# Hybrid Completeness

@article{Blackburn1998HybridC, title={Hybrid Completeness}, author={Patrick Blackburn and Miroslava Tzakova}, journal={Log. J. IGPL}, year={1998}, volume={6}, pages={625-650} }

In this paper we discuss two hybrid languages , L(∀) and L(↓), and provide them with complete axiomatizations. Both languages combine features of modal and classical logic. Like modal languages, they contain modal operators and have a Kripke semantics. Unlike modal languages, in these systems it is possible to ‘label’ states by using ∀ and ↓ to bind special state variables . This paper explores the consequences of hybridization for completeness. As we shall show, the challenge is to blend the…

## 28 Citations

### Hybrid Languages and Temporal Logic (Full Version)

- Computer Science
- 1998

It is argued that the idea of sorted atomic symbols which underpins the hybrid enterprise can be developed much further, and the advantages and disadvantages of a simple hybrid language which can quantify over paths are discussed.

### Hybrid logics: characterization, interpolation and complexity

- Computer ScienceJournal of Symbolic Logic
- 2001

It is shown that (↓, @) enjoys (strong) interpolation, provide counterexamples for its finite variable fragments, and show that weak interpolation holds for the sublanguage (@).

### 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.

### On Hybrid Arrow Logic

- Computer Science
- 2002

A system obtained from a hybridization of Arrow Logic much as H(↓,@) was obtained from the basic modal language, which may be regarded as the “standard hybrid formalism”.

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

- Computer Science
- 2019

This paper introduces HΣ(@z,∀), a strengthening of the system from [10] which allows the satisfaction operators @z to also range over state variables, and shows that it is equivalent to Matching Logic with the definedness operator when restricted to global deduction.

### 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.

### Term-Modal Logics

- PhilosophyStud Logica
- 2000

Many powerful logics exist today for reasoning about multi-agent systems, but in most of these it is hard to reason about an infinite or indeterminate number of agents. Also the naming schemes used…

### Sahlqvist Formulas in Hybrid Polyadic Modal Logics

- MathematicsJ. Log. Comput.
- 2001

Sahlqvist formulas in hybrid polyadic modal languages containing nominals and universal modality or satisfaction operators are defined to ensure first-order definability and canonicity of these formulas immediately transfers to arbitrary polyadic languages.

### Representation, Reasoning, and Relational Structures: a Hybrid Logic Manifesto

- Philosophy, Computer ScienceLog. J. IGPL
- 2000

This paper is about the good side of modal logic, the bad side of modem logic, and how hybrid logic takes the good and fixes the bad, and why hybrid logic is a rather unusual modal upgrade.

### 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.

## References

SHOWING 1-10 OF 25 REFERENCES

### Modal logic with names

- PhilosophyJ. Philos. Log.
- 1993

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.

### 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.

### 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.

### Hybrid Languages and Temporal Logic

- PhilosophyLog. J. IGPL
- 1999

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.

### Entities and indices

- Philosophy
- 1990

I Multiple Indexing.- 1 A basic intensional language.- 2 'Now' and 'then'.- 3 'Actually'.- 4 Indices and world variables.- 5 Mediated relations.- 6 A second-order treatment.- II Ontological…

### 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.