducted in Spring 2012. Many ways of thinking emerged through the grounded theory analysis of the data, but only eight were identified as robust. These robust ways of thinking were classified into three categories: Subsets, Odometer, and Problem Posing. The Subsets category encompasses two ways of thinking, both of which ultimately involve envisioning the solution set as the union of subsets. The three ways of thinking in Odometer category involve holding an item or a set of items constant and systematically varying the other items involved in the counting process. The ways of thinking belonging to Problem Posing category involve spontaneously posing new, related combinatorics problems and finding relationships between the solution sets of the original and the new problem. The evolution of students' ways of thinking in the Problem Posing category was analyzed. This entailed examining the perturbation experienced by students and the resulting accommodation of their thinking. It was found that such perturbation and its resolution was often the result of an instructional intervention. Implications for teaching practice are discussed.
ContributorsHalani, Aviva (Author) / Roh, Kyeong Hah (Thesis advisor) / Fishel, Susanna (Committee member) / Saldanha, Luis (Committee member) / Thompson, Patrick (Committee member) / Zandieh, Michelle (Committee member) / Arizona State University (Publisher)
Created2013
Description
Biological organisms are made up of cells containing numerous interconnected biochemical processes. Diseases occur when normal functionality of these processes is disrupted, manifesting as disease symptoms. Thus, understanding these biochemical processes and their interrelationships is a primary task in biomedical research and a prerequisite for activities including diagnosing diseases and drug development. Scientists studying these interconnected processes have identified various pathways involved in drug metabolism, diseases, and signal transduction, etc. High-throughput technologies, new algorithms and speed improvements over the last decade have resulted in deeper knowledge about biological systems, leading to more refined pathways. Such pathways tend to be large and complex, making it difficult for an individual to remember all aspects. Thus, computer models are needed to represent and analyze them. The refinement activity itself requires reasoning with a pathway model by posing queries against it and comparing the results against the real biological system. Many existing models focus on structural and/or factoid questions, relying on surface-level information. These are generally not the kind of questions that a biologist may ask someone to test their understanding of biological processes. Examples of questions requiring understanding of biological processes are available in introductory college level biology text books. Such questions serve as a model for the question answering system developed in this thesis. Thus, the main goal of this thesis is to develop a system that allows the encoding of knowledge about biological pathways to answer questions demonstrating understanding of the pathways. To that end, a language is developed to specify a pathway and pose questions against it. Some existing tools are modified and used to accomplish this goal. The utility of the framework developed in this thesis is illustrated with applications in the biological domain. Finally, the question answering system is used in real world applications by extracting pathway knowledge from text and answering questions related to drug development.
ContributorsAnwar, Saadat (Author) / Baral, Chitta (Thesis advisor) / Inoue, Katsumi (Committee member) / Chen, Yi (Committee member) / Davulcu, Hasan (Committee member) / Lee, Joohyung (Committee member) / Arizona State University (Publisher)
Created2014
Description
Modeling dynamic systems is an interesting problem in Knowledge Representation (KR) due to their usefulness in reasoning about real-world environments. In order to effectively do this, a number of different formalisms have been considered ranging from low-level languages, such as Answer Set Programming (ASP), to high-level action languages, such as C+ and BC. These languages show a lot of promise over many traditional approaches as they allow a developer to automate many tasks which require reasoning within dynamic environments in a succinct and elaboration tolerant manner. However, despite their strengths, they are still insufficient for modeling many systems, especially those of non-trivial scale or that require the ability to cope with exceptions which occur during execution, such as unexpected events or unintended consequences to actions which have been performed. In order to address these challenges, a theoretical framework is created which focuses on improving the feasibility of applying KR techniques to such problems. The framework is centered on the action language BC+, which integrates many of the strengths of existing KR formalisms, and provides the ability to perform efficient reasoning in an incremental fashion while handling exceptions which occur during execution. The result is a developer friendly formalism suitable for performing reasoning in an online environment. Finally, the newly enhanced Cplus2ASP 2 is introduced, which provides a number of improvements over the original version. These improvements include implementing BC+ among several additional languages, providing enhanced developer support, and exhibiting a significant performance increase over its predecessors and similar systems.
ContributorsBabb, Joseph (Author) / Lee, Joohyung (Thesis advisor) / Lee, Yann-Hang (Committee member) / Baral, Chitta (Committee member) / Arizona State University (Publisher)
Created2014
Description
Due to government initiatives, education in the classroom has focused on high stakes test scores measuring student achievement on basic skills. The purpose of this action research study was to augment fourth grade students' knowledge of basic content by teaching greater meaning and depth of understanding--to teach critical thinking using Socratic circles. Using a constructivist approach, a comprehensive plan was designed and implemented that included an age-appropriate platform for argument and inquiry, a process that required critical thinking skills, and allowed the intellectual standards for critical thinking to be developed and measured. Ten students representing the academic levels of the whole class were selected and participated in seven Socratic circles. Over a period of 15 weeks, a mixed methods approach was employed to determine how students were able to apply the intellectual standards to reasoning during Socratic circles, how this innovation provoked participation in student-centered dialogue, and how Socratic circles improved students' evaluation of competing ideas during their reasoned discourse. Results suggested that Comprehensive Socratic Circles increased participation in reasoned discourse. Students' ability to evaluate competing ideas improved, and their application of the intellectual standards for critical thinking to their reasoning increased. Students also increased their use of student-centered dialogue across the sessions. These findings suggest that Socratic circles is a flexible and effective teaching strategy that fosters critical thinking in fourth graders.
