Matching Items (8)

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An inverse lambda calculus algorithm for natural language processing

Description

Natural Language Processing is a subject that combines computer science and linguistics, aiming to provide computers with the ability to understand natural language and to develop a more intuitive human-computer

Natural Language Processing is a subject that combines computer science and linguistics, aiming to provide computers with the ability to understand natural language and to develop a more intuitive human-computer interaction. The research community has developed ways to translate natural language to mathematical formalisms. It has not yet been shown, however, how to automatically translate different kinds of knowledge in English to distinct formal languages. Most of the recent work presents the problem that the translation method aims to a specific formal language or is hard to generalize. In this research, I take a first step to overcome this difficulty and present two algorithms which take as input two lambda-calculus expressions G and H and compute a lambda-calculus expression F. The expression F returned by the first algorithm satisfies F@G=H and, in the case of the second algorithm, we obtain G@F=H. The lambda expressions represent the meanings of words and sentences. For each formal language that one desires to use with the algorithms, the language must be defined in terms of lambda calculus. Also, some additional concepts must be included. After doing this, given a sentence, its representation and knowing the representation of several words in the sentence, the algorithms can be used to obtain the representation of the other words in that sentence. In this work, I define two languages and show examples of their use with the algorithms. The algorithms are illustrated along with soundness and completeness proofs, the latter with respect to typed lambda-calculus formulas up to the second order. These algorithms are a core part of a natural language semantics system that translates sentences from English to formulas in different formal languages.

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Date Created
  • 2010

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On the Relationships Among Probabilistic Extensions of Answer Set Semantics

Description

Answer Set Programming (ASP) is one of the main formalisms in Knowledge Representation (KR) that is being widely applied in a large number of applications. While ASP is effective on

Answer Set Programming (ASP) is one of the main formalisms in Knowledge Representation (KR) that is being widely applied in a large number of applications. While ASP is effective on Boolean decision problems, it has difficulty in expressing quantitative uncertainty and probability in a natural way.

Logic Programs under the answer set semantics and Markov Logic Network (LPMLN) is a recent extension of answer set programs to overcome the limitation of the deterministic nature of ASP by adopting the log-linear weight scheme of Markov Logic. This thesis investigates the relationships between LPMLN and two other extensions of ASP: weak constraints to express a quantitative preference among answer sets, and P-log to incorporate probabilistic uncertainty. The studied relationships show how different extensions of answer set programs are related to each other, and how they are related to formalisms in Statistical Relational Learning, such as Problog and MLN, which have shown to be closely related to LPMLN. The studied relationships compare the properties of the involved languages and provide ways to compute one language using an implementation of another language.

This thesis first presents a translation of LPMLN into programs with weak constraints. The translation allows for computing the most probable stable models (i.e., MAP estimates) or probability distribution in LPMLN programs using standard ASP solvers so that the well-developed techniques in ASP can be utilized. This result can be extended to other formalisms, such as Markov Logic, ProbLog, and Pearl’s Causal Models, that are shown to be translatable into LPMLN.

This thesis also presents a translation of P-log into LPMLN. The translation tells how probabilistic nonmonotonicity (the ability of the reasoner to change his probabilistic model as a result of new information) of P-log can be represented in LPMLN, which yields a way to compute P-log using standard ASP solvers or MLN solvers.

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Date Created
  • 2017

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Answer set programming modulo theories

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

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.

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Date Created
  • 2016

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Reasoning and Learning with Probabilistic Answer Set Programming

Description

Knowledge Representation (KR) is one of the prominent approaches to Artificial Intelligence (AI) that is concerned with representing knowledge in a form that computer systems can utilize to solve complex

Knowledge Representation (KR) is one of the prominent approaches to Artificial Intelligence (AI) that is concerned with representing knowledge in a form that computer systems can utilize to solve complex problems. Answer Set Programming (ASP), based on the stable model semantics, is a widely-used KR framework that facilitates elegant and efficient representations for many problem domains that require complex reasoning.

However, while ASP is effective on deterministic problem domains, it is not suitable for applications involving quantitative uncertainty, for example, those that require probabilistic reasoning. Furthermore, it is hard to utilize information that can be statistically induced from data with ASP problem modeling.

