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

Bart Jacobs

RAIRO - Theoretical Informatics and Applications (2010)

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

Abstract

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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.

How to cite

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Jacobs, 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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