Inquiry Calculus and the Issue of Negative Higher Order Informations
In this paper, we will give the derivation of an inquiry calculus, or, equivalently, a Bayesian information theory. From simple ordering follow lattices, or, equivalently, algebras. Lattices admit a quantification, or, equivalently, algebras may be extended to calculi. The general rules of quantific...
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-11-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/19/11/622 |
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| author | H. R. Noel van Erp Ronald O. Linger Pieter H. A. J. M. van Gelder |
| author_facet | H. R. Noel van Erp Ronald O. Linger Pieter H. A. J. M. van Gelder |
| author_sort | H. R. Noel van Erp |
| collection | DOAJ |
| description | In this paper, we will give the derivation of an inquiry calculus, or, equivalently, a Bayesian information theory. From simple ordering follow lattices, or, equivalently, algebras. Lattices admit a quantification, or, equivalently, algebras may be extended to calculi. The general rules of quantification are the sum and chain rules. Probability theory follows from a quantification on the specific lattice of statements that has an upper context. Inquiry calculus follows from a quantification on the specific lattice of questions that has a lower context. There will be given here a relevance measure and a product rule for relevances, which, taken together with the sum rule of relevances, will allow us to perform inquiry analyses in an algorithmic manner. |
| first_indexed | 2024-04-12T19:33:50Z |
| format | Article |
| id | doaj.art-23cd80c0aff64ef490b82bbc0ee05fec |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-12T19:33:50Z |
| publishDate | 2017-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-23cd80c0aff64ef490b82bbc0ee05fec2022-12-22T03:19:15ZengMDPI AGEntropy1099-43002017-11-01191162210.3390/e19110622e19110622Inquiry Calculus and the Issue of Negative Higher Order InformationsH. R. Noel van Erp0Ronald O. Linger1Pieter H. A. J. M. van Gelder2Safety and Security Science Group, TU Delft, 2628 BX Delft, The NetherlandsSafety and Security Science Group, TU Delft, 2628 BX Delft, The NetherlandsSafety and Security Science Group, TU Delft, 2628 BX Delft, The NetherlandsIn this paper, we will give the derivation of an inquiry calculus, or, equivalently, a Bayesian information theory. From simple ordering follow lattices, or, equivalently, algebras. Lattices admit a quantification, or, equivalently, algebras may be extended to calculi. The general rules of quantification are the sum and chain rules. Probability theory follows from a quantification on the specific lattice of statements that has an upper context. Inquiry calculus follows from a quantification on the specific lattice of questions that has a lower context. There will be given here a relevance measure and a product rule for relevances, which, taken together with the sum rule of relevances, will allow us to perform inquiry analyses in an algorithmic manner.https://www.mdpi.com/1099-4300/19/11/622inquiry calculusBayesianinformation theoryproduct rulerelevancemeasureautomated inquiry |
| spellingShingle | H. R. Noel van Erp Ronald O. Linger Pieter H. A. J. M. van Gelder Inquiry Calculus and the Issue of Negative Higher Order Informations Entropy inquiry calculus Bayesian information theory product rule relevance measure automated inquiry |
| title | Inquiry Calculus and the Issue of Negative Higher Order Informations |
| title_full | Inquiry Calculus and the Issue of Negative Higher Order Informations |
| title_fullStr | Inquiry Calculus and the Issue of Negative Higher Order Informations |
| title_full_unstemmed | Inquiry Calculus and the Issue of Negative Higher Order Informations |
| title_short | Inquiry Calculus and the Issue of Negative Higher Order Informations |
| title_sort | inquiry calculus and the issue of negative higher order informations |
| topic | inquiry calculus Bayesian information theory product rule relevance measure automated inquiry |
| url | https://www.mdpi.com/1099-4300/19/11/622 |
| work_keys_str_mv | AT hrnoelvanerp inquirycalculusandtheissueofnegativehigherorderinformations AT ronaldolinger inquirycalculusandtheissueofnegativehigherorderinformations AT pieterhajmvangelder inquirycalculusandtheissueofnegativehigherorderinformations |