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49 lines
1.5 KiB
49 lines
1.5 KiB
What 'model' means in the formal systems literature
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(for details, see http://www.w3.org/XML/9711theory/
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esp http://www.w3.org/XML/9711theory/FormalSystem)
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term ::= constantI
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| variable
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| constantF(term, term, ...)
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atom ::= constantP(term, term, ...)
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formula ::= atom
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| forumula AND formula
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| formula OR formula
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| NOT fomula
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| FORALL(variable) formula
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| THEREEXISTS(variable) formula
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An _interpretation_ is
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-- a set of _objects_, often called the domain, D
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-- a mapping of constantI's to D
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-- a mapping of constantF's to (DxDxDx...)->D i.e. functions over D
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-- a mapping of constantP's to DxDxDxDx... i.e. relations over D
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e.g.
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D = { objDan, objTim, objUs }
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constantI(Dan) = objDan
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constantI(Tim) = objTim
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constantI(Us) = objUs, i.e. ... the set of folks in the room...
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constantP(in) = {<objDan,objUs>, <objTim, objUs>}
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so... in(Dan, Us) is interpreted as true.
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a formula is satisfyable if there are _objects_ from D
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that (to paraphrase) can be plugged into the formula in the
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right places to make it work out.
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and interpretation is a _model_ for a set of formulas
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if each of the formulas is satisfyable in that interpretation.
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folks specify logics by specifying what constitutes a model;
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i.e. which formulas should be regarded as true.
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$Log: formalSys.txt,v $
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Revision 1.2 2001/04/09 16:34:49 connolly
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fixed a few typos and
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refined the 'see also' link
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