RIF Core Dialect (Second Edition)

RIF Core Dialect (Second Edition)
RIF Core Dialect (Second Edition)
W3C Recommendation 5 February 2013
This version:
Latest version:
Previous version:
Editors:
Harold Boley, National Research Council Canada
Gary Hallmark, Oracle Corporation
Michael Kifer, State University of New York at Stony Brook, USA
Adrian Paschke, Freie Universitaet Berlin
Axel Polleres, DERI
Dave Reynolds, Hewlett-Packard Laboratories, Bristol UK
Please refer to the
errata
for this document, which may include some normative corrections.
color-coded version of this document showing changes made since the previous version
is also available.
This document is also available in these non-normative formats:
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See also
translations
W3C
MIT
ERCIM
Keio
Beihang
), All Rights Reserved. W3C
liability
trademark
and
document use
rules apply.
Abstract
This document, developed by the
Rule Interchange Format (RIF) Working Group
, specifies RIF-Core, a common subset of RIF-BLD and RIF-PRD based on RIF-DTB 1.0. The RIF-Core presentation syntax and semantics are specified by restriction in two different ways. First, RIF-Core is specified by restricting the syntax and semantics of RIF-BLD, and second, by restricting RIF-PRD. The XML serialization syntax of RIF-Core is specified by a mapping from the presentation syntax. A normative XML schema is also provided.
Status of this Document
May Be Superseded
This section describes the status of this document at the time of its publication. Other documents may supersede this document. A list of current W3C publications and the latest revision of this technical report can be found in the
W3C technical reports index
at http://www.w3.org/TR/.
Set of Documents
This document is being published as one of a set of 13 documents:
RIF Overview (Second Edition)
RIF Use Cases and Requirements (Second Edition)
RIF Core Dialect (Second Edition)
(this document)
RIF Basic Logic Dialect (Second Edition)
RIF Production Rule Dialect (Second Edition)
RIF Framework for Logic Dialects (Second Edition)
RIF Datatypes and Built-Ins 1.0 (Second Edition)
RIF RDF and OWL Compatibility (Second Edition)
OWL 2 RL in RIF (Second Edition)
RIF Combination with XML data (Second Edition)
RIF In RDF (Second Edition)
RIF Test Cases (Second Edition)
RIF Primer (Second Edition)
Document Unchanged
There have been no changes to the body of this document since the
previous version
. For details on earlier changes, see the
change log
Please Send Comments
Please send any comments to
public-rif-comments@w3.org
public
archive
). Although work on this document by the
Rule Interchange Format (RIF) Working Group
is complete, comments may be addressed in the
errata
or in future revisions. Open discussion among developers is welcome at
public-rif-dev@w3.org
public archive
).
Endorsed By W3C
This document has been reviewed by W3C Members, by software developers, and by other W3C groups and interested parties, and is endorsed by the Director as a W3C Recommendation. It is a stable document and may be used as reference material or cited from another document. W3C's role in making the Recommendation is to draw attention to the specification and to promote its widespread deployment. This enhances the functionality and interoperability of the Web.
Patents
This document was produced by a group operating under the
5 February 2004 W3C Patent Policy
. W3C maintains a
public list of any patent disclosures
made in connection with the deliverables of the group; that page also includes instructions for disclosing a patent.
Table of Contents
Overview
RIF-Core Presentation Syntax
2.1
Alphabet of RIF-Core
2.2
Terms of RIF-Core
2.3
Formulas of RIF-Core
2.4
Annotations and Documents
2.5
Well-formed Formulas
2.6
EBNF Grammar for the Presentation Syntax of RIF-Core
2.6.1
EBNF for the RIF-Core Condition Language
2.6.2
EBNF for the RIF-Core Rule Language
2.6.3
EBNF for RIF-Core Annotations
RIF-Core as a Specialization of RIF-PRD
3.1
Alphabet of RIF-Core
3.2
Terms of RIF-Core
3.3
Formulas of RIF-Core
3.4
Annotations and Documents
3.5
Well-formed Formulas
3.6
Rules and Groups
RIF-Core Semantics
XML Serialization Syntax for RIF-Core
Safeness Criteria
6.1
Safeness
6.2
Strong Safeness (Informative)
Conformance Clauses
Acknowledgements
References
9.1
Normative References
9.2
Informational References
10
Appendix: XML Schema for RIF-Core
10.1
Condition Language
10.2
Rule Language
11
Appendix: RIF Media Type Registration
12
Appendix: Change Log (Informative)
1 Overview
This specification describes
RIF-Core
(the Core dialect of the Rule Interchange Format). From a theoretical perspective, RIF-Core corresponds to the language of definite Horn rules without function symbols (often called 'Datalog') with a standard first-order semantics. RIF-Core thus is a subset of RIF-BLD [
RIF-BLD
]. At the same time, RIF-Core is a language of production rules where conclusions are interpreted as assert actions. RIF-Core thus also is a subset of RIF-PRD [
RIF-PRD
]. Moreover, RIF-Core is based on built-in functions and predicates over selected XML Schema datatypes, as specified in RIF-DTB 1.0 [
RIF-DTB
]. The common subset of RIF-BLD and RIF-PRD is specified based on RIF-DTB 1.0.
Syntactically, RIF-Core has a number of Datalog extensions to support features such as objects and frames as in F-logic [
KLW95
], internationalized resource identifiers (or IRIs, defined by [
RFC-3987
]) as identifiers for concepts, and XML Schema datatypes [
XML-SCHEMA2
]. In addition, RIF RDF and OWL Compatibility [
RIF-RDF+OWL
] defines the syntax and semantics of integrated RIF-Core/RDF and RIF-Core/OWL languages. These features make RIF-Core a Web-aware language. However, it should be kept in mind that RIF is designed to enable interoperability among rule languages in general, and its uses are not limited to the Web.
RIF-Core is defined as a specialization of RIF-BLD (hence of [
RIF-FLD
], making it a starting point of the RIF extensibility framework). It is a syntactic subset of RIF-BLD, so that a well-formed RIF-Core formula (including document and condition formulas) is also a well-formed RIF-BLD formula.
RIF-Core is also a syntactic subset of [
RIF-PRD
]. It is intended that a RIF-PRD consumer can treat a RIF-Core document as if it was a RIF-PRD rule set while it also conforms to the normative RIF-Core first order semantics. However, due to the presence of builtin functions and predicates there are rule sets in the syntactic intersection of RIF-PRD and RIF-BLD which would not terminate under RIF-PRD semantics. We therefore define a notion of safe RIF-Core rules, which is a subset of RIF-Core rules that can be executed using a forward chaining strategy, and we define conformance in terms of such safe rules. These notions of safeness and conformance are defined formally in section 5
Conformance and Safeness
RIF-Core is not the
maximal
common subset of RIF-BLD and RIF-PRD. It omits some features from the intersection which do not significantly add to the expressiveness of the language and are judged to be not widely supported by rule languages.
To give a preview, here is a simple complete RIF-Core example deriving a ternary relation from its inverse.
Example 1
(An introductory RIF-Core example).
A rule can be written in English to derive
buy
relationships from the
sell
relationships that are
stored as facts (e.g., as exemplified by the English statements below):
A buyer buys an item from a seller
if the seller sells the item to the buyer.
John sells LeRif to Mary.
The fact
Mary buys LeRif from John
can be logically derived by a
modus ponens
argument.
Assuming Web IRIs for the predicates
buy
and
sell
, as well as for the individuals
John
Mary
, and
LeRif
, the above English phrase can be represented in RIF-Core Presentation Syntax as follows.
Document(
Prefix(cpt )
Prefix(ppl )
Prefix(bks )

