Expressivity of Logics of Knowledge and Action

Bouke Kuijer

Expressivity of Logics of Knowledge and Action

Bouke Kuijer

VIDI Kooi

Research output: Thesis › Thesis fully internal (DIV)

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Abstract

Consider two languages, say, English and Dutch. It is possible to translate between these languages, so if I take an English sentence I can find a Dutch sentence with the same meaning and if I take a Dutch sentence I can find an English sentence with the same meaning.
Logics are formal languages, and therefore also languages. This means that if we take two logics L_1 and L_2 we can try to translate from L_1 to L_2. But unlike with natural languages (like English and Dutch) it is sometimes impossible to translate from one logic to another.
If it is possible to translate from L_1 to L_2 and impossible to translate from L_2 to L_1 we say that L_2 is more expressive than L_1. If it is possible to translate from L_1 to L_2 and also possible to translate from L_2 to L_1 we say that L_1 and L_2 are equally expressive.
In this thesis we look at a number of logics and determine which ones are the most expressive. Specifically, we look at the logics L_CP, L_CPS, L_R, L_CPU and L_U*. We conclude that L_CPS is more expressive than L_CP, that L_U* is more expressive than L_R and that L_CPU and L_U* are equally expressive.

Translated title of the contribution	Expressivity of Logics of Knowledge and Action
Original language	English
Qualification	Doctor of Philosophy
Awarding Institution	University of Groningen
Supervisors/Advisors	Kooi, Barteld, Supervisor Tamminga, Allard, Co-supervisor
Award date	11-Dec-2014
Place of Publication	[S.l.]
Publisher	[S.n.]
Print ISBNs	978-90-367-7434-5
Electronic ISBNs	978-90-367-7433-8
Publication status	Published - 2014

Access to Document

Title and contents Final publisher's version, 235 KB
AcknowledgmentsFinal publisher's version, 138 KB
Chapter 1Final publisher's version, 303 KB
Chapter 2Final publisher's version, 513 KB
Chapter 3Final publisher's version, 542 KB
Chapter 4Final publisher's version, 511 KB
Chapter 5Final publisher's version, 454 KB
Chapter 6Final publisher's version, 589 KB
Chapter 7Final publisher's version, 287 KB
AppendixFinal publisher's version, 509 KB
Dutch summaryFinal publisher's version, 259 KB
BibliographyFinal publisher's version, 170 KB
Complete dissertationFinal publisher's version, 1.25 MB
PropositionsFinal publisher's version, 76.6 KB

http://dissertations.ub.rug.nl/faculties/fil/2014/l.b.kuijer/

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Cite this

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title = "Expressivity of Logics of Knowledge and Action",

abstract = "Consider two languages, say, English and Dutch. It is possible to translate between these languages, so if I take an English sentence I can find a Dutch sentence with the same meaning and if I take a Dutch sentence I can find an English sentence with the same meaning.Logics are formal languages, and therefore also languages. This means that if we take two logics L_1 and L_2 we can try to translate from L_1 to L_2. But unlike with natural languages (like English and Dutch) it is sometimes impossible to translate from one logic to another.If it is possible to translate from L_1 to L_2 and impossible to translate from L_2 to L_1 we say that L_2 is more expressive than L_1. If it is possible to translate from L_1 to L_2 and also possible to translate from L_2 to L_1 we say that L_1 and L_2 are equally expressive. In this thesis we look at a number of logics and determine which ones are the most expressive. Specifically, we look at the logics L_CP, L_CPS, L_R, L_CPU and L_U*. We conclude that L_CPS is more expressive than L_CP, that L_U* is more expressive than L_R and that L_CPU and L_U* are equally expressive.",

author = "Bouke Kuijer",

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publisher = "[S.n.]",

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AU - Kuijer, Bouke

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N2 - Consider two languages, say, English and Dutch. It is possible to translate between these languages, so if I take an English sentence I can find a Dutch sentence with the same meaning and if I take a Dutch sentence I can find an English sentence with the same meaning.Logics are formal languages, and therefore also languages. This means that if we take two logics L_1 and L_2 we can try to translate from L_1 to L_2. But unlike with natural languages (like English and Dutch) it is sometimes impossible to translate from one logic to another.If it is possible to translate from L_1 to L_2 and impossible to translate from L_2 to L_1 we say that L_2 is more expressive than L_1. If it is possible to translate from L_1 to L_2 and also possible to translate from L_2 to L_1 we say that L_1 and L_2 are equally expressive. In this thesis we look at a number of logics and determine which ones are the most expressive. Specifically, we look at the logics L_CP, L_CPS, L_R, L_CPU and L_U*. We conclude that L_CPS is more expressive than L_CP, that L_U* is more expressive than L_R and that L_CPU and L_U* are equally expressive.

AB - Consider two languages, say, English and Dutch. It is possible to translate between these languages, so if I take an English sentence I can find a Dutch sentence with the same meaning and if I take a Dutch sentence I can find an English sentence with the same meaning.Logics are formal languages, and therefore also languages. This means that if we take two logics L_1 and L_2 we can try to translate from L_1 to L_2. But unlike with natural languages (like English and Dutch) it is sometimes impossible to translate from one logic to another.If it is possible to translate from L_1 to L_2 and impossible to translate from L_2 to L_1 we say that L_2 is more expressive than L_1. If it is possible to translate from L_1 to L_2 and also possible to translate from L_2 to L_1 we say that L_1 and L_2 are equally expressive. In this thesis we look at a number of logics and determine which ones are the most expressive. Specifically, we look at the logics L_CP, L_CPS, L_R, L_CPU and L_U*. We conclude that L_CPS is more expressive than L_CP, that L_U* is more expressive than L_R and that L_CPU and L_U* are equally expressive.

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SN - 978-90-367-7434-5

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