Awareness, negation and Logical omniscience | Zendy

Zhisheng Huang | Zendy; Karen L. Kwast | Zendy

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Awareness, negation and Logical omniscience

Author(s) -

Zhisheng Huang,

Karen L. Kwast

Publication year - 1991

Publication title -

lecture notes in computer science

Language(s) - English

Resource type - Book series

SCImago Journal Rank - 0.249

H-Index - 400

eISSN - 1611-3349

pISSN - 0302-9743

ISBN - 0-387-53686-8

DOI - 10.1007/bfb0018448

Subject(s) - negation , omniscience , intuition , epistemology , computer science , closure (psychology) , logical consequence , negation as failure , mathematics , calculus (dental) , artificial intelligence , philosophy , programming language , autoepistemic logic , description logic , medicine , dentistry , multimodal logic , economics , market economy

General Epistemic Logics suer from the problem of logical omniscience, which is that an agent's knowledge and beliefs are closed under implication. There have been many attempts to solve the problem of logical omniscience. However, accord- ing to our intuition, sometimes an agent's knowledge and beliefs are indeed closed under implication. Based on the notion of awareness, we introduce two kinds of negations: general negation and strong negation. Moreover, four kinds of impli- cations, general implication, strong implication, weak implication, and semi-strong implication, are introduced to correspond with the two kinds of negations. In our logics of regular awareness, explicit beliefs are not necessarily closed under general implication, which means that agents are not logically omniscient. However, ex- plicit beliefs are closed under strong implication and semi-strong implication, which captures an intuitive closure property of beliefs.

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