Group
Forall ?Buyer ?Item ?Seller (
cpt:buy(?Buyer ?Item ?Seller) :- cpt:sell(?Seller ?Item ?Buyer)

cpt:sell(ppl:John bks:LeRif ppl:Mary)
For the interchange of documents containing such rules (and facts), an equivalent RIF-Core XML syntax is provided in this specification. To formalize their meaning, a RIF-Core Semantics is specified.
This document assumes familiarity with [
RIF-BLD
] or [
RIF-PRD
], as RIF-Core is derived from these documents via syntactic restrictions.
2 RIF-Core Presentation Syntax
Like RIF-BLD and RIF-PRD, RIF-Core has both a
presentation syntax
and an
XML syntax
It is defined in "mathematical English," a special form
of English for communicating mathematical definitions, examples, etc. and by an EBNF syntax.
The mathematical English is normative, the EBNF is not normative; both instances of the presentation syntax are not intended to be a concrete
syntax for RIF-Core. The English presentation syntax deliberately leaves out details such as the delimiters
of the various syntactic components, escape symbols, parenthesizing,
precedence of operators, and the like. Since RIF is an interchange format,
it uses XML, and only XML, as its concrete syntax. RIF-Core conformance is described in
terms of semantics-preserving mappings.
Since RIF-Core is a syntactic subset of RIF-BLD, this section defines
the presentation syntax of RIF-Core as a restriction on
the presentation syntax of RIF-BLD
2.1 Alphabet of RIF-Core
The
alphabet
of the presentation language of RIF-Core is the
alphabet of the RIF-BLD presentation language
with the exclusion of the symbol
##
(subclass) and the set of symbols
ArgNames
(used for named-argument uniterms).
2.2 Terms of RIF-Core
The
of RIF-Core are the
terms of RIF-BLD
with the exclusion of
subclass terms
and of
terms with named arguments
In RIF-Core there are only
closed ground
lists.
Definition (List Term)
closed ground list
has the form
List(t
...
, where
m≥0
and
, ..., t
are ground terms (no tail and no variables are allowed).
A closed list of the form
List()
(i.e., a list in which
m=0
) is called the
empty list
2.3 Formulas of RIF-Core
The
Formulas
of RIF-Core are the
formulas of RIF-BLD
with the following restrictions.
Subterms that occur inside atomic formulas can be variables, constants, ground list, or external positional terms. This implies that RIF-Core only allows external function applications.
Equality terms and class membership terms
cannot
occur in rule conclusions -- they are allowed only in rule premises.
Terms with named arguments and subclass terms are excluded from RIF-Core.
2.4 Annotations and Documents
RIF-Core allows every term and formula to be optionally annotated in the same way as in RIF-BLD. The frame formulas that are allowed as part of an annotation must be syntactically correct for RIF-Core. In particular, no function symbols are allowed in such a formula.
2.5 Well-formed Formulas
A syntactically correct RIF-Core formula that passes the
well-formedness test for RIF-BLD
is also a well-formed RIF-Core formula.
Recall that RIF-Core does not allow uninterpreted (i.e., non-external) function symbols. Therefore no symbol in RIF-Core can occur in the
context
of an (uninterpreted) function symbol.
2.6 EBNF Grammar for the Presentation Syntax of RIF-Core
Until now, we have used mathematical English to specify the syntax of RIF-Core as a restriction on RIF-BLD. Tool developers, however, may prefer EBNF notation, which provides a more succinct view of the syntax. However, EBNF is unable to express all of the well-formedness conditions. For instance, the requirement that each symbol appear in only one context cannot be expressed in EBNF. As a result, the EBNF grammar defines a strict superset of RIF-Core. For that reason this section is
not normative
The EBNF for the RIF-Core presentation syntax is given as follows. For convenience of reading we show the entire EBNF divided into three parts (rules, conditions, and annotations); these are derived from the
ENBF for RIF-BLD
by applying the restrictions described above.
Rule Language:
Document ::= IRIMETA? 'Document' '(' Base? Prefix* Import* Group? ')'
Base ::= 'Base' '('
ANGLEBRACKIRI
')'
Prefix ::= 'Prefix' '('
NCName
ANGLEBRACKIRI
')'
Import ::= IRIMETA? 'Import' '(' LOCATOR PROFILE? ')'
Group ::= IRIMETA? 'Group' '(' (RULE | Group)* ')'
RULE ::= (IRIMETA? 'Forall' Var+ '(' CLAUSE ')') | CLAUSE
CLAUSE ::= Implies | ATOMIC
Implies ::= IRIMETA? (ATOMIC | 'And' '(' ATOMIC* ')') ':-' FORMULA
LOCATOR ::=
ANGLEBRACKIRI
PROFILE ::=
ANGLEBRACKIRI
Condition Language:
FORMULA ::= IRIMETA? 'And' '(' FORMULA* ')' |
IRIMETA? 'Or' '(' FORMULA* ')' |
IRIMETA? 'Exists' Var+ '(' FORMULA ')' |
ATOMIC |
IRIMETA? Equal |
IRIMETA? Member |
IRIMETA? 'External' '(' Atom ')'
ATOMIC ::= IRIMETA? (Atom | Frame)
Atom ::= UNITERM
UNITERM ::= Const '(' (TERM* ')'
GROUNDUNITERM ::= Const '(' GROUNDTERM* ')'
Equal ::= TERM '=' TERM
Member ::= TERM '#' TERM
Frame ::= TERM '[' (TERM '->' TERM)* ']'
TERM ::= IRIMETA? (Const | Var | List | 'External' '(' Expr ')')
GROUNDTERM ::= IRIMETA? (Const | List | 'External' '(' GROUNDUNITERM ')')
Expr ::= UNITERM
List ::= 'List' '(' GROUNDTERM* ')'
Const ::= '"'
UNICODESTRING
'"^^' SYMSPACE |
CONSTSHORT
Var ::= '?' Name
Name ::=
NCName
| '"'
UNICODESTRING
'"'
SYMSPACE ::=
ANGLEBRACKIRI
CURIE
Annotations:
IRIMETA ::= '(*' IRICONST? (Frame | 'And' '(' Frame* ')')? '*)'
ANGLEBRACKIRI
CURIE
CONSTSHORT
, and
UNICODESTRING
are defined in Section
Shortcuts for Constants in RIF's Presentation Syntax
