Abstract
A useful 3-valued provability predicate Demos is defined, that can provably simulate non-classical logics and connectives (like autoepistemic logic and negation-as-failure) and that, despite its 3-valued semantics, is able to capture thoroughly classical notions of provability and unprovability. Demos is largely tolerant to self-reference, and can be axiomatised consistently. Its semantics provides a guide to the development of effective axiomatisations and meta-interpreters that do not fall under the scope of the well known negative results on incompleteness and inconsistency.
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References
G. Attardi, M. Simi. Reflections about reflection. Proc. of KR91, Principles of Knowledge Representation and Reasoning, 2nd Int. Conf. (1991).
P. A. Bonatti. A more general solution to the multiple expansion problem. In Proc. Workshop on Non-Monotonic Reasoning and Logic Programming, NACLP'90.
P. A. Bonatti. Beliefs as stable conjectures. In Proc. of the First Int. Workshop on Logic Programming and Non-Monotonic Reasoning, Washington D.C., 1991, MIT Press.
P. A. Bonatti. A family of three valued autoepistemic logics. To appear in the Proc. of the II Congresso dell'Associazione Italiana per l'Intelligenza Artificiale (AI*IA), 1991.
K. A. Bowen, R. A. Kowalski. Amalgamating language and metalanguage in logic programming. In K. L. Clark, S. Tarnlund (eds.) Logic Programming, Academic Press (1982).
S. Costantini, G. A. Lanzarone. A metalogic programming language. In G. Levi, M. Martelli (eds), Logic Programming: Proc. of the Sixth Int. Conference, MIT Press, (1989).
N. Davies. Toward a first-order theory of reasoning agents. Proc. of 9th European Conference on Artificial Intelligence, Stockholm (1990).
S. Feferman. Transfinite recursive progressions of axiomatic theories.J. of Symbolic Logic 27 (1962), 259–316.
M. Gelfond. On Stratified Autoepistemic Theories. In Proceedings AAAI-87, 207–211, 1987.
H. G. Herzberger. Notes on Naive Semantics. In the Journal of Phil. Logic 11 (1982), 61–102. Reprinted in [14].
K. Konolige. On the relation between default theories and autoepistemic logic. In Proc. of IJCAI'87, Int. Joint Conf. on Artificial Intelligence, Milano, 1987, pp. 394–401. An extended version appears as On the relation between default logic and autoepistemic theories in Artificial Intelligence 35, pp. 343–382.
D. McDermott, J. Doyle. Non-monotonic logic I. In Artificial Intelligence, 13:41–72, 1980.
D. McDermott. Non-monotonic logic II: nonmonotonic modal theories. In the Journal of the Association for Computing machinery, 29:33–57, 1982.
R. L. Martin (ed.). Recent essays on truth and the liar paradox. Clarendon Press, Oxford, 1984.
R. Moore. Semantical considerations on nonmonotonic logics. In Artificial Intelligence 25, (1985), pp. 75–94.
D. Perlis. Languages with self-reference I: Foundations. Artificial Intelligence 25, (1985), 301–322.
D. Perlis. Languages with self-reference II: Knowledge, Belief and Modality. Artificial Intelligence 34, (1988), 179–212.
T. Przymusinski. On the declarative and procedural semantics of logic programs. Journal of Automated Reasoning, 4, 1988.
R. Reiter. A logic for default reasoning. In Artificial Intelligence 13 (1980) 81–132.
C. Smoryński. Self-reference and modal logic. Springer-Verlag 1985.
A-M. Turing. Systems of logic based on ordinals. Proc. of the London Mathematical Society, ser. 2, vol. 45 (1939), 161–228.
R. Turner. Truth and Modality for Knowledge Representation. MIT Press.
B. Van Fraassen. Singular terms, truth value gaps and free logic. In The Journal of Philosophy 63 (1966), pp. 481–95.
A. Varzi. Complementary sentential logics. Bulletin of the Sector of Logic 19, (4), 1990, pp 112–116.
R. Weyhrauch. Prolegomena to a theory of mechanized formal reasoning. In Artificial Intelligence 13 (1980), pp 133–170.
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© 1992 Springer-Verlag Berlin Heidelberg
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Bonatti, P.A. (1992). Model theoretic semantics for Demo. In: Pettorossi, A. (eds) Meta-Programming in Logic. META 1992. Lecture Notes in Computer Science, vol 649. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56282-6_15
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DOI: https://doi.org/10.1007/3-540-56282-6_15
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