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<p>This paper explores two distinct forms of forgetting within epistemic logic: forgetting the truth value of atomic propositions and forgetting the awareness of atomic propositions. It demonstrates that the modal operators corresponding to these types of forgetting maintain closure under conjunction and disjunction operations. We have provided a definition of bisimulation and proved that bisimulation implies modal equivalence under our language. The paper introduces an axiom system for the Epistemic Logic of Forgetting (FEL) and establishes its soundness. Using the axioms and rules, we have derived two theorems which are analogous to the “No Miracles” property in Epistemic Temporal Logic (ETL). Furthermore, through the application of reduction axioms, it proves that FEL can be reduced to Awareness Logic (AL), thus demonstrating its completeness.</p>

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The epistemic logic of forgetting: forgetting awareness and forgetting truth values

  • 期刊论文

  • 发表日期：

    2026年2月23日

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  • Linlin Han,
  • Meiyun Guo

摘要

This paper explores two distinct forms of forgetting within epistemic logic: forgetting the truth value of atomic propositions and forgetting the awareness of atomic propositions. It demonstrates that the modal operators corresponding to these types of forgetting maintain closure under conjunction and disjunction operations. We have provided a definition of bisimulation and proved that bisimulation implies modal equivalence under our language. The paper introduces an axiom system for the Epistemic Logic of Forgetting (FEL) and establishes its soundness. Using the axioms and rules, we have derived two theorems which are analogous to the “No Miracles” property in Epistemic Temporal Logic (ETL). Furthermore, through the application of reduction axioms, it proves that FEL can be reduced to Awareness Logic (AL), thus demonstrating its completeness.