By Ulrich Kohlenbach, Pablo Barceló, Ruy J G B de Queiroz

Edited in collaboration with FoLLI, the organization of good judgment, Language and data this e-book constitutes the refereed court cases of the twenty first Workshop on good judgment, Language, info and verbal exchange, WoLLIC 2014, held in Valparaiso, Chile, in September 2014. The 15 contributed papers awarded including 6 invited lectures have been conscientiously reviewed and chosen from 29 submissions. the focal point of the workshop used to be at the following topics Inter-Disciplinary study concerning Formal good judgment, Computing and Programming thought, and typical Language and Reasoning.

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Extra info for Logic, Language, Information, and Computation: 21st International Workshop, WoLLIC 2014, Valparaíso, Chile, September 1-4, 2014. Proceedings

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For all i ∈ {1, . . , n}, T |= Trxi (Σi )[vi ], and for all j ∈ {1, . . , m}, T |= Tryj (Γj )[wj ]; by item 1 of Proposition 8 this implies that T |= Trxi (Σi )[vi ] and T |= Tryj (Γj )[wj ]; iii. vn ∼ wm in T , and hence in T . Since Tr is truth preserving, we have that for all i ∈ {1, . . , n}, T , vi |= Σi , and for all j ∈ {1, . . , m}, T , wi |= Γi . Together with i and iii we conclude that Σ1 , . . , Σn and Γ1 , . . , Γm are =↓n,m -satisfiable at T , u. For item 2, let Γ be a set of XPath= -formulas.

M are not =↓n,m -satisfiable at T , u which is a contradiction. Proposition 4. Let T and T be ↓-saturated data trees, and let u ∈ T and u ∈ T . If T , u ≡↓ T , u , then T , u ↔↓ T , u . Proof. We show that Z, defined by xZx iff T , x ≡↓ T , x is a ↓-bisimulation between T , u and T , u . Clearly uZu , and Harmony holds. We only need to show that Zig and Zag are satisfied. We see only Zig, as Zag is analogous. Suppose xZx , x = v0 → v1 → · · · → vn and x = w0 → w1 → · · · → wm are paths on T , and data(vn ) = data(wm ) (the case data(vn ) = data(wm ) is shown analogously).

In: Proceedings of AAMAS (2013) 19. : A qualitative modal representation of quantum state transformations. In: Proceedings of the 38th ISMVL. IEEE CS Press (2008) 20. : Modal Deduction Systems for Quantum State Transformations. Multiple-Valued Logic and Soft Computing 17(5-6), 475–519 (2011) 21. : The modal logic of quantum logic. J. Philos. Logic 8(4), 479–504 (1979) 22. : Quantum computation and quantum information. Cambridge University Press (2000) 23. : Natural Deduction: a Proof-Theoretical Study.

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