of [
RIF-DTB
].
The following subsections explain and exemplify the Condition Language, Rule Language, and Annotations parts.
2.6.1 EBNF for the RIF-Core Condition Language
The RIF-Core Condition Language represents formulas that can be used in the premises of RIF-Core rules (also called rule bodies). The EBNF grammar for a superset of the RIF-Core condition language is shown in the above
conditions part
This is a specialization of the EBNF for the RIF-BLD condition language specified in the
RIF-BLD conditions part
reflecting the syntax restrictions on RIF-Core described normatively in sections 2.1 through 2.5 above.
Example 3
from the RIF-BLD document, illustrates some RIF-BLD conditions. All the conditions, except for the terms with named arguments and the equalities with (non-ground) list terms, are also RIF-Core conditions.
2.6.2 EBNF for the RIF-Core Rule Language
The presentation syntax for RIF-Core rules is based on the syntax in Section
EBNF for the RIF-Core Condition Language
with the productions shown in the above
rules part
Again, this is a specialization of the EBNF for the RIF-BLD rule language specified in the
RIF-BLD rules part
reflecting the syntax restrictions on RIF-Core described normatively in sections 2.1 through 2.5 above.
Example 4
from the RIF-BLD document also illustrates a set of RIF-Core rules.
In contrast,
Example 7
from the RIF-BLD document shows a formula that is
not
in RIF-Core because it includes terms with named arguments, which are not allowed in this dialect.
2.6.3 EBNF for RIF-Core Annotations
The presentation syntax for RIF-Core annotations uses the production shown in the above
annotations part
This defines the specialization of the EBNF for the RIF-BLD annotation language specified through the
RIF-BLD annotations part
where annotation frames use the more restricted TERMs defined in the above
conditions part
of RIF-Core.
Example 5
from the RIF-BLD document also illustrates a RIF-Core document that contains an annotated group formula.
3 RIF-Core as a Specialization of RIF-PRD
RIF-Core is a syntactic subset of RIF-PRD
, and this section defines
the presentation syntax of RIF-Core as a restriction on
the presentation syntax of RIF-PRD
Conditions
Actions
, and
Rules
3.1 Alphabet of RIF-Core
The
alphabet
of the presentation language of RIF-Core is the alphabet of the RIF-PRD presentation language (
Conditions
Actions
, and
Rules
) with the exclusion of the symbols
##
such that
Not
INeg
Do
Assert
Retract
Modify
Execute
, and
New
3.2 Terms of RIF-Core
The
of RIF-Core are the
of RIF-PRD with the exclusion of
subclass terms
. In Core there are only
closed ground
lists.
3.3 Formulas of RIF-Core
The
Formulas
of RIF-Core are the
formulas of RIF-PRD
with the exclusion of
negation formulas
3.4 Annotations and Documents
RIF-Core allows every term and formula to be optionally annotated in the same way as in RIF-PRD. The frame formulas that are allowed as part of an annotation must be syntactically correct for RIF-Core.
3.5 Well-formed Formulas
A syntactically correct RIF-Core formula that passes the
well-formedness test for RIF-PRD
is also a well-formed RIF-Core formula.
3.6 Rules and Groups
A RIF-Core rule is a
well-formed RIF-PRD rule
rule with no nested forall, no binding pattern, and where the action block is a single atom, a single frame, or a conjunction
of atoms and/or frames. A RIF-Core group is a RIF-PRD group without
strategy
and without
priority
4 RIF-Core Semantics
RIF-Core is a syntactic subset of RIF-BLD, and the semantics of RIF-Core is identical to the semantics of RIF-BLD for that subset. RIF-Core is also a syntactic subset of RIF-PRD, and the semantics of RIF-Core is also identical to the semantics of RIF-PRD for that subset.
5 XML Serialization Syntax for RIF-Core
The XML syntax of RIF-Core is a subset of the
XML syntax of RIF-BLD
. All XML tags of RIF-BLD (except
Subclass
sub
and
super
) are supported, but the XML schema of RIF-Core restricts their context with respect to what is allowed by the XML schema of RIF-BLD. The semantics of the XML syntax for RIF-Core is defined through the same
RIF-BLD XML-to-presentation syntax mapping
XML serialization of a complete RIF-Core document appears in the RIF-BLD specification as
Example 8
6 Safeness Criteria
RIF-Core is a syntactic subset of both RIF-BLD and RIF-PRD. The semantics of a RIF-Core formula is the same as the semantics given to it by RIF-BLD.
All RIF-Core documents are also syntactically valid RIF-PRD documents. However, some formulas may be
unsafe
and cannot be executed under the RIF-PRD operational semantics. Thus, in order to allow production rule systems and logic programming systems to interchange rules via RIF-Core, we restrict RIF-Core to
safe
rules so that the logical semantics of RIF-BLD and the operational fixed-point semantics of RIF-PRD coincide.
6.1 Safeness
Intuitively, safeness of rules guarantees that, when performing reasoning in a forward-chaining manner, it is possible to find bindings for all the variables in the rule so that the condition can be evaluated.
To define safeness, we need to define, first, the notion of
binding patterns
for externally defined terms, as well as under what conditions variables are considered
bound
Definition (Binding pattern).
Binding patterns
are lists of the form (
...
), such that
or
, for
1 ≤ i ≤ n
stands for a "bound" and
stands for an "unbound" argument.   ☐
Each external function or predicate has an associated list of