This dissertation presents the language LP^MLN, which is a probabilistic extension of the stable model semantics with the concept of weighted rules, inspired by Markov Logic. An LP^MLN program defines a probability distribution over "soft" stable models, which may not satisfy all rules, but the more rules with the bigger weights they satisfy, the bigger their probabilities. LP^MLN takes advantage of both ASP and Markov Logic in a single framework, allowing representation of problems that require both logical and probabilistic reasoning in an intuitive and elaboration tolerant way.

This dissertation establishes formal relations between LP^MLN and several other formalisms, discusses inference and weight learning algorithms under LP^MLN, and presents systems implementing the algorithms. LP^MLN systems can be used to compute other languages translatable into LP^MLN.

The advantage of LP^MLN for probabilistic reasoning is illustrated by a probabilistic extension of the action language BC+, called pBC+, defined as a high-level notation of LP^MLN for describing transition systems. Various probabilistic reasoning about transition systems, especially probabilistic diagnosis, can be modeled in pBC+ and computed using LP^MLN systems. pBC+ is further extended with the notion of utility, through a decision-theoretic extension of LP^MLN, and related with Markov Decision Process (MDP) in terms of policy optimization problems. pBC+ can be used to represent (PO)MDP in a succinct and elaboration tolerant way, which enables planning with (PO)MDP algorithms in action domains whose description requires rich KR constructs, such as recursive definitions and indirect effects of actions.

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Created

Date Created
  • 2019

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Towards efficient online reasoning about actions

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

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.

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Date Created
  • 2014

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Representing and Reasoning about Dynamic Multi-Agent Domains: An Action Language Approach

Description

Reasoning about actions forms the basis of many tasks such as prediction, planning, and diagnosis in a dynamic domain. Within the reasoning about actions community, a broad class of languages,

Reasoning about actions forms the basis of many tasks such as prediction, planning, and diagnosis in a dynamic domain. Within the reasoning about actions community, a broad class of languages, called action languages, has been developed together with a methodology for their use in representing and reasoning about dynamic domains. With a few notable exceptions, the focus of these efforts has largely centered around single-agent systems. Agents rarely operate in a vacuum however, and almost in parallel, substantial work has been done within the dynamic epistemic logic community towards understanding how the actions of an agent may effect not just his own knowledge and/or beliefs, but those of his fellow agents as well. What is less understood by both communities is how to represent and reason about both the direct and indirect effects of both ontic and epistemic actions within a multi-agent setting. This dissertation presents ongoing research towards a framework for representing and reasoning about dynamic multi-agent domains involving both classes of actions.

The contributions of this work are as follows: the formulation of a precise mathematical model of a dynamic multi-agent domain based on the notion of a transition diagram; the development of the multi-agent action languages mA+ and mAL based upon this model, as well as preliminary investigations of their properties and implementations via logic programming under the answer set semantics; precise formulations of the temporal projection, and planning problems within a multi-agent context; and an investigation of the application of the proposed approach to the representation of, and reasoning about, scenarios involving the modalities of knowledge and belief.

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Date Created
  • 2018

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Answer set programming and other computing paradigms

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

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.

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Date Created
  • 2013

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Representing the language of the causal calculator in answer set programming

Description

Action language C+ is a formalism for describing properties of actions, which is based on nonmonotonic causal logic. The definite fragment of C+ is implemented in the Causal Calculator

Action language C+ is a formalism for describing properties of actions, which is based on nonmonotonic causal logic. The definite fragment of C+ is implemented in the Causal Calculator (CCalc), which is based on the reduction of nonmonotonic causal logic to propositional logic. This thesis describes the language of CCalc in terms of answer set programming (ASP), based on the translation of nonmonotonic causal logic to formulas under the stable model semantics. I designed a standard library which describes the constructs of the input language of CCalc in terms of ASP, allowing a simple modular method to represent CCalc input programs in the language of ASP. Using the combination of system F2LP and answer set solvers, this method achieves functionality close to that of CCalc while taking advantage of answer set solvers to yield efficient computation that is orders of magnitude faster than CCalc for many benchmark examples. In support of this, I created an automated translation system Cplus2ASP that implements the translation and encoding method and automatically invokes the necessary software to solve the translated input programs.

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Created

Date Created
  • 2011