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### The Syntax of RIF-BLD as a Specialization of RIF-FLD

This section defines the precise relationship between the syntax of RIF-BLD and the syntactic framework of RIF-FLD. The other sections describe RIF-BLD largely independently of RIF-FLD.

The syntax of the RIF Basic Logic Dialect is defined by specialization from the syntax of the Syntactic Framework for Logic Dialects of RIF. Section Syntax of a RIF Dialect as a Specialization of RIF-FLD in that document lists the parameters of the syntactic framework, which we will now specialize for RIF-BLD.

• Alphabet.

• The alphabet of RIF-BLD is the alphabet of RIF-FLD with the negation symbols neg and naf excluded

• Assignment of signatures to each constant symbol.

• The signature set of RIF-BLD contains the following signatures:
• term{ }, atomic{ }, bi_atomic{ }, where bi_atomic<atomic.

• The signature term{ } represents the context in which individual objects (but not atomic formulas) can appear. The signature bi_atomic{ } represents atomic formulas for builtin predicates (such as fn:substring). Since bi_atomic<atomic, builtin atomic formulas are also atomic formulas, but normally most atomic formulas are user-defined and they will have the signature atomic rather than bi_atomic.

• For every integer n ≥ 0, there are signatures fn{(term ... term) ⇒ term}, pn{(term ... term) ⇒ atomic}, and bin{(term ... term) ⇒ bi_atomic} (in each case there are n terms inside the parentheses). These represent function symbols of arity n, user-defined predicate symbols of arity n, and n-ary builtin predicates, respectively.

• For every set of symbols s1,...,skSigNames, there are signatures fs1...sk{(s1->term ... sk->term) ⇒ term} and ps1...sk{(s1->term ... sk->term) ⇒ atomic}. These are signatures for terms with named arguments and predicates with arguments named s1, ..., sk, respectively.

• A symbol in Const can have exactly one signature, term, fn, pn, or bin, where n ≥ 0, or fs1...sk{(s1->term ... sk->term) ⇒ term}, ps1...sk{(s1->term ... sk->term) ⇒ atomic}, for some s1,...,skSigNames. It cannot have the signature atomic or bi_atomic, since only complex terms can have such signatures. Thus, by itself a symbol cannot be a proposition in RIF-BLD, but a term of the form p() can be.

• Thus, in RIF-BLD each constant symbol can be either an individual, a predicate of one particular arity or with certain argument names, a builtin of one particular arity, or a function symbol of one particular arity -- it is not possible for the same symbol to play more than one role.
• The constant symbols that correspond to XML Schema data types all have the signature term in RIF-BLD. The symbols of type rif:iri and rif:local can have the following signatures in RIF-BLD: term, fn, pn, or bin, for n = 0,1,....; or fs1...sk, ps1...sk, for some argument names s1,...,skSigNames.

• All variables are associated with signature term{ }, so they can range only over individuals.

• The signature for equality is ={(term term)atomic,   (term term)term}. This means that equality can compare only those terms whose signature is term; it cannot compare predicate names or function symbols.

• The frame signature, ->, is ->{(term term term)atomic,   (term term term)term}.

• The membership signature, #, is #{(term term)atomic,   (term term)term}.

• The signature for the subclass relationship is ##{(term term)atomic,   (term term)term}.

• RIF-BLD uses no extra syntax for declaring signatures. Instead, signatures are inferred. Since RIF-BLD requires that each symbol is associated with a unique signature, the signature can be determined from the context in which the symbol is used. If a symbol is used in more than one context, the parser should treat it as a syntax error. If no errors are found, all terms and atomic formulas are guaranteed to be well-formed. As a consequence, signatures are not part of the RIF-BLD language and term, atomic, and bi_atomic are not reserved keywords in RIF-BLD.

• Supported types of terms.

• RIF-BLD supports all the term types defined by the syntactic framework (see Well-formed Terms and Formulas):

• constants
• variables
• positional
• with named arguments
• equality
• frame
• membership
• subclass
Compared to RIF-FLD, terms (both positional and with named arguments) have significant restrictions:
• The signature for the variable symbols does not permit them to occur in the context of predicates, functions, or formulas. In particular, unlike in RIF-FLD, a variable is not an atomic formula in RIF-BLD.
• Likewise, a symbol cannot be an atomic formula by itself. That is, if pConst then p is not a well-formed atomic formula. However, p() can be an atomic formula.

