Hybrid Languages and Temporal Logic

  title={Hybrid Languages and Temporal Logic},
  author={Patrick Blackburn and Miroslava Tzakova},
  journal={Log. J. IGPL},
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 

Hybrid logic is the bounded fragment of first order logic.

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

Many-Sorted Hybrid Modal Languages

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

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

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

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

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

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

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.

Completeness results for memory logics




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.

Fine Grained Theories of Time

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

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

  • Y. Venema
  • Computer Science
    Notre 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

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

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

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

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

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.