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Towards a many‐valued logic of quantified belief: The information lattice
Department of Computer and Information Science, University of Linköping, Linköping, Sweden. (AASS)ORCID iD: 0000-0002-9477-4044
1991 (English)In: International Journal of Intelligent Systems, ISSN 0884-8173, Vol. 6, no 2, 135-166 p.Article in journal (Refereed) Published
Abstract [en]

In a previous article we introduced extended logical operators, based on the Dubois family of T-norms and their dual T-conorms, to induce a semantics for a language involving and, or, and negation. Thus, given these logical operators and an arbitrary set-up S (a mapping from atomic formulas into a set of truth-values), we extended S to a mapping of all formulas into a set of truth-values defined as belief/disbelief pairs. Then using a particular partial order between belief/disbelief pairs to define entailment we were able to derive a many-valued variant of the so-called relevance logic. Here we introduce the notion of the so-called information lattice built upon another type of partial order between belief/disbelief pairs. Furthermore, we introduce specific meet and join operations and use them to provide answers to three fundamental questions: How does the reasoning machine represent belief and/or disbelief in the validity of the constituents of a complex formula when it is supplied with belief and/or disbelief in the validity of this complex formula as a whole; how does it determine the amount of belief and/or disbelief to be assigned to complex formulas in an epistemic state, that is, a collection of set-ups; and finally, how does it change its present belief and/or disbelief in the validity of formulas already in its data base, when provided with an input bringing in new belief and/or disbelief in the validity of these formulas.

Place, publisher, year, edition, pages
John Wiley & Sons, 1991. Vol. 6, no 2, 135-166 p.
Keyword [en]
symbolic reasoning, reasoning with uncertainty, representation of uncertainty
National Category
Engineering and Technology
Research subject
Computer Science; Computer Engineering
Identifiers
URN: urn:nbn:se:oru:diva-42522DOI: 10.1002/int.4550060204ISI: A1991FB18100003Scopus ID: 2-s2.0-0026123597OAI: oai:DiVA.org:oru-42522DiVA: diva2:786840
Available from: 2015-02-06 Created: 2015-02-06 Last updated: 2017-10-17Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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  • Other style
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Language
  • de-DE
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