• Signatures permit only constant symbols to occur in the context of function or predicate names. Indeed, RIF-BLD signatures ensure that all variables have the signature term{ } and all other terms, except for the constants from Const, can have either the signature term{ } or atomic{ }. Therefore, if t is a (non-Const) term then t(...) is not a well-formed term.

• Supported symbol spaces.

• RIF-BLD supports all the symbol spaces defined in Section Symbol Spaces of the syntactic framework:

• xsd:string

• xsd:decimal

• xsd:time

• xsd:date

• xsd:dateTime

• rdf:XMLLiteral

• rif:text

• rif:iri

• rif:local

• Supported formulas.

• RIF-BLD supports the following types of formulas (see Well-formed Terms and Formulas for the definitions):

• RIF-BLD condition

• A RIF-BLD condition is a conjunctive and disjunctive combination of atomic formulas with optional existential quantification of variables.
• RIF-BLD rule

• A RIF-BLD rule is a RIF-FLD rule with the following restrictions:
• The head (or conclusion) of the rule is an atomic formula, which is not a builtin predicate (i.e., its signature is atomic, but not bi_atomic).

• The body (or premise) of the rule is a RIF-BLD condition.
• The free variables in the rule can be optionally quantified with Forall outside of the rule (i.e., Forall ?vars (head :- body)).

Recall that negation (classical or default) is not supported by RIF-BLD in either the rule head or the body.

In order to make this document self-contained, we will now define the syntax of RIF-BLD with no references to RIF-FLD -- except for Symbol Spaces whose definition we do not duplicate here.

### Alphabet of RIF-BLD

The alphabet of RIF-BLD consists of a countably infinite set of constant symbols Const, a countably infinite set of variable symbols Var (disjoint from Const), a countably infinite set of argument names, ArgNames (disjoint from Const and Var), connective symbols And and Or, quantifiers Exists and Forall, the symbols =, #, ##, ->, :-, and auxiliary symbols, such as "(" and ")". The set of connective symbols, quantifiers, =, etc., is disjoint from Const and Var. Variables are written as Unicode strings preceded with the symbol "?". The syntax for constant symbols is given in Section Symbol Spaces of RIF-FLD.

The language of RIF-BLD is the set of formulas constructed using the above alphabet according to the rules spelled out below.

### Terms

RIF-BLD supports several kinds of terms: constants and variables, positional terms, terms with named arguments, equality, membership, and subclass terms, and frames. The word "term" will be used to refer to any kind of terms. Formally, terms are defined as follows:

• Constants and variables. If tConst or tVar then t is a simple term.

• Positional terms. If tConst and t1, ..., tn are terms then t(t1 ... tn) is a positional term.

• Terms with named arguments. A term with named arguments (a term with named arguments) is of the form t(s1->v1 ... sn->vn), where tConst, v1 , ..., vn are terms (positional, with named arguments, frame, etc.), and s1, ..., sn are (not necessarily distinct) symbols from the set ArgNames. The term t here represents a predicate or a function; s1, ..., sn represent argument names; and v1 , ..., vn represent argument values. Terms with named arguments are like positional terms except that the arguments are named and their order is immaterial. Note that a term like f() is both positional and with named arguments.

• Equality terms. If t and s are terms then t = s is an equality term.

• Class membership terms (or just membership terms). t#s is a membership term if t and s are arbitrary terms.

• Subclass terms. t##s is a subclass term if t and s are arbitrary terms.

• Frame terms. t[p1->v1 ... pn->vn] is a frame term (or simply a frame) if t, p1, ..., pn, v1, ..., vn, n ≥ 0, are arbitrary terms.

Membership, subclass, and frame terms are used to describe objects in object-based logics like F-logic [KLW95]. These terms can be readily mixed both with positional terms and terms with named arguments: p(?X  q#r[v(1,2)->s] t(d->e f->g)).