valid binding patterns
. We define here the binding patterns valid for the functions and predicates defined in [
RIF-DTB
].
Every function or predicate
defined in [
RIF-DTB
] has a valid binding pattern for each of its schemas with only the symbol
such that its length is the number of arguments in the schema. In addition,
the external predicate
pred:iri-string
has the valid binding patterns (
) and (
) and
the external predicate
pred:list-contains
has the valid binding pattern (
).
The functions and predicates defined in [
RIF-DTB
] have no other valid binding patterns.
To keep the definitions concise and intuitive,
boundedness
and
safeness
are defined, below, for condition formulas in disjunctive normal form, that can be existentially quantified themselves, but that contain, otherwise, no existential sub-formula. The definitions apply to any valid RIF-Core condition formula, because they can always, in principle, be put in that form, by applying the following syntactic transforms, in sequence:
if
contains existential sub-formulas, all the quantified variables are renamed, if necessary, and given a name that is unique in
, and the scope of the quantifiers is extended to
. Assume, for instance, that
has an existential sub-formula,
sf =
Exists v
...v
(sf')
, n ≥ 1
, such that the names
...v
do not occur in
outside of
sf
. After the transform,
becomes
Exists v
...v
(f')
, where
f'
is
with
sf
replaced by
sf'
. The transform is applied iteratively to all the existential sub-formulas in
the (possibly existentially quantified) resulting formula is rewritten in disjunctive normal form ([
Mendelson97
], p. 30).
Definition (Boundedness).
An external function term
External(f(t
,...,t
))
is
bound
in a condition formula, if and only if
has a valid binding pattern (
...
) and, for all
j, 1 ≤ j ≤ n
, such that
is bound in the formula.
A variable,
, is
bound
in an atomic formula,
, if and only if
is neither an equality nor an external predicate, and
occurs as an argument in
or
is bound in the conjunction formula
f =
And(a)
A variable,
, is
bound
in a conjunction formula,
f =
And(c
...c
, n ≥ 1
, if and only if, either
is bound in at least one of the conjuncts;
or
occurs as the
j-th
argument in a conjunct,
, that is an externally defined predicate, and the
j-th
position in a binding pattern that is associated with
is
, and all the arguments that occur, in
, in positions with value
in the same binding pattern are bound in
f' =
And(c
...c
i-1
i+1
...c
or
occurs in a conjunct,
, that is an equality formula, and
occurs as the term on one side of the equality, and the term on the other side of the equality is bound in
f' =
And(c
...c
i-1
i+1
...c
A variable,
, is
bound
in a disjunction formula, if and only if
is bound in every disjunct where it occurs;
A variable,
, is
bound
in an existential formula,
Exists v
,...,v
(f')
n ≥ 1
, if and only if
is bound in
f'
.   ☐
Notice that the variables,
,...,v
, that are existentially quantified in an existential formula
f =
Exists v
,...,v
(f')
, are bound in any formula,
, that contains
as a sub-formula, if and only if they are bound in
, since they do not exist outside of
Definition (Safeness).
A variable,
, is
safe
in a condition formula,
, if and only if
is an atomic formula and
is not an equality formula in which both terms are variables, and
occurs in
or
is a conjunction,
f =
And(c
...c
, n ≥ 1
, and
is safe in at least one conjunct in
, or
occurs in a conjunct,
, that is an equality formula in which both terms are variables, and
occurs as the term on one side of the equality, and the variable on the other side of the equality is safe in
f' =
And(c
...c
i-1
i+1
...c
or
is a disjunction, and
is safe in every disjunct;
or
is an existential formula,
f =
Exists v
,...,v
(f')
, n ≥ 1
, and
is safe in
f'
A RIF-Core rule,
is
safe
if and only if
is a variable free atomic formula,
or
is a universal fact,
Forall v
,...,v
(f)
n ≥ 1
, and
is variable free,
or
is a rule implication,
φ :- ψ
, and all the variables that occur in
are safe in
, and all the variables that occur in
are bound in
or
is a universal rule,
Forall v
,...,v
(r')
n ≥ 1
, and
r'
is safe.
A group,
Group (s
...s
n ≥ 0
, is
safe
if and only if
it is empty, that is,
n = 0
or
and ... and
are safe.
A document is
safe
if and only if
it contains a safe group, or no group at all,
and all the documents that it imports are safe.   ☐
Example.
Consider the following formula:
Forall ?x ?y ?z ?u
(ex:p(?x) :- Or( And( ex:q(?z)
External(pred:iri-string(?x ?z))))
And( ?x=?y ?y=?u ex:q(?u)))
One can verify that this formula is safe, in the following way: the only variable appearing in the conclusion of the rule is
?x
?x
is safe in the first component of the disjunction, because it occurs in the atomic formula
pred:iri-string(?x,?z)
. It is also safe in the second disjunct, because it occurs as the left term in an equality formula where the right term is
?y
, which is safe because it occurs as the left term in an equality formula where the right term is
?u
, which is safe because it occurs in the atomic formula
ex:q(?u)
. Being safe in both disjuncts,
?x
is safe in the disjunction.
Moreover,
?x
?y
?z
and
?u
are all bound in the body of the rule:
?z
is bound in the first disjunct because it occurs as an argument in the atom
ex:q(?z)
. Therefore, it is bound in the disjunction because it does not occur in the other disjunct;
?u
is bound in the second disjunct because it occurs as an argument in the atom
ex:q(?u)
