# Many-Sorted Coalgebraic Modal Logic: a Model-theoretic Study

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 35, Issue: 1, page 31-59
- ISSN: 0988-3754

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topJacobs, Bart. "Many-Sorted Coalgebraic Modal Logic: a Model-theoretic Study." RAIRO - Theoretical Informatics and Applications 35.1 (2010): 31-59. <http://eudml.org/doc/222078>.

@article{Jacobs2010,

abstract = {
This paper gives a semantical underpinning for a many-sorted modal
logic associated with certain dynamical systems, like transition
systems, automata or classes in object-oriented languages. These
systems will be described as coalgebras of so-called polynomial
functors, built up from constants and identities, using products,
coproducts and powersets. The semantical account involves Boolean
algebras with operators indexed by polynomial functors, called MBAOs,
for Many-sorted Boolean Algebras with Operators, combining
standard (categorical) models of modal logic and of many-sorted
predicate logic. In this setting we will see Lindenbaum MBAO models as
initial objects, and canonical coalgebraic models of maximally
consistent sets of formulas as final objects. They will be used to
(re)prove completeness results, and Hennessey-Milner style
characterisation results for the modal logic, first established by
Rößiger.
},

author = {Jacobs, Bart},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Modal logic; coalgebra; Boolean algebra with operators.; modal logic; coalgebras; many-sorted logic; many-sorted Boolean algebras with operators},

language = {eng},

month = {3},

number = {1},

pages = {31-59},

publisher = {EDP Sciences},

title = {Many-Sorted Coalgebraic Modal Logic: a Model-theoretic Study},

url = {http://eudml.org/doc/222078},

volume = {35},

year = {2010},

}

TY - JOUR

AU - Jacobs, Bart

TI - Many-Sorted Coalgebraic Modal Logic: a Model-theoretic Study

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/3//

PB - EDP Sciences

VL - 35

IS - 1

SP - 31

EP - 59

AB -
This paper gives a semantical underpinning for a many-sorted modal
logic associated with certain dynamical systems, like transition
systems, automata or classes in object-oriented languages. These
systems will be described as coalgebras of so-called polynomial
functors, built up from constants and identities, using products,
coproducts and powersets. The semantical account involves Boolean
algebras with operators indexed by polynomial functors, called MBAOs,
for Many-sorted Boolean Algebras with Operators, combining
standard (categorical) models of modal logic and of many-sorted
predicate logic. In this setting we will see Lindenbaum MBAO models as
initial objects, and canonical coalgebraic models of maximally
consistent sets of formulas as final objects. They will be used to
(re)prove completeness results, and Hennessey-Milner style
characterisation results for the modal logic, first established by
Rößiger.

LA - eng

KW - Modal logic; coalgebra; Boolean algebra with operators.; modal logic; coalgebras; many-sorted logic; many-sorted Boolean algebras with operators

UR - http://eudml.org/doc/222078

ER -

## References

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