A three-valued quantificational logic of context
In this paper we set a three-valued quantificational multi-modal logic which can be used in characterizing the general logical properties of contexts and those of agents. A new non-Kripke style framework of semantics is introduced, and a Hilbert style proof system is proposed for this logic which is proved to be sound and complete as main results of this paper. This logic extends standard quantificational multi-modal logic of knowledge and belief in three directions. Firstly, we can make explicit quantification over modalities. Secondly, it is not necessary that all first-order structures in a particular model have the same domain and the same language. Each context or agent not only may have its own language and domain of objects, but also deferent languages and domains in the view-points of deferent contexts or agents. Thirdly, this logic is three-valued and any sentence in a particular model may be true, false and meaningless.
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- 1.McCarthy, J.: Generality in artificial intelligence. Comm. of ACM,30 (1987) 1030–1035.Google Scholar
- 2.Guha, R.V.: Context: A formalization an Some Applications. Ph.D. thesis, Stanford University, 1991Google Scholar
- 3.Guha, R.V and Lenat, D.B.:Cyc: A midterm report, Af Magazine, 11 (1990) 32–59.Google Scholar
- 4.McCarthy, J.: Notes on formalizing context. In Proceedings IJCAI-93.Google Scholar
- 5.Shoham, Y.: Varieties of context. In Vladimir Lifschitz, editor, Artificial Intelligence and Mathematical Theory of Computation: Papers in Honor of John McCarthy, Academic Press, 1991.Google Scholar
- 6.Weyhrauch, R.W.: Prolegomena to a Theory of Mechanized Formal Reasoning. Artificial Intelligence. 13 (1980): 133–176.Google Scholar
- 7.Buvac, S., Buvac, V. and Mason, I.A.: Metamathematics of contexts. Fundamenta Informaticae. 23 (3)(1995).Google Scholar
- 8.Giunchiglia, F. and Serafini, L.: Multilanguage first order theories of propositional attitudes. In Proceedings of 3 rd Scandinavian Conference on Artificial Intelligence, Roskilde University, 1991.Google Scholar
- 9.Attardi,G.: and Simi,M.: A formalization of viewpoints, Fundamenta Informaticae. 23 (3)(1995).Google Scholar
- 10.Gabbay, D. and Nossum, R.: Structured context with fibred semantics. In Procedings of International and Interdisciplinary Conference on context, 1997.Google Scholar
- 11.Buvac, S.: Quantificational logic of context. In Procedings of AAAI-96.Google Scholar
- 12.Giunchiglia, F. and Bouquet, P.: Introduction to contextual reasoning, in B.-Kokinov (ed.), Perspectives on Cognitive Science, 3, NBU Press, Sofia, 1997.Google Scholar