. Therefore, it is bound in the disjunction because it does not occur in the other disjunct;
?y
is bound in the second disjunct because it occurs as the left term in an equality formula where the right term is
?u
, which is bound in the conjunction without that equality formula. Therefore, it is bound in the disjunction because it does not occur in the other disjunct;
?x
is bound in the first disjunct because
(u,b)
is a valid binding pattern for
pred:iri-string
, where
?x
occurs as the first argument, and
?z
, which occurs as the second argument, is bound in the conjunction without the external predicate.
?x
is also bound in the second disjunct, because it occurs as the left term in an equality formula where the right term is
?y
, which is bound in the conjunction without that equality formula. Therefore,
?x
is bound in the disjunction.
6.2 Strong Safeness (Informative)
While safeness guarantees the possibility to do forward chaining with the rules, it does not guarantee that it is possible to construct a finite grounding. For this purpose we define strong safeness.
The conformance clauses for RIF-Core only require conformance over safe rule sets as defined above. However, some rule engines, such as some Datalog engines, are only able to process rule sets which can be finitely grounded. For maximum interoperability with such systems it is recommended that RIF-Core producers restrict themselves to strongly safe rule sets where possible.
Let R be a set of safe rule implications
φ :- ψ
and let
be the set of pairs
(p,n)
, where
is a predicate symbol and
is a nonnegative integer (an arity). For the purposes of the definitions in this section we view frames
a[b -> c]
and membership formulas
a#b
, respectively, as ternary and binary predicate symbols, and so
(->,3)
(#,2)
. Note that equality
does not appear in
We define the
graph of variable dependencies
of a set of atomic formulas A as a labeled directed graph G
=(V, E, L), where the labeling function L maps edges to sets of external function and predicate symbols, V is the set of variables appearing in A, and E is the smallest set and L' is the smallest function such that for every variable
?V
for every atomic formula
?V=t
or
t=?V
in A and every variable
?V'≠?V
appearing in
such that
, ..., f
0 ≤ n
, are the function symbols of the terms in
(including
itself) in which
?V'
appears, (
?V,?V'
) ∈ E and {
, ..., f
} ∈ L'((
?V,?V'
)), and
for every external atomic formula
External(f(t
,...,t
))
in A, every
∈ {
1,...,n
} such that
?V
, every valid binding pattern (
...
) of
such that
, and every variable
?V'
appearing in some t
such that
and
, ..., f
0 ≤ m
, are the function symbols of the terms in
in which
?V'
appears, (
?V,?V'
) ∈ E and {
, ..., f
} ∈ L'((
?V,?V'
)).
Finally, L is defined as: for every (e,e') ∈ E, L((e,e')) is the union of the minimal sets in L'((e,e')).
For every rule implication,
φ :- ψ
, we define the collection, B
, of the sets of the atomic formulas in each of the conjunctions that are the components of
ψ'
, where
ψ'
is
rewritten as a condition formula in disjunctive normal form, possibly existentially quantified itself, but otherwise containing no existential sub-formula (see description of the transform in the section
Safeness
, above).
The
dependency graph
of a set of implications R is a labelled directed graph G
=(V, E), where edges are triples (v,v',l) such that v, v' ∈ V and l is a set of external function and predicate symbols. V is defined as: for every
(p,n)
and every integer
such that
1 ≤ i ≤ n
(p,n)/i
∈ V.
E is the smallest set such that for every
(p,n)/i
∈ V and every
φ :- ψ
in R such that there is an atomic subformula
p(t
,...,t
,...,t
of
, then for every variable
?V
appearing in
for every non-external and non-equality atomic formula with predicate symbol
p'
and
arguments in any A ∈ B
and every
∈ {
1,...,m
} such that a variable
?V'
is the
th argument and there is a path from
?V
to
?V'
in the graph of variable dependencies of A and F is the union of the labels of the shortest path, (
(p,n)/i,(p',m)/j, F ∪ {f
,...,f
) ∈ E, where
, ..., f
0 ≤ l
, are the function symbols of the terms in
in which
?V
appears.
Definition (Strong safeness).
A set of rule implications
is
strongly safe
if its dependency graph does not contain cycles involving edges labelled with sets involving a function defined in [
RIF-DTB
] that is not a casting function. A RIF document
is strongly safe if the set
of rule implications that are subformulas of
is strongly safe.
7 Conformance Clauses
RIF-Core conformance is described in terms of semantics-preserving transformations.
Let Τ be a set of datatypes and symbol spaces that includes the datatypes specified in [
RIF-DTB
] and the symbol spaces
rif:iri
and
rif:local
. Suppose also that Ε is a set of external predicates and functions that includes the built-ins listed in [
RIF-DTB
]. We say that a formula φ is a
Core
Τ,Ε
formula iff
φ is a well-formed Core formula,
all the datatypes and symbol spaces used in φ are in Τ, and
all the externally defined functions and predicates used in φ are in Ε.
A RIF processor is a
conformant
Core
Τ,Ε
consumer
iff it implements a
semantics-preserving mapping
from the set of all
safe
Core
Τ,Ε
formulas to the language
of the processor.
A RIF processor is a
conformant
Core
Τ,Ε
producer
iff it implements a
semantics-preserving mapping
from the language
of the processor to a set of
safe
Core
Τ,Ε
formulas.
An
admissible document
is an XML document that conforms to all the syntactic
