MoL-2005-03: Algebraizing Hybrid Logic

MoL-2005-03: Tzanis, Evangelos (2005) Algebraizing Hybrid Logic. [Report]

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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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