Towards the full information chain theory: answer depth and source models

David Grace; Eugene Perevalov

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Towards the full information chain theory: answer depth and source models

Eugene Perevalov, David Grace

Data Analysis, Statistics and Probability · Submitted 12 Dec 2012

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim It turns out to be possible to introduce a notion of an information source capacity as the highest value of the answer depth the source is capable of providing.

how it is stated · hedged possibility 0.66 read the record →

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,451 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.37 · human participants 0.03 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.16 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

A problem of optimal information acquisition for its use in general decision making problems is considered. This motivates the need for developing quantitative measures of information sources' capabilities for supplying accurate information depending on the particular content of the latter. A companion article developed the notion of a question difficulty functional for questions concerning input data for a decision making problem. Here, answers which an information source may provide in response to such questions are considered. In particular, a real valued answer depth functional measuring the degree of accuracy of such answers is introduced and its overall form is derived under the assumption of isotropic knowledge structure of the information source. Additionally, information source models that relate answer depth to question difficulty are discussed. It turns out to be possible to introduce a notion of an information source capacity as the highest value of the answer depth the source is capable of providing.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	A problem of optimal information acquisition for its use in general decision making problems is considered.	background 0.99	0.45	0.04	asserted 0.85
s1	This motivates the need for developing quantitative measures of information sources' capabilities for supplying accurate information depending on the particular content of the latter.	background 0.56	0.10	0.04	asserted 0.97
s2	A companion article developed the notion of a question difficulty functional for questions concerning input data for a decision making problem.	background 0.99	0.26	0.03	asserted 1.00
s3	Here, answers which an information source may provide in response to such questions are considered.	contribution 0.65	0.50	0.02	asserted 0.75
s4	In particular, a real valued answer depth functional measuring the degree of accuracy of such answers is introduced and its overall form is derived under the assumption of isotropic knowledge structure of the information source.	contribution 0.86	0.92	0.22	asserted 1.00
s5	Additionally, information source models that relate answer depth to question difficulty are discussed.	contribution 0.69	0.73	0.06	asserted 0.78
s6	It turns out to be possible to introduce a notion of an information source capacity as the highest value of the answer depth the source is capable of providing.	result 0.63	0.87	0.57	hedged possibility 0.66

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

A problem of optimal information acquisition for its use in general decision making problems is considered. This motivates the need for developing quantitative measures of information sources' capabilities for supplying accurate information depending on the particular content of the latter. A companion article developed the notion of a question difficulty functional for questions concerning input data for a decision making problem. Here, answers which an information source may provide in response to such questions are considered. In particular, a real valued answer depth functional measuring the degree of accuracy of such answers is introduced and its overall form is derived under the assumption of isotropic knowledge structure of the information source. Additionally, information source models that relate answer depth to question difficulty are discussed. It turns out to be possible to introduce a notion of an information source capacity as the highest value of the answer depth the source is capable of providing.

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How the literature uses it

3 arXiv papers cite this in 26 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 21 sentences without a confident label

Builds on it 1 paper

Our work in [ref] goes beyond that on the calculus of inquiry in that it introduces the concept of pseudoenergy as a measure of source specific difficulty of various questions to the given information source.

Towards the full information chain theory: expected loss and information relevance · Related work · 0.85

Uses its method or tool 1 paper

The approach developed here is based on a theory of information exchange between the agent and information source(s) that is developed in [ref] .

Towards the full information chain theory: solution methods for optimal information acquisition problem · Introduction · 0.80

Cites it as support 1 paper

In other words, the information-related complexity for the given task is inherently a real-valued function, and not just a real number. * It was argued, based on results of [ref] , that the minimum information quantity necessary to complete the task to the given degree should be really interpreted as appropriate quasi-quantity that takes into account the degree of difficulty of obtaining the corresponding information in the given environment.

Information-related complexity: a problem-oriented approach · Conclusion · 0.98

Cites it as background 1 paper

In Section [ref], main results of [ref] that are necessary for the developments in this paper are reviewed.

Towards the full information chain theory: solution methods for optimal information acquisition problem · Introduction · 0.80

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