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