Abstract
The aim of the present paper is to analyse compactness properties of non-monotonic inference operations within the framework of model theory. For this purpose the concepts of a deductive frame and its semantical counterpart, a semantical frame are introduced. Compactness properties play a fundamental in the study of non-monotonic inference, and in the paper several new versions of compactness are studied. It is proved that minimal reasoning in propositional logic is weakly supracompact and that the associated inference operator is uniquely determined by its finitary restriction via an extension operator Δ4. Furthermore, some generalizations of these results to predicate logic are shown.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Barwise, J., S. Feferman: Model-Theoretic Logics, Springer-Verlag, 1985
Bell, J.: Pragmatic Logics, in: Proc. of 2nd. Int. Conference of Knowledge Representation and Reasoning, Cambridge MA, 1991
Dietrich, J.: Deductive Bases of Nonmonotonic Inference Operations; NTZ Report, Universit”a Leipzig, 1994
Dietrich, J., Herre, H.: Outline of Nonmonotonic Model Theory; NTZ Report, Universit” at Leipzig, 1994
Freund, M., Lehmann, D., Makinson, D.: Canonical Extensions to the Infinite Case of Finitary Nonmonotonic Inference Operations; Arbeitspapiere der GMD 443, 1990
Dix, J.: Nichtmonotones Schliessen und dessen Anwendung auf Semantiken logischer Programme, Doctoral Dissertation, Karlsruhe, 1992
Freund, M.: Supracompact inference operations, LNCS vol. 543, 59–73 (1991)
Freund, M. D. Lehmann: Nonmontonic inference operations; Preprint, Hebrew University of Jerusalem, 1993
Herre, H.: Nonmonotonic Reasoning and Logic Programs NIL'91, LNCS vol. 543, p. 38–58
Herre, H.:Contributions to nonmonotonic model theory, Workshop on Nonclassical Logics in Computer Science, Dagstuhl-Berichte (ed. Marek, V., A. Nerode, P.H. Schmitt), 1993
Kraus, S., D. Lehmann, M. Magidor: Nonmonotonic Reasoning, Preferential models and cumulative logics; A.I. 44 (1990), 167–207
Kolaitis, P.G., J.A.Väänänen: Generalized Quantifiers and Pebble Games on Finite Structures, Preprint, University of Helsinki, 1993
Lindström, P.: On extensions of elementary logic, Theoria, 35, 1–11 (1969)
Lindström, S.:A semantic approach to nonmonotonic reasoning: inference operations and choice; Dept. of Philosophy, Uppsala University, Preprint, 1991
Makinson, D.: General Theory of Cumulative Inference, in: Reinfrank, M.(Ed.) Non-monotonic Reasoning, LNAI vol. 346 Berlin Springer-Verlag, 1989, 1–18
Makinson, D.: General Patterns in Nonmonotonic Reasoning; in: D. Gabbay (ed.) Handbook of Logic in Artificial Intelligence and Logic Programming, Oxford University Press, 1993
Pearce, D.: Remarks on Monmonotonicity and Supraclassicality, Preprint, Berlin, 1993
Rautenberg, W.: Klassische und nichtklassische Aussagenlogik, Vieweg, 1979
Tarski, A.: Logic, Semantics, Metamathematics. Papers from 1923–1938. Clarendon Press, Oxford, 1956
Thiele, H.: Monotones und nichtmonotones Schliessen; in: Grabowski, J., Jantke, H.-J., H. Thiele: Grundlagen der Kuenstlichen Intelligenz, 80–160, Akademie-Verlag, Berlin 1989
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Herre, H. (1994). Compactness properties of nonmonotonic inference operations. In: MacNish, C., Pearce, D., Pereira, L.M. (eds) Logics in Artificial Intelligence. JELIA 1994. Lecture Notes in Computer Science, vol 838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0021962
Download citation
DOI: https://doi.org/10.1007/BFb0021962
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58332-5
Online ISBN: 978-3-540-48657-2
eBook Packages: Springer Book Archive