The modal logic of continuous functions on the rational numbers
| Abstract | Let L be a propositional language with standard Boolean connectives plus two modalities: an S4-ish topological modality and a temporal modality ◦, understood as ‘next’. We extend the topological semantic for S4 to a semantics for the language L by interpreting L in dynamic topological systems, i.e., ordered pairs X, f , where X is a topological space and f is a continuous function on X. Artemov, Davoren and Nerode have axiomatized a logic S4C, and have shown that S4C is sound and complete for this semantics. S4C is also complete for continuous functions on Cantor space (Mints and Zhang, Kremer), and on the real plane (Fern´andez Duque); but incomplete for continuous functions on the real line (Kremer and Mints, Slavnov). Here we show that S4C is complete for continuous functions on the rational numbers. | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,709 |
| External links |
  Try with proxy. |
| Through your library | Only published papers are available at libraries |
Similar books and articlesSteffen Lewitzka (2007). Abstract Logics, Logic Maps, and Logic Homomorphisms. Logica Universalis 1 (2).
Lawrence P. Belluce & Antonio Di Nola (2005). Frames and MV-Algebras. Studia Logica 81 (3):357 - 385.
David Fernández-Duque (2011). Dynamic Topological Logic Interpreted Over Minimal Systems. Journal of Philosophical Logic 40 (6):767-804.
Thomas Mormann (1998). Continuous Lattices and Whiteheadian Theory of Space. Logic and Logical Philosophy 6:35 - 54.
Grigori Mints (2006). Cut Elimination for S4c: A Case Study. Studia Logica 82 (1):121 - 132.
Analytics
Monthly downloads |
Added to index2009-01-28Total downloads11 ( #99,650 of 549,753 )Recent downloads (6 months)1 ( #63,425 of 549,753 )How can I increase my downloads? |
My notes
Discussion