constraints of RIF-Core, including ones that cannot be checked by an XML
Schema validator. Note that the concrete presentation syntax given in Section 2.6 is purely informative (to help implementers see the set of language structures supported by RIF-Core); the only normative concrete syntax for RIF-Core is the XML syntax.
In addition:
Conformant Core producers and consumers are required to support only the entailments of the form φ |=
CORE
ψ, where ψ is a
closed RIF-Core condition formulas
, that is a RIF-Core condition formula which also meets the criteria for closed condition formula defined in
RIF-BLD
conformant Core consumer
must reject any document containing features it does not support.
conformant Core producer
is a conformant Core
Τ,Ε
producer which produces documents that include only the symbol spaces, datatypes, and externals that are required by Core.
8 Acknowledgements
This document is the product of the Rules Interchange Format (RIF) Working Group (see below) whose
members deserve recognition for their time and commitment. The editors extend special thanks to Jos de Bruijn for his safeness definition and to: Jos de Bruijn, Leora Morgenstern, Christian de Sainte-Marie, Stella Mitchell and Changhai Ke for their thorough reviews and insightful discussions; the working group chairs, Chris Welty and Christian de Sainte-Marie, for their invaluable technical help and inspirational leadership; and W3C staff contact Sandro Hawke, a constant source of ideas, help, and feedback.
The regular attendees at meetings of the Rule Interchange Format (RIF) Working Group at the time of the publication were:
Adrian Paschke (Freie Universitaet Berlin),
Axel Polleres (DERI),
Chris Welty (IBM),
Christian de Sainte Marie (IBM),
Dave Reynolds (HP),
Gary Hallmark (ORACLE),
Harold Boley (NRC),
Jos de Bruijn (FUB),
Leora Morgenstern (IBM),
Michael Kifer (Stony Brook),
Mike Dean (BBN),
Sandro Hawke (W3C/MIT), and
Stella Mitchell (IBM).
9 References
9.1 Normative References
[RDF-CONCEPTS]
Resource Description Framework (RDF): Concepts and Abstract Syntax
, Klyne G., Carroll J. (Editors), W3C Recommendation, 10 February 2004,
. Latest version available at
[RFC-3066]
RFC 3066
- Tags for the Identification of Languages
, H. Alvestrand, IETF, January 2001. This document is
[RFC-3987]
RFC 3987
- Internationalized Resource Identifiers (IRIs)
, M. Duerst and M. Suignard, IETF, January 2005. This document is
[RIF-BLD]
RIF Basic Logic Dialect (Second Edition)
Harold Boley, Michael Kifer, eds. W3C Recommendation, 5 February 2013,
. Latest version available at
[RIF-DTB]
RIF Datatypes and Built-Ins 1.0 (Second Edition)
Axel Polleres, Harold Boley, Michael Kifer, eds. W3C Recommendation, 5 February 2013,
. Latest version available at
[RIF-FLD]
RIF Framework for Logic Dialects (Second Edition)
Harold Boley, Michael Kifer, eds. W3C Recommendation, 5 February 2013,
. Latest version available at
[RIF-RDF+OWL]
RIF RDF and OWL Compatibility (Second Edition)
Jos de Bruijn, Chris Welty, eds. W3C Recommendation, 5 February 2013,
. Latest version available at
[RIF-PRD]
RIF Production Rule Dialect (Second Edition)
Christian de Sainte Marie, Gary Hallmark, Adrian Paschke, eds. W3C Recommendation, 5 February 2013,
. Latest version available at
[XML1.0]
Extensible Markup Language (XML) 1.0 (Fourth Edition)
, W3C Recommendation, World Wide Web Consortium, 16 August 2006, edited in place 29 September 2006. This version is
[XML-Base]
XML Base
, W3C Recommendation, World Wide Web Consortium, 27 June 2001. This version is
. The latest version is available at
[XML-SCHEMA2]
XML Schema Part 2: Datatypes
, W3C Recommendation, World Wide Web Consortium, 2 May 2001. This version is
. The latest version is available at
9.2 Informational References
[ANF01]
Normal Form Conventions for XML Representations of Structured Data
, Henry S. Thompson. October 2001. Available at
[CL73]
Symbolic Logic and Mechanical Theorem Proving
, C.L. Chang and R.C.T. Lee. Academic Press, 1973.
[CURIE]
CURIE Syntax 1.0
, S. McCarron, M. Birbeck, Editors, W3C Working Group Note, 16 December 2010,
. Latest version available at
[Enderton01]
A Mathematical Introduction to Logic, Second Edition
, H. B. Enderton. Academic Press, 2001.
[KLW95]
Logical foundations of object-oriented and frame-based languages,
M. Kifer, G. Lausen, J. Wu. Journal of ACM, July 1995, pp. 741--843.
[Mendelson97]
Introduction to Mathematical Logic, Fourth Edition
, E. Mendelson. Chapman & Hall, 1997.
[OWL-Reference]
OWL Web Ontology Language Reference
, M. Dean, G. Schreiber, Editors, W3C Recommendation, 10 February 2004. Latest version available at
[RDFSYN04]
RDF/XML Syntax Specification (Revised)
, Dave Beckett, Editor, W3C Recommendation, 10 February 2004,
. Latest version available at
[RIF-UCR]
RIF Use Cases and Requirements (Second Edition)
Adrian Paschke, Leora Morgenstern, David Hirtle, Allen Ginsberg, Paula-Lavinia Patranjan, Frank McCabe, eds. W3C Working Group Note, 5 February 2013,
. Latest version available at
[TRT03]
Object-Oriented RuleML: User-Level Roles, URI-Grounded Clauses, and Order-Sorted Terms
, H. Boley. Springer LNCS 2876, Oct. 2003, pp. 1-16. Available at
[vEK76]
The semantics of predicate logic as a programming language
, M. van Emden and R. Kowalski. Journal of the ACM 23 (1976), pp. 733-742.
10 Appendix: XML Schema for RIF-Core
The
namespace
of RIF is "
".
XML schemas for the RIF-Core sublanguages are defined below and are also available at
with additional examples.
10.1 Condition Language

