Logic and Probabilistic Update

Demey, Lorenz; Kooi, Barteld

doi:10.1007/978-3-319-06025-5_13

Cited by 10 publications

(11 citation statements)

References 38 publications

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“…The natural idea is to define a logical probability system, as Keynes [24], Reichenbach [9], Popper [7], and Carnap [18] did. Some researchers use probabilities as logical variables to set up probability logic [25], such as two types of probability logic proposed by Reichenbach [9] and Adams [26]. Additionally, many researchers want to unify probabilities and fuzzy sets [27][28][29] following Zadeh.…”

Section: Purpose Methods and Structure Of This Papermentioning

confidence: 99%

The P–T Probability Framework for Semantic Communication, Falsification, Confirmation, and Bayesian Reasoning

2020

Philosophies

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Many researchers want to unify probability and logic by defining logical probability or probabilistic logic reasonably. This paper tries to unify statistics and logic so that we can use both statistical probability and logical probability at the same time. For this purpose, this paper proposes the P–T probability framework, which is assembled with Shannon’s statistical probability framework for communication, Kolmogorov’s probability axioms for logical probability, and Zadeh’s membership functions used as truth functions. Two kinds of probabilities are connected by an extended Bayes’ theorem, with which we can convert a likelihood function and a truth function from one to another. Hence, we can train truth functions (in logic) by sampling distributions (in statistics). This probability framework was developed in the author’s long-term studies on semantic information, statistical learning, and color vision. This paper first proposes the P–T probability framework and explains different probabilities in it by its applications to semantic information theory. Then, this framework and the semantic information methods are applied to statistical learning, statistical mechanics, hypothesis evaluation (including falsification), confirmation, and Bayesian reasoning. Theoretical applications illustrate the reasonability and practicability of this framework. This framework is helpful for interpretable AI. To interpret neural networks, we need further study.

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Section: Purpose Methods and Structure Of This Papermentioning

confidence: 99%

The P–T Probability Framework for Semantic Communication, Falsification, Confirmation, and Bayesian Reasoning

2020

Philosophies

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“…In [38], dynamic logic is extended for knowledge, subjective probabilities and stochastic outcomes. Extending that framework, the notion of updating epistemic states in the presence of announcements and nested beliefs has been studied more comprehensively in [71,22,23]. Treating continuous probabilities is also considered for that family of logics in [60].…”

Section: Related Workmentioning

confidence: 99%

Regression and progression in stochastic domains

Belle

Levesque

2020

Artificial Intelligence

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Reasoning about degrees of belief in uncertain dynamic worlds is fundamental to many applications, such as robotics and planning, where actions modify state properties and sensors provide measurements, both of which are prone to noise. With the exception of limited cases such as Gaussian processes over linear phenomena, belief state evolution can be complex and hard to reason with in a general way, especially when the agent has to deal with categorical assertions, incomplete information such as disjunctive knowledge, as well as probabilistic knowledge. Among the many approaches for reasoning about degrees of belief in the presence of noisy sensing and acting, the logical account proposed by Bacchus, Halpern, and Levesque is perhaps the most expressive, allowing for such belief states to be expressed naturally as constraints. While that proposal is powerful, the task of how to plan effectively is not addressed. In fact, at a more fundamental level, the task of projection, that of reasoning about beliefs effectively after acting and sensing, is left entirely open. To aid planning algorithms, we study the projection problem in this work. In the reasoning about actions literature, there are two main solutions to projection: regression and progression. Both of these have proven enormously useful for the design of logical agents, essentially paving the way for cognitive robotics. Roughly, regression reduces a query about the future to a query about the initial state. Progression, on the other hand, changes the initial state according to the effects of each action and then checks whether the formula holds in the updated state. In this work, we show how both of these generalize in the presence of degrees of belief, noisy acting and sensing. Our results allow for both discrete and continuous probability distributions to be used in the specification of beliefs and dynamics.

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“…that is able to tackle these problems, thereby allowing us to capture a wide range of dynamic-epistemic situations more accurately. As an added bonus, many of the ideas we develop are well-suited for other applications in probabilistic dynamic epistemic logic [DK15,DS15].…”

Section: Introductionmentioning

confidence: 99%

“…And of course, <-and >-type probability formulas can be defined as the negations of the corresponding ≥-and ≤-type formulas, respectively.4 Note that this language has many commonalities with that ofDemey [Dem15]; also cf [DK15,DS15]…”

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confidence: 99%

The perfect surprise: a new analysis in dynamic epistemic logic

Vignero

Demey

2019

Logic Journal of the IGPL

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In this article, we present a new logical framework to think about surprise. This research does not just aim to better understand, model and predict human behaviour, but also attempts to provide tools for implementing artificial agents. Moreover, these artificial agents should then also be able to reap the same epistemic benefits from surprise as humans do. We start by discussing the dominant literature regarding propositional surprise and explore its shortcomings. These shortcomings are of both an empirical and a conceptual nature. Next, we propose a philosophical solution to the problems that ail these systems, based on the notion of issue of epistemic interest. Finally, we give a formal framework to think about surprise. More specifically, we develop a probabilistic dynamic epistemic logic (called $\mathcal{SURPRISE!}$) that succeeds at formalizing the relevant philosophical concepts. This will be done through an issue management system grounded in topology. As an added bonus, the additional expressive power allows us to capture a richer variety of scenarios, and it also enables a more careful analysis of said scenarios.

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Logic and Probabilistic Update

Cited by 10 publications

References 38 publications

The P–T Probability Framework for Semantic Communication, Falsification, Confirmation, and Bayesian Reasoning

The P–T Probability Framework for Semantic Communication, Falsification, Confirmation, and Bayesian Reasoning

Regression and progression in stochastic domains

The perfect surprise: a new analysis in dynamic epistemic logic

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