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Non-finite axiomatizability of dynamic topological logic

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Abstract
Dynamic topological logic (DTL) is a polymodal logic designed for reasoning about dynamic topological systems. These are pairs < X, f >, where X is a topological space and f : X. X is continuous. DTL uses a language L which combines the topological S4 modality square with temporal operators from linear temporal logic. Recently, we gave a sound and complete axiomatization DTL* for an extension of the logic to the language L*, where lozenge is allowed to act on finite sets of formulas and is interpreted as a tangled closure operator. No complete axiomatization is known in the language L, although one proof system, which we shall call KM, was conjectured to be complete by Kremer and Mints. In this article, we show that given any language L' such that L subset of L' subset of L*, the set of valid formulas of L' is not finitely axiomatizable. It follows, in particular, that KM is incomplete.
Keywords
Theory, Languages, Dynamical systems, temporal logic, spatial reasoning, theory complexity

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MLA
Fernández-Duque, David. “Non-finite Axiomatizability of Dynamic Topological Logic.” ACM TRANSACTIONS ON COMPUTATIONAL LOGIC 15.1 (2014): n. pag. Print.
APA
Fernández-Duque, D. (2014). Non-finite axiomatizability of dynamic topological logic. ACM TRANSACTIONS ON COMPUTATIONAL LOGIC, 15(1).
Chicago author-date
Fernández-Duque, David. 2014. “Non-finite Axiomatizability of Dynamic Topological Logic.” Acm Transactions on Computational Logic 15 (1).
Chicago author-date (all authors)
Fernández-Duque, David. 2014. “Non-finite Axiomatizability of Dynamic Topological Logic.” Acm Transactions on Computational Logic 15 (1).
Vancouver
1.
Fernández-Duque D. Non-finite axiomatizability of dynamic topological logic. ACM TRANSACTIONS ON COMPUTATIONAL LOGIC. 2014;15(1).
IEEE
[1]
D. Fernández-Duque, “Non-finite axiomatizability of dynamic topological logic,” ACM TRANSACTIONS ON COMPUTATIONAL LOGIC, vol. 15, no. 1, 2014.
@article{8566418,
  abstract     = {Dynamic topological logic (DTL) is a polymodal logic designed for reasoning about dynamic topological systems. These are pairs < X, f >, where X is a topological space and f : X. X is continuous. DTL uses a language L which combines the topological S4 modality square with temporal operators from linear temporal logic. 
Recently, we gave a sound and complete axiomatization DTL* for an extension of the logic to the language L*, where lozenge is allowed to act on finite sets of formulas and is interpreted as a tangled closure operator. No complete axiomatization is known in the language L, although one proof system, which we shall call KM, was conjectured to be complete by Kremer and Mints. 
In this article, we show that given any language L' such that L subset of L' subset of L*, the set of valid formulas of L' is not finitely axiomatizable. It follows, in particular, that KM is incomplete.},
  articleno    = {4},
  author       = {Fernández-Duque, David},
  issn         = {1529-3785},
  journal      = {ACM TRANSACTIONS ON COMPUTATIONAL LOGIC},
  keywords     = {Theory,Languages,Dynamical systems,temporal logic,spatial reasoning,theory complexity},
  language     = {eng},
  number       = {1},
  pages        = {18},
  title        = {Non-finite axiomatizability of dynamic topological logic},
  url          = {http://dx.doi.org/10.1145/2489334},
  volume       = {15},
  year         = {2014},
}

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