Abstracting probabilistic models: Relations, constraints and beyond

Belle, Vaishak

doi:10.1016/j.knosys.2020.105976

Cited by 4 publications

(7 citation statements)

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“…By using abstraction, we can get rid of noisy actions and we may abstract away sensors such that the high-level reasoner no longer needs to reason about probabilistic sensors or effectors. While abstractions need to be manually constructed, future work may explore abstraction generation algorithms based on (Holtzen, van den Broeck, and Millstein 2018;Belle 2020). A further extension to our work might be to provide conditions under which we can modify the low-level program, with for example new sensors and actuators with different error profiles, but still show that of the high-level program remains unmodified to achieve the intended high-level goal.…”

Section: Discussionmentioning

confidence: 99%

“…In contrast to this work, they assume non-probabilistic and deterministic actions. On the other hand, Belle (2020) defines abstraction in a probabilistic but static propositional language and describes a search algorithm to derive such abstractions. In this paper, we build on the two approaches to obtain abstraction in a probabilistic and dynamic first-order language with an unbounded domain.…”

Section: Background and Related Workmentioning

confidence: 99%

“…Abstraction typically involves suppressing irrelevant information and therefore allows reasoning about complex problems that would otherwise be infeasible. In the context of intelligent agents, abstraction typically serves three purposes (Belle 2020): (1) it provides a way to structure knowledge, (2) it allows reasoning about larger problems by abstracting the problem domain, resulting in a smaller search space, (3) it may provide more meaningful explanations and is therefore critical for explainable AI. The need for abstraction becomes particularly apparent when dealing with robotic systems: as a robot acts in a dynamic environment with imperfect sensors and actuators, its actions are inherently noisy.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we present an abstraction framework for robot programs with probabilistic belief: Starting with the logic DS (Belle and Lakemeyer 2017), a modal variant of the situation calculus with probabilistic belief, we describe a transition semantics for noisy GOLOG programs in Section 3. Based on this transition semantics, we then propose a notion of abstraction of noisy programs, building on top of abstraction of probabilistic static models (Belle 2020) and deterministic dynamic models (Banihashemi, De Giacomo, and Lespérance 2017). We do so by defining a notion of bisimulation of probabilistic dynamic systems in Section 4 and we show that the notions of sound and complete abstraction carry over.…”

Section: Introductionmentioning

confidence: 99%

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Abstracting Noisy Robot Programs

Hofmann¹,

Belle²

2022

Preprint

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ion is a commonly used process to represent some low-level system by a more coarse specification with the goal to omit unnecessary details while preserving important aspects. While recent work on abstraction in the situation calculus has focused on non-probabilistic domains, we describe an approach to abstraction of probabilistic and dynamic systems. Based on a variant of the situation calculus with probabilistic belief, we define a notion of bisimulation that allows to abstract a detailed probabilistic basic action theory with noisy actuators and sensors by a possibly deterministic basic action theory. By doing so, we obtain abstract Golog programs that omit unnecessary details and which can be translated back to a detailed program for actual execution. This simplifies the implementation of noisy robot programs, opens up the possibility of using deterministic reasoning methods (e.g., planning) on probabilistic problems, and provides domain descriptions that are more easily understandable and explainable.

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Section: Discussionmentioning

confidence: 99%

Section: Background and Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Abstracting Noisy Robot Programs

Hofmann¹,

Belle²

2022

Preprint

Self Cite

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“…In particular, in computer science, it is often understood as the process of mapping one representation onto a simpler representation by suppressing irrelevant information. In fact, integrating low-level behavior with high-level reasoning, exploiting relational representations to reduce the number of inference computations, and many other search space reduction techniques can all loosely be seen as instances of abstraction [8].…”

Section: Logic For Machine Learningmentioning

confidence: 99%

Symbolic Logic Meets Machine Learning: A Brief Survey in Infinite Domains

Belle

2020

Lecture Notes in Computer Science

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The tension between deduction and induction is perhaps the most fundamental issue in areas such as philosophy, cognition and artificial intelligence (AI). The deduction camp concerns itself with questions about the expressiveness of formal languages for capturing knowledge about the world, together with proof systems for reasoning from such knowledge bases. The learning camp attempts to generalize from examples about partial descriptions about the world. In AI, historically, these camps have loosely divided the development of the field, but advances in cross-over areas such as statistical relational learning, neuro-symbolic systems, and high-level control have illustrated that the dichotomy is not very constructive, and perhaps even ill-formed. In this article, we survey work that provides further evidence for the connections between logic and learning. Our narrative is structured in terms of three strands: logic versus learning, machine learning for logic, and logic for machine learning, but naturally, there is considerable overlap. We place an emphasis on the following "sore" point: there is a common misconception that logic is for discrete properties, whereas probability theory and machine learning, more generally, is for continuous properties. We report on results that challenge this view on the limitations of logic, and expose the role that logic can play for learning in infinite domains.

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Knowledge representation and acquisition for ethical AI: challenges and opportunities

Belle

2023

Ethics Inf Technol

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Machine learning (ML) techniques have become pervasive across a range of different applications, and are now widely used in areas as disparate as recidivism prediction, consumer credit-risk analysis, and insurance pricing. Likewise, in the physical world, ML models are critical components in autonomous agents such as robotic surgeons and self-driving cars. Among the many ethical dimensions that arise in the use of ML technology in such applications, analyzing morally permissible actions is both immediate and profound. For example, there is the potential for learned algorithms to become biased against certain groups. More generally, in so much that the decisions of ML models impact society, both virtually (e.g., denying a loan) and physically (e.g., driving into a pedestrian), notions of accountability, blame and responsibility need to be carefully considered. In this article, we advocate for a two-pronged approach ethical decision-making enabled using rich models of autonomous agency: on the one hand, we need to draw on philosophical notions of such as beliefs, causes, effects and intentions, and look to formalise them, as attempted by the knowledge representation community, but on the other, from a computational perspective, such theories need to also address the problems of tractable reasoning and (probabilistic) knowledge acquisition. As a concrete instance of this tradeoff, we report on a few preliminary results that apply (propositional) tractable probabilistic models to problems in fair ML and automated reasoning of moral principles. Such models are compilation targets for certain types of knowledge representation languages, and can effectively reason in service some computational tasks. They can also be learned from data. Concretely, current evidence suggests that they are attractive structures for jointly addressing three fundamental challenges: reasoning about possible worlds + tractable computation + knowledge acquisition. Thus, these seems like a good starting point for modelling reasoning robots as part of the larger ecosystem where accountability and responsibility is understood more broadly.

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Abstracting probabilistic models: Relations, constraints and beyond

Cited by 4 publications

References 46 publications

Abstracting Noisy Robot Programs

Abstracting Noisy Robot Programs

Symbolic Logic Meets Machine Learning: A Brief Survey in Infinite Domains

Knowledge representation and acquisition for ethical AI: challenges and opportunities

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