# Hybrid Languages and Temporal Logic

@article{Blackburn1999HybridLA, title={Hybrid Languages and Temporal Logic}, author={Patrick Blackburn and Miroslava Tzakova}, journal={Log. J. IGPL}, year={1999}, volume={7}, pages={27-54} }

Hybridization is a method invented by Arthur Prior for extending the expressive power of modal languages Although developed in interesting ways by Robert Bull and by the So a school notably George Gargov Valentin Goranko Solomon Passy and Tinko Tinchev the method re mains little known In our view this has deprived temporal logic of a

## 107 Citations

### Hybrid logic is the bounded fragment of first order logic.

- Computer Science
- 1999

The purpose of the present paper is to show in detail that H(↓,@) is a modally natural system that corresponds precisely to the first-order fragment which is invariant for generated submodels.

### Many-Sorted Hybrid Modal Languages

- Computer Science
- 2020

A fragment of the full logic is identified, for which sound and complete deduction is proved and it is shown that it is powerful enough to represent both the programs and their semantics in an uniform way.

### From Hybrid Modal Logic to Matching Logic and back

- PhilosophyFROM
- 2019

This work identifies modal logic equivalents for Matching Logic, a logic for program specification and verification, which provides a rigorous way to transfer results between the two approaches, which should benefit both systems.

### Internalization: The Case of Hybrid Logics

- Computer ScienceJ. Log. Comput.
- 2001

The semantic theory of hybrid logic is formalized using a sequent calculus for predicate logic plus axioms, which is quite general and can be applied to a wide range of hybrid and modal logics.

### Hybridizing concept languages

- Computer ScienceAnnals of Mathematics and Artificial Intelligence
- 2004

This paper shows how to increase the expressivity of concept languages using a strategy called hybridization, combining aspects of modal and first-order logic in this manner, making it possible to define number restrictions, collections of individuals, irreflexivity of roles, and TBox- and ABox-statements.

### A Seligman-Style Tableau System

- Computer ScienceLPAR
- 2013

The purpose of this paper is to introduce a Seligman-style tableau system for proof systems for hybrid logic, first introduced and explored by JerrySeligman in the setting of natural deduction and sequent calculus in the late 1990s.

### Tableau Calculi for Hybrid Logics

- Computer Science, PhilosophyTABLEAUX
- 1999

This work presents prefixed tableau calculi for weak hybrid logics (proper fragments of classical logic) as well as for hybridlogics having full first-order expressive power, and gives a general method for proving completeness.

### Hybrid Logics: The Old and the New

- Philosophy, Computer Science
- 2007

This paper will start by introducing hybrid logics from that perspective, and will later have a closer look to the ↓ binder, and propose an alternative way to think about it.

## References

SHOWING 1-10 OF 48 REFERENCES

### Hybrid languages

- Computer ScienceJ. Log. Lang. Inf.
- 1995

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.

### Fine Grained Theories of Time

- Philosophy
- 2001

This paper uses hybrid logic, a form of modal logic in which times can be named, to draw together ideas from the philosophical tradition of temporal logic (notably the ideas of Arthur Prior) and…

### Tableau Calculi for Hybrid Logics

- Computer Science, PhilosophyTABLEAUX
- 1999

This work presents prefixed tableau calculi for weak hybrid logics (proper fragments of classical logic) as well as for hybridlogics having full first-order expressive power, and gives a general method for proving completeness.

### Expressiveness and Completeness of an Interval Tense Logic

- Computer ScienceNotre Dame J. Formal Log.
- 1990

It is proved that this logic has a greater capacity to distinguish frames than any temporal logic based on points and it is shown that neither this nor any other finite set of operators can be functionally complete on the class of dense orders.

### Hierarchies of modal and temporal logics with reference pointers

- Computer ScienceJ. Log. Lang. Inf.
- 1996

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.

### Proof Methods for Modal and Intuitionistic Logics

- Philosophy
- 1983

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

### Hybrid Completeness

- Computer ScienceLog. J. IGPL
- 1998

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 ∗.

### Temporal Logic with Reference Pointers

- PhilosophyICTL
- 1994

The minimal temporal logic K trp of this language is axiomatized and strong completeness theorem is proved for it and extended to an important class of extensions of Ktrp .

### Verifying Modal Formulas over I/O-Automata by means of Type Theory

- Computer Science
- 1995

It is illustrated how the question whether or not an execution in a given I/O-automaton is a model for formula o can be reduced to an inhabitation problem in the Calculus of Inductive Constructions.