Belief, awareness, and limited reasoning
Artificial Intelligence
Reasoning about knowledge
A Deduction Model of Belief
Models for the Logic of Proofs
LFCS '97 Proceedings of the 4th International Symposium on Logical Foundations of Computer Science
Reasoning about knowledge in philosophy: the paradigm of epistemic logic
TARK '86 Proceedings of the 1986 conference on Theoretical aspects of reasoning about knowledge
On epistemic logic and logical omniscience
TARK '86 Proceedings of the 1986 conference on Theoretical aspects of reasoning about knowledge
Theoretical Computer Science - Clifford lectures and the mathematical foundations of programming semantics
Making knowledge explicit: how hard it is
Theoretical Computer Science - Clifford lectures and the mathematical foundations of programming semantics
On the complexity of the reflected logic of proofs
Theoretical Computer Science - Clifford lectures and the mathematical foundations of programming semantics
Introducing Justification into Epistemic Logic
Journal of Logic and Computation
Avoiding logical omniscience and perfect reasoning: a survey
AI Communications
Dealing with logical omniscience
TARK '07 Proceedings of the 11th conference on Theoretical aspects of rationality and knowledge
Evidence reconstruction of epistemic modal logic S5
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Logical omniscience via proof complexity
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
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It is well known that Modal Epistemic logic (MEL) suffers from the problem of logical omniscience. In this paper, we will argue that in order to solve the problem, the temporal dimension of knowledge has to be revealed and following this analysis, we present a general epistemic framework, timed Modal Epistemic Logic (tMEL), modified from MEL, such that the time at which a formula is known by an agent based on his reasoning procedure is explicitly stated. With the help of the additional temporal devices, we are able to determine what is actually known by the agent within a reasonable time of reasoning. The discussions will focus on tS4, the tMEL counterpart of S4, but the method can be uniformly generalized to the study of other tMEL logics. Both the semantics and axiomatic proof systems will be provided, accompanied by soundness and completeness results, and other technical features of tMEL are also examined. This work originates from the study of Justification Logic, which shapes many aspects of this paper, and is also a direct response to the request to utilize the use of awareness functions such that time can be added to the picture. A generalized awareness function is employed in the semantics to trace when a formula is deduced.