Tableau Calculi for Hybrid Logics

@inproceedings{Tzakova1999TableauCF,
  title={Tableau Calculi for Hybrid Logics},
  author={Miroslava Tzakova},
  booktitle={TABLEAUX},
  year={1999}
}
Hybrid logics were proposed in [15] as a way of boosting the expressivity of modal logics via a novel mechanism: adding labels for states in Kripke models and viewing these labels as formulae. In addition, hybrid logics may contain quantifiers to bind the labels. Thus, hybrid logics have both Kripke semantics and a first-order binding apparatus. We present prefixed tableau calculi for weak hybrid logics (proper fragments of classical logic) as well as for hybrid logics having full first-order… 

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References

SHOWING 1-10 OF 15 REFERENCES

Hybrid Completeness

This paper discusses two hybrid languages, L(∀) and L(↓), and provides them with complete axiomatizations, and shows how to overcome the difficulty of blending the modal idea of canonical models with the classical idea of witnessed maximal consistent sets by using COV ∗.

Hierarchies of modal and temporal logics with reference pointers

The basic modal and temporal logics with reference pointers are uniformly axiomatized and a strong completeness theorem is proved for them and extended to some classes of their extensions.

Hybrid languages

It is shown that all three binders give rise to languages strictly weaker than the corresponding first-order language, that full first- order expressivity can be gained by adding the universal modality, and that allThree binders can force the existence of infinite models and have undecidable satisfiability problems.

Internalizing labelled deduction

This paper shows how to internalize the Kripke satisfaction definition using the basic hybrid language and explores the proof theoretic consequences of doing so, and concludes with some reflections on the status of labelling in modal logic.

Modal logic with names

Every ℒc-logic axiomatized by formulae containing only names (but not propositional variables) is proved to be strongly frame-complete and strong completeness of the normal ℓc- logics is proved with respect to models in which all worlds are named.

Proof Methods for Modal and Intuitionistic Logics

One / Background.- Two / Analytic Modal Tableaus and Consistency Properties.- Three / Logical Consequence, Compactness, Interpolation, and Other Topics.- Four / Axiom Systems and Natural Deduction.-

Hybrid Languages and Temporal Logic

Hybridization is a method invented by Arthur Prior for extending the expressive power of modal languages but in this work the method is little known and temporal logic of the language has been deprived.

An Essay in Combinatory Dynamic Logic

Modal Languages and Bounded Fragments of Predicate Logic

Les nouvelles directions que peuvent prendre les theoremes de Tarski dans un environnement mathematique are indique celle des contraintes structurelles speciales, des extensions infinies, de the logique modale etendue and d'une semantique dynamique.

FIRST-ORDER LOGIC