xmlns:xs="http://www.w3.org/2001/XMLSchema"
xmlns:xml="http://www.w3.org/XML/1998/namespace"
xmlns="http://www.w3.org/2007/rif#"
targetNamespace="http://www.w3.org/2007/rif#"
elementFormDefault="qualified"
version="Id: CoreCond.xsd, v. 1.4, 2010-05-08, hboley/apaschke">

schemaLocation='http://www.w3.org/2001/xml.xsd'/>

This is the XML schema for the Condition Language as defined by
the RIF-Core dialect.

The schema is based on the following EBNF for the RIF-Core Condition Language
(prepared for generalization to the RIF-BLD and RIF-PRD Condition Languages):

FORMULA ::= IRIMETA? 'And' '(' FORMULA* ')' |
IRIMETA? 'Or' '(' FORMULA* ')' |
IRIMETA? 'Exists' Var+ '(' FORMULA ')' |
ATOMIC |
IRIMETA? Equal |
IRIMETA? Member |
IRIMETA? 'External' '(' Atom ')'
ATOMIC ::= IRIMETA? (Atom | Frame)
Atom ::= UNITERM
UNITERM ::= Const '(' (TERM* ')'
GROUNDUNITERM ::= Const '(' GROUNDTERM* ')'
Equal ::= TERM '=' TERM
Member ::= TERM '#' TERM
Frame ::= TERM '[' (TERM '->' TERM)* ']'
TERM ::= IRIMETA? (Const | Var | List | 'External' '(' Expr ')')
GROUNDTERM ::= IRIMETA? (Const | List | 'External' '(' GROUNDUNITERM ')')
Expr ::= UNITERM
List ::= 'List' '(' GROUNDTERM* ')'
Const ::= '"' UNICODESTRING '"^^' SYMSPACE | CONSTSHORT
Var ::= '?' Name
Name ::= NCName | '"' UNICODESTRING '"'
SYMSPACE ::= ANGLEBRACKIRI | CURIE

IRIMETA ::= '(*' IRICONST? (Frame | 'And' '(' Frame* ')')? '*)'

10.2 Rule Language

This is the XML schema for the Rule Language as defined by
the RIF-Core dialect.

