A proposal for a unitary RIF phase 1

	A Proposal for a Unitary Language for RIF Phase 1

Peter F. Patel-Schneider

Overview:

1/ The language of RIF Phase 1 is function-free Horn clauses.  There
    is a human-readable, functional-style syntax, plus an XML
    interchange syntax.

2/ RIF Phase 1 includes predicates for the reasonable XML Schema
    datatypes, plus various built-in predicates over these datatypes.

3/ A RIF Phase 1 knowledge base is a set of RIF Phase 1 documents plus
    an optional set of OWL DL documents closed under OWL imports.

4/ The meaning of a RIF Phase 1 knowledge base is given by a standard
    model-theoretical semantics.

5/ Compliance for formalism X will be determined by the presence of a
    non-trivial subset of X that can be mapped into RIF Phase 1
    knowledge bases in a deduction-preserving mapping.


Functional-style Syntax for RIF Phase 1:

This syntax is a modification of the previous proposed syntax
from http://lists.w3.org/Archives/Public/public-rif-wg/2006Apr/0068.html

   Data     ::= RDF typed or untyped data value
   Ind      ::= URI
   Var      ::= '?' name
   Rel      ::= URI
   Term     ::= Data | Ind | Var
   Atom     ::= Rel '(' Term* ')' | Term '=' Term
   Rule	   ::= Atom <- Atom*

Each variable in the consequent of a rule must also be present in the
antecedent.


XML INTERCHANGE SYNTAX

TBD


SEMANTICS

An interpretation is an extension of an OWL DL interpretation
(http://www.w3.org/TR/owl-semantics/direct.html), extending the
vocabulary to include RIF relation names and mapping them to tuples
over R union LV.  RIF relation names that are OWL DL class names,
datatype names, individual-valued property names, data-valued property
names, or annotation property names have the same extension as given
by the appropriate part of the OWL semantics.

A RIF rule is true in a RIF interpretation precisely when every
mapping from variables in the rule into R union LV that makes each
atom in the antecedent of the rule true in the obvious extension of
the OWL DL semantics also makes the consequent in the rule true in the
same way.


COMPLIANCE

Compliance for formalism X will be measured as follows.
a/ Partial mappings will be provided between the syntaxes of X and RIF
    Phase 1, including mappings between X's data language and OWL DL.
b/ A subset of RIF Phase 1 will be identified as being X-compliant.
c/ For that subset the deductive behaviour of X must mirror reasoning
    in the RIF Phase 1 in the sense that ground consequences for
    knowledge bases in this subset are the same for RIF Phase 1 and its
    mapping into the syntax of X.

Compliance of a rule system with RIF Phase 1 will be defined as follows.
1/ The formalism underlying the rule system must be RIF Phase 1
    compliant as defined above.
2/ There must be a tool that implements the syntax mapping.
3/ There must be a comprehensive set of RIF knowledge bases for which
    the equivalence of deductive behaviour has been reasonably demonstrated.

	A Proposal for a Unitary Language for RIF Phase 1

Peter F. Patel-Schneider

Overview:

1/ The language of RIF Phase 1 is function-free Horn clauses.  There
   is a human-readable, functional-style syntax, plus an XML
   interchange syntax.

2/ RIF Phase 1 includes predicates for the reasonable XML Schema
   datatypes, plus various built-in predicates over these datatypes.

3/ A RIF Phase 1 knowledge base is a set of RIF Phase 1 documents plus
   an optional set of OWL DL documents closed under OWL imports.

4/ The meaning of a RIF Phase 1 knowledge base is given by a standard
   model-theoretical semantics.

5/ Compliance for formalism X will be determined by the presence of a
   non-trivial subset of X that can be mapped into RIF Phase 1
   knowledge bases in a deduction-preserving mapping.


Functional-style Syntax for RIF Phase 1:

This syntax is a modification of the previous proposed syntax
from http://lists.w3.org/Archives/Public/public-rif-wg/2006Apr/0068.html

  Data     ::= RDF typed or untyped data value
  Ind      ::= URI
  Var      ::= '?' name
  Rel      ::= URI
  Term     ::= Data | Ind | Var
  Atom     ::= Rel '(' Term* ')' | Term '=' Term
  Rule	   ::= Atom <- Atom*

Each variable in the consequent of a rule must also be present in the
antecedent.


XML INTERCHANGE SYNTAX

TBD


SEMANTICS

An interpretation is an extension of an OWL DL interpretation
(http://www.w3.org/TR/owl-semantics/direct.html), extending the
vocabulary to include RIF relation names and mapping them to tuples
over R union LV.  RIF relation names that are OWL DL class names,
datatype names, individual-valued property names, data-valued property
names, or annotation property names have the same extension as given
by the appropriate part of the OWL semantics.

A RIF rule is true in a RIF interpretation precisely when every
mapping from variables in the rule into R union LV that makes each
atom in the antecedent of the rule true in the obvious extension of
the OWL DL semantics also makes the consequent in the rule true in the
same way.


COMPLIANCE

Compliance for formalism X will be measured as follows.
a/ Partial mappings will be provided between the syntaxes of X and RIF
   Phase 1, including mappings between X's data language and OWL DL.
b/ A subset of RIF Phase 1 will be identified as being X-compliant.
c/ For that subset the deductive behaviour of X must mirror reasoning
   in the RIF Phase 1 in the sense that ground consequences for
   knowledge bases in this subset are the same for RIF Phase 1 and its
   mapping into the syntax of X.

Compliance of a rule system with RIF Phase 1 will be defined as follows.
1/ The formalism underlying the rule system must be RIF Phase 1
   compliant as defined above.
2/ There must be a tool that implements the syntax mapping.
3/ There must be a comprehensive set of RIF knowledge bases for which
   the equivalence of deductive behaviour has been reasonably demonstrated.