# Tableau Calculi for Hybrid Logics

@inproceedings{Tzakova1999TableauCF, title={Tableau Calculi for Hybrid Logics}, author={Miroslava Tzakova}, booktitle={International Conference on Theorem Proving with Analytic Tableaux and Related Methods}, 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…

## 54 Citations

### Michał Zawidzki DECISION PROCEDURES FOR SOME STRONG HYBRID LOGICS

- Computer Science
- 2014

This paper introduces a sound, complete and terminating tableau calculus TH(@,E,D,♦−) for hybrid logics with the satisfaction operators, the universal modality, the difference modality and the inverse modality as well as the corresponding sequent calculus SH(@),E, D, �−.

### Tableau-based Decision Procedure for Hybrid Logic with Satisfaction Operators , Universal Modality and Difference Modality

- Computer Science
- 2012

This paper introduces a sound, complete and terminating tableau calculus TH(@,E,D) for hybrid logics with satisfaction operators, universal modality and difference modality, and exploits the unrestricted blocking mechanism introduced as an explicit, sound tableau rule.

### Coalgebraic Hybrid Logic

- Philosophy, Computer ScienceFoSSaCS
- 2009

A generic finite model property and an ensuing weak completeness result are proved, and a semantic criterion for decidability in PSPACE is given, which is a fully internalised PSPACE tableau calculus.

### Constraint Tableaux for Hybrid Logics Draft

- Computer Science
- 2002

An improved tableau system for hybrid logic that handles equality for nominals by substitution and generation of inequality constraints, thus allowing for efficient equality reasoning is presented.

### Terminating Tableau Calculi for Hybrid Logics Extending K

- Computer ScienceElectron. Notes Theor. Comput. Sci.
- 2009

### T^aches de raisonnement en logiques hybrides

- Computer Science, Philosophy
- 2010

This thesis presents several tableaux-based algorithms for expressive hybrid logics, and presents an implementation of these calculi and describes correctness and performance tests carried out, and the tools that enable these.

### A Tableau Compiled Labelled Deductive System for Hybrid Logic

- Computer Science, Philosophy
- 2007

This extended abstract gives a brief presentation of the CLDS framework and outlines how it can be applied to develop a labeled tableau system for Hybrid Logic.

### Higher-Order Syntax and Saturation Algorithms for Hybrid Logic

- Computer ScienceElectron. Notes Theor. Comput. Sci.
- 2007

### Sequent Calculi for Nominal Tense Logics: A Step Towards Mechanization?

- MathematicsTABLEAUX
- 1999

These calculi are based on d'Agostino and Mondadori's calculus KE and therefore they admit a restricted cut-rule that is not eliminable, but the use of those calculi for mechanization is however doubtful.

### A Road-Map on Complexity for Hybrid Logics

- Computer Science, PhilosophyCSL
- 1999

A general expressivity result is proved showing that even the weak form of binding offered by the ↓ operator easily leads to undecidability in hybrid languages in which it is possible to bind nominals.

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