Abstract
In multiple-agent logic, a formula is in the form of (a, A) where a is a propositional formula and A is a subset of agents. It states that at least all agents in A believe that a is true. This paper presents a method of refutation for this logic, based on a general resolution principle and using a linear strategy, which is sound and complete. This strategy is then extended so as to deal with certainty levels. It manipulates formulas in the form \((a,\alpha /A)\) expressing that all agents in set A believe at least at some level \(\alpha \) that a is true. Finally, an experimental study is provided with the aim to estimate the performance of the proposed algorithms.
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Notes
- 1.
It should be noticed that a base \(\varSigma =\{(a_1, \alpha _1/A_1), ..., (a_n, \alpha _n/ A_n)\}\) can be equivalently rewritten as a collection of at most \(2^n\) possibilistic logic bases, each of them associated with an element of the partition of All induced by the \(A_i\)’s. However, it is in generally computationally better to handle the initial base in a global way using the procedure described in this paper.
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Belhadi, A., Dubois, D., Khellaf-Haned, F., Prade, H. (2016). Reasoning with Multiple-Agent Possibilistic Logic. In: Schockaert, S., Senellart, P. (eds) Scalable Uncertainty Management. SUM 2016. Lecture Notes in Computer Science(), vol 9858. Springer, Cham. https://doi.org/10.1007/978-3-319-45856-4_5
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