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LogAG: An algebraic non-monotonic logic for reasoning with graded propositions

LogAG: An algebraic non-monotonic logic for reasoning with graded propositions We present LogAG, a weighted algebraic non-monotonic logic for reasoning with graded beliefs. LogAG is algebraic in that it is a language of only terms, some of which denote propositions and may be associated with ordered grades. The grades could be taken to represent a wide variety of phenomena including preference degrees, priority levels, trust ranks, and uncertainty measures. Reasoning in LogAG is non-monotonic and may give rise to contradictions. Belief revision is, hence, an integral part of reasoning and is guided by the grades. This yields a quite expressive language providing an interesting alternative to the currently existing approaches to non-monotonicity. We show how LogAG can be utilised for modelling resource-bounded reasoning; simulating inconclusive reasoning with circular, liar-like sentences; and reasoning about information arriving over a chain of sources each with a different degree of trust. While there certainly are accounts in the literature for each of these issues, we are not aware of any single framework that accounts for them all like LogAG does. We also show how LogAG captures a wide variety of non-monotonic logical formalisms. As such, LogAG is a unifying framework for non-monotonicity which is flexible enough to admit a wide array of potential uses. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Mathematics and Artificial Intelligence Springer Journals

LogAG: An algebraic non-monotonic logic for reasoning with graded propositions

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References (85)

Publisher
Springer Journals
Copyright
Copyright © Springer Nature Switzerland AG 2020. corrected publication 2020
ISSN
1012-2443
eISSN
1573-7470
DOI
10.1007/s10472-020-09697-0
Publisher site
See Article on Publisher Site

Abstract

We present LogAG, a weighted algebraic non-monotonic logic for reasoning with graded beliefs. LogAG is algebraic in that it is a language of only terms, some of which denote propositions and may be associated with ordered grades. The grades could be taken to represent a wide variety of phenomena including preference degrees, priority levels, trust ranks, and uncertainty measures. Reasoning in LogAG is non-monotonic and may give rise to contradictions. Belief revision is, hence, an integral part of reasoning and is guided by the grades. This yields a quite expressive language providing an interesting alternative to the currently existing approaches to non-monotonicity. We show how LogAG can be utilised for modelling resource-bounded reasoning; simulating inconclusive reasoning with circular, liar-like sentences; and reasoning about information arriving over a chain of sources each with a different degree of trust. While there certainly are accounts in the literature for each of these issues, we are not aware of any single framework that accounts for them all like LogAG does. We also show how LogAG captures a wide variety of non-monotonic logical formalisms. As such, LogAG is a unifying framework for non-monotonicity which is flexible enough to admit a wide array of potential uses.

Journal

Annals of Mathematics and Artificial Intelligence – Springer Journals

Published: Jun 20, 2020

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