scholarly journals Distribution Bisimilarity via the Power of Convex Algebras

2021 ◽  
Vol Volume 17, Issue 3 ◽  
Author(s):  
Filippo Bonchi ◽  
Alexandra Silva ◽  
Ana Sokolova
Keyword(s):  
Probability Distributions ◽  
Belief State ◽  
Proof Technique ◽  
Extended Version ◽  
Transition Systems ◽  
Probabilistic Automata ◽  
Abstract Approach ◽  
Belief States ◽  
Combine Probability ◽  
Do So

Probabilistic automata (PA), also known as probabilistic nondeterministic labelled transition systems, combine probability and nondeterminism. They can be given different semantics, like strong bisimilarity, convex bisimilarity, or (more recently) distribution bisimilarity. The latter is based on the view of PA as transformers of probability distributions, also called belief states, and promotes distributions to first-class citizens. We give a coalgebraic account of distribution bisimilarity, and explain the genesis of the belief-state transformer from a PA. To do so, we make explicit the convex algebraic structure present in PA and identify belief-state transformers as transition systems with state space that carries a convex algebra. As a consequence of our abstract approach, we can give a sound proof technique which we call bisimulation up-to convex hull. Comment: Full (extended) version of a CONCUR 2017 paper, minor revision of the LMCS submission

Epistemic Teleology

2018 ◽  
Author(s):  
Ralph Wedgwood
Keyword(s):  
Belief State ◽  
Epistemic Consequentialism ◽  
The Difference ◽  
Belief States ◽  
Epistemic Teleology

Wedgwood focuses his discussion around two evaluative concepts: correctness and rationality. Wedgwood proposes that these two concepts are related in the following way: one belief state is more rational than another if and only if the first has less expected inaccuracy than the former. He argues, however, that this view should not be understood as a form of consequentialism since it is not the total consequences of a belief state that determine its rationality. The view is rather a version of epistemic teleology. Wedgwood deploys this view to illuminate the difference between synchronic and diachronic evaluation of belief states as well as to disarm objections that have been leveled against epistemic consequentialism.

Epistemic and Doxastic Contents

2019 ◽  
pp. 213-238
Author(s):  
Francesco Berto ◽  
Mark Jago
Keyword(s):  
Bounded Rationality ◽  
Logical Consequence ◽  
External World ◽  
Belief State ◽  
Impossible Worlds ◽  
Formal Models ◽  
Closure Principle ◽  
Primary Focus ◽  
Belief States ◽  
Trivial Consequence

The case for making belief states the primary focus of our analysis and for including impossible worlds in that analysis is outlined in this chapter. This allows the reader to deny various closure principles, although this won’t help defeat worries about external-world scepticism. The issue that concerns the authors most is the problem of bounded rationality: belief states seem to be closed under ‘easy’ trivial consequence, but not under full logical consequence, and yet the former implies the latter. The solution presented here is that some trivial closure principle must fail on a given belief state, yet it is indeterminate just where this occurs. Formal models of belief states along these lines are given and it is shown that they respect the indeterminacy-of-closure intuition. Finally, the chapter discusses how we might square this approach with the fact that some people seem to believe contradictions.

scholarly journals Revising Probabilities and Full Beliefs

2020 ◽  
Vol 49 (5) ◽  
pp. 1005-1039 ◽  
Author(s):  
Sven Ove Hansson
Keyword(s):  
Formal Model ◽  
Belief Change ◽  
Learning From Experience ◽  
Epistemic Agent ◽  
Set Operations ◽  
Proposed Model ◽  
Formal Properties ◽  
Belief States ◽  
Do So ◽  
Belief Set

Abstract A new formal model of belief dynamics is proposed, in which the epistemic agent has both probabilistic beliefs and full beliefs. The agent has full belief in a proposition if and only if she considers the probability that it is false to be so close to zero that she chooses to disregard that probability. She treats such a proposition as having the probability 1, but, importantly, she is still willing and able to revise that probability assignment if she receives information that gives her sufficient reasons to do so. Such a proposition is (presently) undoubted, but not undoubtable (incorrigible). In the formal model it is assigned a probability 1 − δ, where δ is an infinitesimal number. The proposed model employs probabilistic belief states that contain several underlying probability functions representing alternative probabilistic states of the world. Furthermore, a distinction is made between update and revision, in the same way as in the literature on (dichotomous) belief change. The formal properties of the model are investigated, including properties relevant for learning from experience. The set of propositions whose probabilities are infinitesimally close to 1 forms a (logically closed) belief set. Operations that change the probabilistic belief state give rise to changes in this belief set, which have much in common with traditional operations of belief change.

scholarly journals A Framework for Sequential Planning in Multi-Agent Settings

2005 ◽  
Vol 24 ◽  
pp. 49-79 ◽  
Author(s):  
P. J. Gmytrasiewicz ◽  
P. Doshi
Keyword(s):  
Traditional Approach ◽  
Value Functions ◽  
Value Iteration ◽  
Markov Decision ◽  
Multi Agent ◽  
Carry Over ◽  
The Cost ◽  
Partially Observable ◽  
Belief States ◽  
Do So

