Re: V0.1 strawman of FOL extension of SWRL

From: Peter F. Patel-Schneider (
Date: 06/07/04

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    Here is a different, minimalist proposal.
    Non-terminals taken from other grammars are prefixed by that grammar
    as in OWL/annotation.  The axiom non-terminal from OWL is not so
    treated, as the idea here is to augment OWL axioms with an axiom that
    provides for assertion of first-order formulae.
    axiom ::= assertion
    assertion ::= 'Assertion(' [ RDF/URIreference ] { OWL/annotation }
    		           'Formula(' foformula ')' ')'
    foformula ::= SWRL/atom
    	    | 'and(' foformula* ')'
    	    | 'or(' foformula* ')'
    	    | 'not(' foformula ')'
    	    | 'implies(' foformula foformula ')'
    	    | 'equivalent(' foformula foformula ')'
    	    | 'forall(' variable+ foformula ')'
    	    | 'exists(' variable+ foformula ')'
    variable ::= SWRL/i-variable
    	   | 'I-variable(' RDF/URIreference OWL/description ')'
    	   | SWRL/d-variable
    	   | 'D-variable(' RDF/URIreference OWL/dataRange ')'
    To be somewhat compatible with RDF, free variables in assertions are
    treated existentially.  The rest of the semantic characterization is
    It would not be hard to allow for predicates with mixed arity, by
    extending SWRL/atom as follows:
    atom ::= RDF/URIreference '(' object* ')'
    object ::= SWRL/i-object | SWRL/d-object
    The denotation of such predicates would be sets of tuples of domain
    elements with the usual shorthand of identifying 1-tuples of domain
    elements with domain elements.

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