ContributorsCleveland, Julie (Author) / Rotheram-Fuller, Erin (Thesis advisor) / Dinn-You Liou, Daniel (Committee member) / Lansdowne, Kimberly (Committee member) / Arizona State University (Publisher)
Created2015
Description
Image Understanding is a long-established discipline in computer vision, which encompasses a body of advanced image processing techniques, that are used to locate (“where”), characterize and recognize (“what”) objects, regions, and their attributes in the image. However, the notion of “understanding” (and the goal of artificial intelligent machines) goes beyond factual recall of the recognized components and includes reasoning and thinking beyond what can be seen (or perceived). Understanding is often evaluated by asking questions of increasing difficulty. Thus, the expected functionalities of an intelligent Image Understanding system can be expressed in terms of the functionalities that are required to answer questions about an image. Answering questions about images require primarily three components: Image Understanding, question (natural language) understanding, and reasoning based on knowledge. Any question, asking beyond what can be directly seen, requires modeling of commonsense (or background/ontological/factual) knowledge and reasoning.
Knowledge and reasoning have seen scarce use in image understanding applications. In this thesis, we demonstrate the utilities of incorporating background knowledge and using explicit reasoning in image understanding applications. We first present a comprehensive survey of the previous work that utilized background knowledge and reasoning in understanding images. This survey outlines the limited use of commonsense knowledge in high-level applications. We then present a set of vision and reasoning-based methods to solve several applications and show that these approaches benefit in terms of accuracy and interpretability from the explicit use of knowledge and reasoning. We propose novel knowledge representations of image, knowledge acquisition methods, and a new implementation of an efficient probabilistic logical reasoning engine that can utilize publicly available commonsense knowledge to solve applications such as visual question answering, image puzzles. Additionally, we identify the need for new datasets that explicitly require external commonsense knowledge to solve. We propose the new task of Image Riddles, which requires a combination of vision, and reasoning based on ontological knowledge; and we collect a sufficiently large dataset to serve as an ideal testbed for vision and reasoning research. Lastly, we propose end-to-end deep architectures that can combine vision, knowledge and reasoning modules together and achieve large performance boosts over state-of-the-art methods.
Knowledge and reasoning have seen scarce use in image understanding applications. In this thesis, we demonstrate the utilities of incorporating background knowledge and using explicit reasoning in image understanding applications. We first present a comprehensive survey of the previous work that utilized background knowledge and reasoning in understanding images. This survey outlines the limited use of commonsense knowledge in high-level applications. We then present a set of vision and reasoning-based methods to solve several applications and show that these approaches benefit in terms of accuracy and interpretability from the explicit use of knowledge and reasoning. We propose novel knowledge representations of image, knowledge acquisition methods, and a new implementation of an efficient probabilistic logical reasoning engine that can utilize publicly available commonsense knowledge to solve applications such as visual question answering, image puzzles. Additionally, we identify the need for new datasets that explicitly require external commonsense knowledge to solve. We propose the new task of Image Riddles, which requires a combination of vision, and reasoning based on ontological knowledge; and we collect a sufficiently large dataset to serve as an ideal testbed for vision and reasoning research. Lastly, we propose end-to-end deep architectures that can combine vision, knowledge and reasoning modules together and achieve large performance boosts over state-of-the-art methods.
ContributorsAditya, Somak (Author) / Baral, Chitta (Thesis advisor) / Yang, Yezhou (Thesis advisor) / Aloimonos, Yiannis (Committee member) / Lee, Joohyung (Committee member) / Li, Baoxin (Committee member) / Arizona State University (Publisher)
Created2018
Description
After surveying the literature on the normativity of logic, the paper answers that logic is normative for reasoning and rationality. The paper then goes on to discuss whether this constitutes a new problem in issues in normativity, and the paper affirms that it does. Finally, the paper concludes by explaining that the logic as model view can address this new problem.
ContributorsCadenas, Haggeo (Author) / Pinillos, Angel (Thesis advisor) / Creath, Richard (Committee member) / Kobes, Bernard (Committee member) / nair, shyam (Committee member) / Arizona State University (Publisher)
Created2017
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
Several physical systems exist in the real world that involve continuous as well as discrete changes. These range from natural dynamic systems like the system of a bouncing ball to robotic dynamic systems such as planning the motion of a robot across obstacles. The key aspects of effectively describing such dynamic systems is to be able to plan and verify the evolution of the continuous components of the system while simultaneously maintaining critical constraints. Developing a framework that can effectively represent and find solutions to such physical systems prove to be highly advantageous. Both hybrid automata and action languages are formal models for describing the evolution of dynamic systems. The action language C+ is a rich and expressive language framework to formalize physical systems, but can be used only with physical systems in the discrete domain and is limited in its support of continuous domain components of such systems. Hybrid Automata is a well established formalism used to represent such complex physical systems at a theoretical level, however it is not expressive enough to capture the complex relations between the components of the system the way C+ does.
