Two-phase deontic logic (bibtex)
by L. Van der Torre, Y.H. Tan
Abstract:
We show that for the adequate representation of some examples of normative reasoning a combination of different operators is needed, where each operator validates different inference rules. The combination of different modal operators imposes the restriction on the proof theory of the logic that a proof rule can be blocked in a derivation due to the fact that another proof rule has been used earlier in the derivation. In this paper we only use two operators and therefore we call the restriction the two-phase approach in the proof theory, which we formalize in two-phase labeled deontic logic (2LDL) and in two-phase dyadic deontic logic (2dl). The preference-based semantics of 2DL is based on an explicit deontic preference ordering between worlds, representing different degrees of ideality. The two different modal operators represent two different usages of the preference ordering, called minimizing and ordering.
Reference:
Two-phase deontic logic (L. Van der Torre, Y.H. Tan), In Logique et Analyse, volume 43, 2000.
Bibtex Entry:
@Article{VanderTorre2000,
  Title                    = {Two-phase deontic logic},
  Author                   = {Van der Torre, L. and Tan, Y.H.},
  Journal                  = {Logique et Analyse},
  Year                     = {2000},
  Pages                    = {411--456},
  Volume                   = {43},

  Abstract                 = {We show that for the adequate representation of some examples of normative reasoning a combination of different operators is needed, where each operator validates different inference rules. The combination of different modal operators imposes the restriction on the proof theory of the logic that a proof rule can be blocked in a derivation due to the fact that another proof rule has been used earlier in the derivation. In this paper we only use two operators and therefore we call the restriction the two-phase approach in the proof theory, which we formalize in two-phase labeled deontic logic (2LDL) and in two-phase dyadic deontic logic (2dl). The preference-based semantics of 2DL is based on an explicit deontic preference ordering between worlds, representing different degrees of ideality. The two different modal operators represent two different usages of the preference ordering, called minimizing and ordering. },
  Bdsk-url-1               = {http://icr.uni.lu/leonvandertorre/papers/leta02.ps.Z},
  Timestamp                = {2013.07.26},
  Url                      = {http://icr.uni.lu/leonvandertorre/papers/leta02.ps.Z}
}
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