### Well-formedness

The set of all symbols, Const, is partitioned into positional predicate symbols, predicate symbols with named arguments, positional function symbols, function symbols with named arguments, and individuals. Each positional predicate and function symbol has precisely one arity, which is a non-negative integer that tells how many arguments the symbol can take. An arity for terms with named arguments (of a symbol with named arguments) is a bag {s1 ... sk} of argument names (siArgNames). Each predicate or function symbol with named arguments has precisely one arity (for terms with named arguments).

The arity of a symbol (or whether it is a predicate, a function, or an individual) is not specified explicitly in RIF-BLD. Instead, it is inferred as follows. Each constant symbol in a RIF-BLD formula (or a set of formulas) is expected to occur in at most one context: as an individual, a function symbol of a particular arity, a predicate symbol of a particular arity, or an individual. The arity of the symbol and its type is then determined by its context. If a symbol from Const occurs in more than one context, the formula (or a set of formulas) is not considered to be well-formed in RIF-BLD.

### Formulas

Any term (positional or with named arguments) of the form p(...), where p is a predicate symbol, is also an atomic formula. Equality, membership, subclass, and frame terms are also atomic formula. Simple terms (constants and variables) are not formulas. Not all atomic formulas are well-formed -- see Section Well-formedness. A well-formed atomic formula is an atomic formula that is also a well-formed term.

More general formulas are constructed out of the atomic formulas with the help of logical connectives. A formula is a statement that can have one of the following forms:

• Atomic: If φ is a well-formed atomic formula then it is also a formula.

• Conjunction: If φ1, ..., φn, n ≥ 0, are formulas then so is And(φ1 ... φn). As a special case, And() is allowed and is treated as a tautology, i.e., a formula that is always true.

• Disjunction: If φ1, ..., φn, n ≥ 0, are formulas then so is Or(φ1 ... φn). When n=0, we get Or() as a special case; it is treated as a formula that is always false.

• Existentials: If φ is a formula and ?V1, ..., ?Vn are variables then Exists ?V1 ... ?Vn(φ) is a formula.

Formulas constructed using the above definitions are called RIF-BLD conditions. RIF-BLD rules are defined as follows:

• Rule: If φ is an atomic formula and ψ is a RIF-BLD condition then φ :- ψ is a formula, provided that φ does not have the signature bi_atomic (i.e., is not a builtin predicate).

• Universals: If φ is a rule and ?V1, ..., ?Vn are variables then Forall ?V1 ... ?Vn(φ) is a formula, called an explicitly quantified rule.

### EBNF Grammar for the Presentation Syntax of RIF-BLD

So far, the syntax of RIF-BLD was specified in Mathematical English. Tool developers, however, prefer the more formal EBNF notation, which we will give next. Several points should be kept in mind regarding this notation.

• The syntax of first-order logic is not context-free, so EBNF cannot capture the syntax of RIF-BLD precisely. For instance, it cannot capture the well-formedness conditions, i.e., the requirement that each symbol in RIF-BLD can occur in at most one context. As a result, the grammar, below, defines only a superset of RIF-BLD.

• The EBNF syntax is not a concrete syntax: it does not address the details of how constants and variables are represented, and it is not sufficiently precise about the delimiters and escape symbols. Instead, white space is informally used as a delimiter, and white space is implied in productions that use Kleene star. For instance, TERM* is to be understood as TERM TERM ... TERM, where each ' ' abstracts from one or more blanks, tabs, newlines, etc. This is done on purpose, since RIF's presentation syntax is intended as a tool for specifying the semantics and for illustration of the main RIF concepts through examples. It is not intended as a concrete syntax for a rule language. RIF defines a concrete syntax only for exchanging rules, and that syntax is XML-based, obtained as a refinement and serialization of the EBNF syntax.

