Languages with self-reference I: foundations (or: we can have everything in first-order logic])
Artificial Intelligence
The liar; an essay in truth and circularity
The liar; an essay in truth and circularity
Logical foundations of artificial intelligence
Logical foundations of artificial intelligence
Languages with self-reference II: knowledge, belief and modality
Artificial Intelligence
Representations of commonsense knowledge
Representations of commonsense knowledge
Handbook of logic in artificial intelligence and logic programming (vol. 1)
Handbook of logic in artificial intelligence and logic programming (vol. 1)
Mechanising Partiality With Re-implementation
KI '97 Proceedings of the 21st Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
A Mechanization of Strong Kleene Logic for Partial Functions
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
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A powerful syntactic theory as well as expressive modal logics have to deal with self-referentiality. Self-referentiality and paradoxes seem to be close neighbours and depending on the logical system, they have devastating consequences, since they introduce contradictions and trivialise the logical system. There is a large amount of different attempts to tackle these problems. Some of them are compared in this paper, futhermore a simple approach based on a three-valued logic is advocated. In this approach paradoxes may occur and are treated formally. However, it is necessary to be very careful, otherwise a system built on such an attempt trivialises as well. In order to be able to formally deal with such a system, the reason for self-referential paradoxes is studied in more detail and a semantical condition on the connectives is given such that paradoxes are excluded.