# 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…

### 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.

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