Languages with self-reference I: foundations (or: we can have everything in first-order logic])
Artificial Intelligence
Generality in artificial intelligence
Communications of the ACM
Languages with self-reference II: knowledge, belief and modality
Artificial Intelligence
Truth and modality for knowledge representation
Truth and modality for knowledge representation
Artificial intelligence and mathematical theory of computation
Multilanguage hierarchical logics, or: how we can do without modal logics
Artificial Intelligence
Viewpoints Subsume Beliefs, Truth and Situations
AI*IA Proceedings of the 2nd Congress of the Italian Association for Artificial Intelligence on Trends in Artificial Intelligence
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
Reasoning about knowledge and action
IJCAI'77 Proceedings of the 5th international joint conference on Artificial intelligence - Volume 1
Propositional logic of context
AAAI'93 Proceedings of the eleventh national conference on Artificial intelligence
On the Dimensions of Context Dependence: Partiality, Approximation, and Perspective
CONTEXT '01 Proceedings of the Third International and Interdisciplinary Conference on Modeling and Using Context
Handling imperfect knowledge handling in Milord II for the identification of marine sponges
Applications of Uncertainty Formalisms
Staged computation with names and necessity
Journal of Functional Programming
ACM Transactions on Computational Logic (TOCL)
Axiom schemata as metalevel axioms: model theory
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
A reflective proof system for reasoning in contexts
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Quantificational logic of context
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
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We present a formalisation for the notion of viewpoint, a construct meant for expressing several varieties of relativised truth. The formalisation consists in a logic which extends first order predicate calculus with its own metalanguage, an axiomatization of provability and proper reflection rules. The extension is not conservative, but consistency is granted. Viewpoints are defined as set of reified meta-level sentences. A proof theory for viewponts is developed which enables to carry out proofs of statements involving several viewpoints. A semantic account of viewpoints is provided, dealing with issues of self referential theories and paradoxes, and exploiting the notion of contextual entailment. Notions such as beliefs, knowledge, absolute truth or truth relative to a situation can be uniformly modeled as provability in specialised viewpoints, obtained by imposing suitable constraints on viewpoints.