This thesis will focus on establishing a formal relationship between these two formalisms by showing how to succinctly represent Hybrid Automata in an action language which in turn is defined as a high-level notation for answer set programming modulo theories (ASPMT) --- an extension of answer set programs in the first-order level. Furthermore, this encoding framework is shown to be more effective and expressive than Hybrid Automata by highlighting its ability in allowing states of a hybrid transition system to be defined by complex relations among components that would otherwise be abstracted away in Hybrid Automata. The framework is further realized in the implementation of the system CPLUS2ASPMT, which takes advantage of state of the art ODE(Ordinary Differential Equations) based SMT solver dReal to provide support for ODE based evolution of continuous components of a dynamic system.
This thesis will focus on establishing a formal relationship between these two formalisms by showing how to succinctly represent Hybrid Automata in an action language which in turn is defined as a high-level notation for answer set programming modulo theories (ASPMT) --- an extension of answer set programs in the first-order level. Furthermore, this encoding framework is shown to be more effective and expressive than Hybrid Automata by highlighting its ability in allowing states of a hybrid transition system to be defined by complex relations among components that would otherwise be abstracted away in Hybrid Automata. The framework is further realized in the implementation of the system CPLUS2ASPMT, which takes advantage of state of the art ODE(Ordinary Differential Equations) based SMT solver dReal to provide support for ODE based evolution of continuous components of a dynamic system.
ContributorsLoney, Nikhil (Author) / Lee, Joohyung (Thesis advisor) / Fainekos, Georgios (Committee member) / Zhang, Yu (Committee member) / Arizona State University (Publisher)
Created2017
Description
The majority of trust research has focused on the benefits trust can have for individual actors, institutions, and organizations. This “optimistic bias” is particularly evident in work focused on institutional trust, where concepts such as procedural justice, shared values, and moral responsibility have gained prominence. But trust in institutions may not be exclusively good. We reveal implications for the “dark side” of institutional trust by reviewing relevant theories and empirical research that can contribute to a more holistic understanding. We frame our discussion by suggesting there may be a “Goldilocks principle” of institutional trust, where trust that is too low (typically the focus) or too high (not usually considered by trust researchers) may be problematic. The chapter focuses on the issue of too-high trust and processes through which such too-high trust might emerge. Specifically, excessive trust might result from external, internal, and intersecting external-internal processes. External processes refer to the actions institutions take that affect public trust, while internal processes refer to intrapersonal factors affecting a trustor’s level of trust. We describe how the beneficial psychological and behavioral outcomes of trust can be mitigated or circumvented through these processes and highlight the implications of a “darkest” side of trust when they intersect. We draw upon research on organizations and legal, governmental, and political systems to demonstrate the dark side of trust in different contexts. The conclusion outlines directions for future research and encourages researchers to consider the ethical nuances of studying how to increase institutional trust.
ContributorsNeal, Tess M.S. (Author) / Shockley, Ellie (Author) / Schilke, Oliver (Author)
Created2016
Description
In natural language processing, language models have achieved remarkable success over the last few years. The Transformers are at the core of most of these models. Their success can be mainly attributed to an enormous amount of curated data they are trained on. Even though such language models are trained on massive curated data, they often need specific extracted knowledge to understand better and reason. This is because often relevant knowledge may be implicit or missing, which hampers machine reasoning. Apart from that, manual knowledge curation is time-consuming and erroneous. Hence, finding fast and effective methods to extract such knowledge from data is important for improving language models. This leads to finding ideal ways to utilize such knowledge by incorporating them into language models. Successful knowledge extraction and integration lead to an important question of knowledge evaluation of such models by developing tools or introducing challenging test suites to learn about their limitations and improve them further. So to improve the transformer-based models, understanding the role of knowledge becomes important. In the pursuit to improve language models with knowledge, in this dissertation I study three broad research directions spanning across the natural language, biomedical and cybersecurity domains: (1) Knowledge Extraction (KX) - How can transformer-based language models be leveraged to extract knowledge from data? (2) Knowledge Integration (KI) - How can such specific knowledge be used to improve such models? (3) Knowledge Evaluation (KE) - How can language models be evaluated for specific skills and understand their limitations?
I propose methods to extract explicit textual, implicit structural, missing textual, and missing structural knowledge from natural language and binary programs using transformer-based language models. I develop ways to improve the language model’s multi-step and commonsense reasoning abilities using external knowledge. Finally, I develop challenging datasets which assess their numerical reasoning skills in both in-domain and out-of-domain settings.
ContributorsPal, Kuntal Kumar (Author) / Baral, Chitta (Thesis advisor) / Wang, Ruoyu (Committee member) / Blanco, Eduardo (Committee member) / Yang, Yezhou (Committee member) / Arizona State University (Publisher)
Created2023