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- All Subjects: Cryptography
- All Subjects: Logic programming
- Creators: Bazzi, Rida
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
Broadcast Encryption is the task of cryptographically securing communication in a broadcast environment so that only a dynamically specified subset of subscribers, called the privileged subset, may decrypt the communication. In practical applications, it is desirable for a Broadcast Encryption Scheme (BES) to demonstrate resilience against attacks by colluding, unprivileged subscribers. Minimal Perfect Hash Families (PHFs) have been shown to provide a basis for the construction of memory-efficient t-resilient Key Pre-distribution Schemes (KPSs) from multiple instances of 1-resilient KPSs. Using this technique, the task of constructing a large t-resilient BES is reduced to finding a near-minimal PHF of appropriate parameters. While combinatorial and probabilistic constructions exist for minimal PHFs with certain parameters, the complexity of constructing them in general is currently unknown. This thesis introduces a new type of hash family, called a Scattering Hash Family (ScHF), which is designed to allow for the scalable and ingredient-independent design of memory-efficient BESs for large parameters, specifically resilience and total number of subscribers. A general BES construction using ScHFs is shown, which constructs t-resilient KPSs from other KPSs of any resilience ≤w≤t. In addition to demonstrating how ScHFs can be used to produce BESs , this thesis explores several ScHF construction techniques. The initial technique demonstrates a probabilistic, non-constructive proof of existence for ScHFs . This construction is then derandomized into a direct, polynomial time construction of near-minimal ScHFs using the method of conditional expectations. As an alternative approach to direct construction, representing ScHFs as a k-restriction problem allows for the indirect construction of ScHFs via randomized post-optimization. Using the methods defined, ScHFs are constructed and the parameters' effects on solution size are analyzed. For large strengths, constructive techniques lose significant performance, and as such, asymptotic analysis is performed using the non-constructive existential results. This work concludes with an analysis of the benefits and disadvantages of BESs based on the constructed ScHFs. Due to the novel nature of ScHFs, the results of this analysis are used as the foundation for an empirical comparison between ScHF-based and PHF-based BESs . The primary bases of comparison are construction efficiency, key material requirements, and message transmission overhead.
ContributorsO'Brien, Devon James (Author) / Colbourn, Charles J (Thesis advisor) / Bazzi, Rida (Committee member) / Richa, Andrea (Committee member) / Arizona State University (Publisher)
Created2012
Description
As computers become a more embedded aspect of daily life, the importance of communicating ideas in computing and technology to the general public has become increasingly apparent. One such growing technology is electronic voting. The feasibility of explaining electronic voting protocols was directly investigated through the generation of a presentation based on journal articles and papers identified by the investigator. Extensive use of analogy and visual aids were used to explain various cryptographic concepts. The presentation was then given to a classroom of ASU freshmen, followed by a feedback survey. A self-evaluation on the presentation methods is conducted, and a procedure for explaining subjects in computer science is proposed based on the researcher's personal process.
ContributorsReniewicki, Peter Josef (Author) / Bazzi, Rida (Thesis director) / Childress, Nancy (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
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