Expressivity of logics of knowledge and action
| PhD ceremony: | Mr L.B. (Bouke) Kuijer |
| When: | December 11, 2014 |
| Start: | 11:00 |
| Supervisor: | dr. B.P. (Barteld) Kooi |
| Co-supervisor: | dr. A.M. Tamminga |
| Where: | Academy building RUG |
| Faculty: | Philosophy |
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.