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Supplement to Deontic Logic

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Suppose that we have:

a set of Propositional Variables (PV):P_{1}, …,P_{i},…—where “i” is a numerical subscript; three propositional operators: ~, →,OB; and a pair of parentheses: (, ).

The set of D-wffs (deontic well-formed formuli) is then the smallest
set satisfying the following conditions (lower case
“*p*” and “*q*” are
metavariables):

FR1. PV is a subset of D-wffs.

FR2. For anyp,pis in D-wffs only if ~pandOBpare also in D-wffs.

FR3. For anypandq,pandqare in D-wffs only if (p→q) is in D-wffs.

We then assume the following abbreviatory definitions:

DF1-3. &, , → as usual.

DF4.PEp=_{df}~OB~p.

DF5.IMp=_{df}OB~p.

DF6.GRp=_{df}~OBp.

DF7.OP=_{df}(~OBp& ~OB~p)

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Paul McNamara mcnamara.p@comcast.net |

Stanford Encyclopedia of Philosophy