This paper extends the framework of partially observable Markov decision processes (POMDPs) to multi-agent settings by incorporating the notion of agent models into the state space. Agents maintain beliefs over physical states of the environment and over models of other agents, and they use Bayesian updates to maintain their beliefs over time. The solutions map belief states to actions. Models of other agents may include their belief states and are related to agent types considered in games of incomplete information. We express the agents' autonomy by postulating that their models are not directly manipulable or observable by other agents. We show that important properties of POMDPs, such as convergence of value iteration, the rate of convergence, and piece-wise linearity and convexity of the value functions carry over to our framework. Our approach complements a more traditional approach to interactive settings which uses Nash equilibria as a solution paradigm. We seek to avoid some of the drawbacks of equilibria which may be non-unique and do not capture off-equilibrium behaviors. We do so at the cost of having to represent, process and continuously revise models of other agents. Since the agent's beliefs may be arbitrarily nested, the optimal solutions to decision making problems are only asymptotically computable. However, approximate belief updates and approximately optimal plans are computable. We illustrate our framework using a simple application domain, and we show examples of belief updates and value functions.

Human Health Risk Assessment via Amalgamation of Probability and Fuzzy Numbers

2019 ◽  
pp. 99-123
Author(s):  
Palash Dutta
Keyword(s):  
Risk Assessment ◽  
Health Risk ◽  
Human Health ◽  
Health Risk Assessment ◽  
Fuzzy Numbers ◽  
Probability Distributions ◽  
Human Health Risk ◽  
Human Health Risk Assessment ◽  
Assessment Model ◽  
Combine Probability

This chapter presents an approach to combine probability distributions with imprecise (fuzzy numbers) parameters (mean and standard deviation) as well as fuzzy numbers (FNs) of various types and shapes within the same framework. The amalgamation of probability distribution and fuzzy numbers are done by generating three algorithms. Human health risk assessment is performed through the proposed algorithms. It is found that the chapter provides an exertion to perform human health risk assessment in a specific manner that has more efficacies because of its capacity to exemplify uncertainties of risk assessment model in its own fashion. It affords assistance to scientists, environmentalists, and experts to perform human health risk assessment providing better efficiency to the output.

scholarly journals The Anisotropic Glassy Properties of Decagonal Quasicrystals

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Dragoş-Victor Anghel ◽  
Dmitry V. Churochkin
Keyword(s):  
Strain Field ◽  
Sound Absorption ◽  
Probability Distributions ◽  
Symmetric Tensor ◽  
Coupling Constants ◽  
Extended Version ◽  
Tunneling Model ◽  
Decagonal Quasicrystals ◽  
Symmetry Properties ◽  
Two Level Systems

We use an extended version of the standard tunneling model to explain the anisotropic sound absorption in decagonal quasicrystals. The glassy properties are determined by an ensemble of two level systems (TLSs), arbitrarily oriented. The TLS is characterized by a 3 × 3 symmetric tensor, [T], which couples to the strain field, [S], through a 3 × 3 × 3 × 3 tensor of coupling constants, [R]. The structure of [R] reflects the symmetry of the quasicrystal. We also analyze the probability distributions of the elements of [T] in this particular model for a better understanding of the characteristics of “isotropic” and “anisotropic” distributions of the ensemble of TLSs. We observe that the distribution of the elements is neither simple nor intuitive and therefore it is difficult to guess ita priory, using qualitative arguments based on the symmetry properties.

scholarly journals Observations on Darwiche and Pearl's Approach for Iterated Belief Revision

2019 ◽  
Author(s):  
Theofanis Aravanis ◽  
Pavlos Peppas ◽  
Mary-Anne Williams
Keyword(s):  
Belief Revision ◽  
Possible Worlds ◽  
Belief State ◽  
Strong Sense ◽  
Preference Ordering ◽  
Satisfactory Solution ◽  
Entire Class ◽  
Seminal Work ◽  
Iterated Belief Revision ◽  
Belief States

Notwithstanding the extensive work on iterated belief revision, there is, still, no fully satisfactory solution within the classical AGM paradigm. The seminal work of Darwiche and Pearl (DP approach, for short) remains the most dominant, despite its well-documented shortcomings. In this article, we make further observations on the DP approach. Firstly, we prove that the DP postulates are, in a strong sense, inconsistent with Parikh's relevance-sensitive axiom (P), extending previous initial conflicts. Immediate consequences of this result are that an entire class of intuitive revision operators, which includes Dalal's operator, violates the DP postulates, as well as that the Independence postulate and Spohn's conditionalization are inconsistent with (P). Lastly, we show that the DP postulates allow for more revision polices than the ones that can be captured by identifying belief states with total preorders over possible worlds, a fact implying that a preference ordering (over possible worlds) is an insufficient representation for a belief state.

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