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Abstract: A theory satisfies the k-variable property if every first-order formula is equivalent to a formula with at most k bound variables (possibly reused). Gabbay has shown that a model of temporal logic satisfies the k-variable property for some k if and only if there exists a finite basis for the temporal connectives over that model. We give a model-theoretic method for establishing the k-variable property, involving a restricted Ehrenfeucht-Fraisse game in which each player has only k pebbles. We... (Update)
Context of citations to this paper: More
.... are related to, but markedly different from, well known Ehrenfeucht Fraisse games for, e.g. k variable first order logic (see, e.g. [IK89]) The most important difference is that k simulation games are peculiarly asymmetric: the Duplicator controls a different number of...
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16: Tense logic and the theory of linear order (context) - Kamp - 1968
12: Upper and lower bounds for first-order expressibility (context) - Immerman - 1982
10: the temporal analysis of fairness (context) - Gabbay, Pnueli et al. - 1980
BibTeX entry: (Update)
N. Immerman and D. Kozen. Definability with bounded number of bound variables. Information and Computation, 83(2):121--139, 1989. http://citeseer.ist.psu.edu/immerman89definability.html More
@inproceedings{ immerman87definability,
author = "Neil Immerman and Dexter Kozen",
title = "Definability with Bounded Number of Bound Variables",
booktitle = "Logic in Computer Science",
pages = "236-244",
year = "1987",
url = "citeseer.ist.psu.edu/immerman89definability.html" }
Citations (may not include all citations):140 Tense Logic and the Theory of Linear Order (context) - Kamp - 1968
115 An Application of Games to the Completeness Problem for Form.. (context) - Ehrenfeucht - 1961
85 Upper and Lower Bounds for First-Order Expressibility (context) - Immerman - 1982
78 On Moschovakis Closure Ordinals (context) - Barwise - 1977 DBLP
48 Linear Orderings (context) - Rosenstein - 1982
43 The Computational Complexity of Logical Theories (context) - Ferrante, Rackoff - 1979
36 Expressive Functional Completeness in Tense Logic (context) - Gabbay - 1981
29 Deux ou Trois Choses que Je Sais de L n (context) - Poizat - 1982
28 Computation Tree Logic CTL and Path Quantifiers in the Monad.. (context) - Hafer, Thomas - 1987
7 Logical Systems Containing Only a Finite Number of Symbols (context) - Henkin - 1967
6 Functional Completeness over the Rationals (context) - Stavi - 1979
4 the Expressive Power of Programming Logics (context) - Erimbetov - 1981
4 Unbounded Program Memory Adds to the Expressive Power of Fir.. (context) - Tiuryn - 1984
3 Sur les Classifications des Systems de Relations (context) - Fraisse - 1954
3 Complexity of Boolean Algebras (context) - Kozen - 1980 DBLP
3 Definability in Dynamic Logic (context) - Meyer, Parikh - 1981 ACM DBLP
2 Preservation of Expressive Completeness in Temporal Models (context) - Amir, Gabbay - 1987 ACM DBLP
1 On Chain Logic, Path Logic, and First-Order Logic over Infin.. (context) - Thomas - 1987 DBLP
The graph only includes citing articles where the year of publication is known.
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