MoL-2005-03:
Tzanis, Evangelos
(2005)
*Algebraizing Hybrid Logic.*
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## Abstract

Algebraizing Hybrid Logic

Evangelos Tzanis

Abstract:

Hybrid logic is the result of extending the basic modal language with

a second sort of atomic propositions called nominals, and with

satisfaction operators. Precisely, the nominals (denoted by i, j, ...)

behave similar to ordinary proposition letters, expect that nominals

are true uniquely at a world. In other words, a nominal names a state

by being true there and nowhere else. An example of a formula

involving nominals is \diamond\diamond i \implies \neg\diamond i. The

language obtained by adding nominals to the basic modal language, is

called the minimal hybrid logic H. Satisfaction operators allow one to

express that a formula holds at the world named by nominal. A formula

of the form @_i\varphi expresses that p holds at the world named by

the nominal i. The extension of the basic modal language with nominals

and satisfaction operators is called the basic hybrid language H(@).

In this thesis we introduce and study an extension of hybrid logic in

which the set of nominals may be endowed with an algebraic

structure. In other words we add modal operators only for

nominals. The main motivation of the paper comes from [4]: you can

name states but you can not give them structure. In this paper we

consider an application of hybrid logics to relational structures on

algebras, thus a set with a relation and an algebraic

structure. Roughly speaking we try to give to nominals a structure, we

study the case where this structure is an algebraic structure. As far

as we know, the possible algebraic structure of nominals has not been

studied in the context of hybrid logic before. We should note that in

[11] there is a complete list of papers which study Kripke frames in

which the universe of possible worlds has a specific algebraic

structure, besides the traditional relational component.

Item Type: | Report |
---|---|

Report Nr: | MoL-2005-03 |

Series Name: | Master of Logic Thesis (MoL) Series |

Year: | 2005 |

Uncontrolled Keywords: | hybrid logic, algebraization |

Subjects: | Logic |

Date Deposited: | 12 Oct 2016 14:38 |

Last Modified: | 12 Oct 2016 14:38 |

URI: | https://eprints.illc.uva.nl/id/eprint/757 |

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