Van Benthem, J./Bergstra, J. (1995). Logic of Transition Systems, JoLLI, vol.3, pp.247-283 Home/Search Document Not in Database Summary Related Articles Check |
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Modal Model Theory - de Rijke (Correct)
....conjunction denote ) Then, for #R the modal operator whose semantics is based on R, we have a 0 j= #R ( Phi 1 ; Phi n ) but b 0 6j= #R ( Phi 1 ; Phi n ) contradicting Za 0 b 0 . a For countable structures a sharper form of Theorem 5. 8 is possible: Van Benthem and Bergstra [4] show that, for vocabularies not containing symbols of arity 2, countable structures are characterized up to bisimilarity by a single BML 1 ( formula; the generalization to arbitrary vocabularies is due to Holger Sturm (personal communication) The reader should compare this result with ....
....to arbitrary vocabularies is due to Holger Sturm (personal communication) The reader should compare this result with Scott s Isomorphism Theorem saying that countable structures are characterized up to isomorphism by a single L 1 sentence (Scott [19] Theorem 5. 9 (Van Benthem Bergstra [4]) Let be a countable vocabulary. For every countable structure A 2 Str[ there is a formula OE in BML 1 ( such that for all a in A, all countable B and all b in B, we have (A; a) B; b) iff (B; b) j= OE. We conclude the section with two brief comments on related work. First, De Rijke ....
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J. van Benthem and J. Bergstra. Logic of transition systems. Technical Report CT-93-03, ILLC, University of Amsterdam, 1993.
Bisimulations and Predicate Logic - Fernando (1994) (Correct)
....over f L; U p ; U q ; g. Setting aside, however, the propositional modal language, and examining the first order language f L; g of transition systems directly, it is easy to see that bisimilarity, in fact, exceeds first order logic. As pointed out in van Benthem and Bergstra [8], bisimilarity cannot be defined by an infinite set of first order sentences. This is strengthened by the following theorem, which considers bisimulations on a transition system (rather than on a pair of different ones) viewed as a first order f L; g model. Theorem A 0 . Bisimilarity is not ....
....defined over the transition system hfg; f(n; m) j n ; mgi. A fact complicating (z) is that bisimilarity is also Pi 1 1 (whence Delta 1 1 ) over well founded transition predicates a result implicit in Barwise, Gandy and Moschovakis [6] p. 115) as well as in van Benthem and Bergstra [8] (p. 27) Hence, we will also consider non well founded transition predicates. Moreover, turning to the co inductive characterization of bisimilarity, note that for bisimilarity to fall outside Pi 1 1 , the co inductive construction must not terminate at any stage named by a recursive ordinal. ....
[Article contains additional citation context not shown here]
J. van Benthem and J. Bergstra. Logic of transition systems. Technical report, ILLC, Amsterdam, March 1993.
Basic Multi-Competence Programming - Bergstra, Bethke, Ponse (2000) Self-citation (Bergstra) (Correct)
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J.F.A.K. van Benthem and J.A. Bergstra. Logic of transition systems.
A Dynamic Logic of Events and States for the Interaction between.. - Naumann (1998) (Correct)
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Van Benthem, J./Bergstra, J. (1995). Logic of Transition Systems, JoLLI, vol.3, pp.247-283
A Dynamic Logic of Events and States for the Interaction between.. - Naumann (1998) (Correct)
No context found.
Van Benthem, J./Bergstra, J. (1995). Logic of Transition Systems, JoLLI, vol.3, pp.247-283
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