The schema is based on the following EBNF for the RIF-Core Rule Language
(prepared for generalization to the RIF-BLD and RIF-PRD Rule Languages):

Document ::= IRIMETA? 'Document' '(' Base? Prefix* Import* Group? ')'
Base ::= 'Base' '(' ANGLEBRACKIRI ')'
Prefix ::= 'Prefix' '(' NCName ANGLEBRACKIRI ')'
Import ::= IRIMETA? 'Import' '(' LOCATOR PROFILE? ')'
Group ::= IRIMETA? 'Group' '(' (RULE | Group)* ')'
RULE ::= (IRIMETA? 'Forall' Var+ '(' CLAUSE ')') | CLAUSE
CLAUSE ::= Implies | ATOMIC
Implies ::= IRIMETA? (ATOMIC | 'And' '(' ATOMIC* ')') ':-' FORMULA
LOCATOR ::= ANGLEBRACKIRI
PROFILE ::= ANGLEBRACKIRI

Note that this is an extension of the syntax for the RIF-Core Condition Language (CoreCond.xsd).

11 Appendix: RIF Media Type Registration
The anticipated RIF media type is "application/rif+xml". The registration for this media type (pending IETF discussion and approval by the IESG) follows.
Type name: application

Subtype name: rif+xml

Required parameters: none

Optional parameters: charset, as per RFC 3023 (XML Media Types)

Encoding considerations: same as RFC 3023 (XML Media Types)

Security considerations:

Systems which consume RIF documents are potentially vulnerable
to attack by malicious producers of RIF documents. The
vulnerabilities and forms of attack are similar to those of
other Web-based formats with programming or scripting
capabilities, such as HTML with embedded Javascript.

Excessive Resource Use / Denial of Service Attacks

Complete processing of a RIF document, even a conformant
RIF Core document, may require arbitrarily great CPU and
memory resources. Through the use of "import", processing
may also require arbitrary URI dereferencing, which may
consume all available network resources on the consuming
system or other systems. RIF consuming systems SHOULD
implement reasonable defenses against these attacks.

Exploiting Implementation Flaws

RIF is a relatively complex format, and rule engines can be
extremely sophisticated, so it is likely that some RIF
consuming systems will have bugs which allow specially
constructed RIF documents to perform inappropriate
operations. We urge RIF implementors to make systems which
carefully anticipate and handle all possible inputs,
including those which present syntactic or semantic errors.

External (Application) Functions

Because RIF may be extended with local, application defined
datatypes and functions, new vulnerabilities may be
introduced. Before being installed on systems which consume
untrusted RIF documents, these external functions should be
closely reviewed for their own vulnerabilities and for the
vulnerabilities that may occur when they are used in
unexpected combinations, like "cross-site scripting"
attacks.

In addition, as this media type uses the "+xml" convention, it
shares the same security considerations as other XML formats;
see RFC 3023 (XML Media Types).

Interoperability considerations:

This media type is intended to be shared with other RIF
dialects, to be specified in the future. Interoperation
between the dialects is governed by the RIF specifications.

Published specifications:

RIF Core Dialect
W3C Working Draft (Recommendation Track)

RIF Datatypes and Builtins
W3C Working Draft (Recommendation Track)

RIF Basic Logic Dialect
W3C Working Draft (Recommendation Track)

RIF Production Rule Dialect
W3C Working Draft (Recommendation Track)

RIF Framework for Logic Dialects
W3C Working Draft (Recommendation Track)

This media type is intended for use by all RIF dialects,
including those to be specified in the future. Identification
of the RIF dialect in use by a document is done by examining
the use of specific XML elements within the document.

Applications that use this media type:

See: http://www.w3.org/2005/rules/wiki/Implementations

Additional information:

Magic number(s):

As with XML in general (See RFC 3023 (XML Media Types)),
there is no magic number for this format.

However, the XML namespace "http://www.w3.org/2007/rif#" will
normally be present in the document. It may theoretically
be missing if the document uses XML entities in an
obfuscatory manner, and may also be present in documents with
ther media types, so use of the namespace is not conclusive.

The hex form of that namespace will depend on the charset.
For utf-8, the hex is: 68 74 74 70 3a 2f 2f 77 77 77 2e 77
33 2e 6f 72.

File extension(s):

.rif (or .xml)

Macintosh file type code(s):

"TEXT" (like other XML)

Person & email address to contact for further information:

Sandro Hawke, sandro@w3.org. Please send technical comments
and questions about RIF to public-rif-comments@w3.org, a
mailing list with a public archive at

Intended usage:

COMMON

Restrictions on usage:

None

Author:

The editor and contact for this media type registration is
Sandro Hawke, sandro@w3.org.

Change controller:

RIF is a product of the Rule Interchange Format (RIF) Working
Group of the World Wide Web Consortium (W3C). See
The W3C (currently acting through this working group) has
change control over the RIF specification.
12 Appendix: Change Log (Informative)
This appendix summarizes the main changes to this document.
Changes since the
draft of July 3, 2009
IRI was replaced with ANGLEBRACKIRI in CoreRule.xsd, v. 1.3.
The complexType ANYURICONST was introduced in CoreRule.xsd, v. 1.3.
A number of typos were found and fixed.
Changes since the
Candidate Recommendation of October 1, 2009
Import's anyURIs were moved directly into location and profile.
Simplified notion of conformant Core consumer.
Fixed List by permitting IRIMETA and aligning syntax to Expr and Atom.
Accommodated DTB-triggered UNICODESTRING/NCName changes of BLD in EBNF.
Changes since the
Recommendation of 22 June, 2010
Definition (Strong safeness): introduced document metavariable D; omitted Editor's Note.