Abstract
In this paper, we propose logics for reasoning about belief and evidence. Starting from justification logic (JL) in which the reasons why a fact is believed are explicitly represented as justification terms, we explore the relationship between justified belief and fused information from different evidential sources. We argue that the expressive power of JL is inadequate for our purpose, because, while a justification formula can represent that a piece of evidence is admissible for the belief, it cannot express whether the evidence has been actually observed. Therefore, to address the issue, we propose more fine-grained JL’s that can express the informational content of evidence, and the actual observation of evidence is definable in such logics. As a byproduct, we also show that the proposed logics are easily extended to accommodate dynamic evidential reasoning. Consequently, we can integrate JL and dynamic epistemic logic (DEL) paradigms in a natural way.
The work is partially supported by the Ministry of Science and Technology of Taiwan under Grants MOST 105-2410-H-346-006-MY2 and MOST 104-2221-E-001-010-MY3.
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Notes
- 1.
For the purpose of the paper, the difference among belief, knowledge, and information is not important. Hence, hereafter, we use epistemic reasoning to denote reasoning about any kind of informational attitude for an agent.
- 2.
An arbitrary subset of formulas of the form \(c_n:c_{n-1}:\cdots c_1:\varphi \) is called a constant specification (CS) [2]. More generally, we can replace the rule with a CS. Then, the rule corresponds to the special case of total CS in which the CS is the set of all such formulas.
- 3.
Syntactically, it seems more natural to use \(\sigma _1\lesssim \sigma _2\) to denote that \(\sigma _1\) is at most as informative as \(\sigma _2\). However, our reading is based on the semantic viewpoint, which means that the set of accessible worlds for \(\sigma _1\) is a subset of that for \(\sigma _2\).
- 4.
\(|\varphi |=\{u\in W\mid u\Vdash \varphi \}\) is the truth set of \(\varphi \).
- 5.
We ignore the quantum observation that may change the outcome of observation itself.
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Fan, TF., Liau, CJ. (2016). Reasoning About Justified Belief Based on the Fusion of Evidence. In: Michael, L., Kakas, A. (eds) Logics in Artificial Intelligence. JELIA 2016. Lecture Notes in Computer Science(), vol 10021. Springer, Cham. https://doi.org/10.1007/978-3-319-48758-8_16
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