Re: V0.1 strawman of FOL extension of SWRL

From: Peter F. Patel-Schneider (pfps@research.bell-labs.com)
Date: 06/07/04

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    Here is a different, minimalist proposal.
    
    peter
    
    
    
    Syntax:
    
    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 ')'
    
    Semantics:
    
    To be somewhat compatible with RDF, free variables in assertions are
    treated existentially.  The rest of the semantic characterization is
    standard.
    
    
    Option:
    
    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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