#### EBNF for RIF-BLD Condition Language

The Condition Language represents formulas that can be used in the body of the RIF-BLD rules. It is supposed to be a common part of a number of RIF dialects, including RIF PRD. The EBNF grammar for a superset of the RIF-BLD condition language is as follows.

```  CONDITION      ::= 'And' '(' CONDITION* ')' |
'Or' '(' CONDITION* ')' |
'Exists' Var+ '(' CONDITION ')' |
COMPOUND
COMPOUND       ::= Uniterm | Equal | Member | Subclass | Frame
Uniterm        ::= Const '(' (TERM* | (Const '->' TERM)*) ')'
Equal          ::= TERM '=' TERM
Member         ::= TERM '#' TERM
Subclass       ::= TERM '##' TERM
Frame          ::= TERM '[' (TERM '->' TERM)* ']'
TERM           ::= Const | Var | COMPOUND
Const          ::= LITERAL '^^' SYMSPACE
Var            ::= '?' VARNAME
```

The production rule for the non-terminal CONDITION represents RIF condition formulas (defined earlier). The connectives And and Or define conjunctions and disjunctions of conditions, respectively. Exists introduces existentially quantified variables. Here Var+ stands for the list of variables that are free in CONDITION. RIF-BLD conditions permit only existential variables, but RIF-FLD syntax allows arbitrary quantification, which can be used in some dialects. A CONDITION can also be a COMPOUND term, i.e. a Uniterm, Equal, Member, Subclass, or Frame. The production for the non-terminal TERM defines RIF-BLD terms -- constants, variables, or COMPOUND terms.

The RIF-BLD presentation syntax does not commit to any particular vocabulary for the names of variables or for the literals used in constant symbols. In the examples, variables are denoted by Unicode character sequences beginning with a ?-sign. Constant symbols have the form: LITERAL^^SYMSPACE, where SYMSPACE is an IRI string that identifies the symbol space of the constant and LITERAL is a Unicode string from the lexical space of that symbol space. Equality, membership, and subclass terms are self-explanatory. Uniterms (Universal terms) are terms that can be either positional or with named arguments. A frame term is a term composed of an object Id and a collection of attribute-value pairs.

Example 1 shows conditions that are composed of uniterms, frames, and existentials. The examples of the frames show that variables can occur in the syntactic positions of object Ids, object properties, or property values.

```Example 1 (RIF-BLD conditions)
We use the prefix bks to abbreviate http://example.com/books#
and the prefix auth for http://example.com/authors#.

Positional terms:
book^^rif:local(auth:rifwg^^rif:iri bks:LeRif^^rif:iri)

Exists ?X (book^^rif:local(?X LeRif^^rif:local))

Terms with named arguments:
book^^rif:local(author^^rif:local->auth:rifwg^^rif:iri
title^^rif:local->bks:LeRif^^rif:iri)

Exists ?X (book^^rif:local(author^^rif:local->?X
title^^rif:local->bks:LeRif^^rif:iri))

Frames:
wd1^^rif:local[author^^rif:local->auth:rifwg^^rif:iri
title^^rif:local->bks:LeRif^^rif:iri ]

Exists ?X (wd2^^rif:local[author^^rif:local->?X
title^^rif:local->bks:LeRif^^rif:iri ])

Exists ?X (wd2^^rif:local#book^^rif:local[author^^rif:local->?X
title^^rif:local->bks:LeRif^^rif:iri])

Exists ?I ?X (?I[author^^rif:local->?X
title^^rif:local->bks:LeRif^^rif:iri])

Exists ?I ?X (?I#book^^rif:local[author^^rif:local->?X
title^^rif:local->bks:LeRif^^rif:iri])

Exists ?S (wd2^^rif:local[author^^rif:local->auth:rifwg^^rif:iri
?S->bks:LeRif^^rif:iri])

Exists ?X ?S (wd2^^rif:local[author^^rif:local->?X
?S->bks:LeRif^^rif:iri])

Exists ?I ?X ?S (?I#book^^rif:local[author->?X
?S->bks:LeRif^^rif:iri])
```

#### EBNF for RIF-BLD Rule Language

The presentation syntax for Horn rules extends the syntax in Section EBNF for RIF-BLD Condition Language with the following productions.

```  Ruleset  ::= RULE*
RULE     ::= 'Forall' Var+ '(' RULE ')' | Implies | COMPOUND
Implies  ::= COMPOUND ':-' CONDITION
```

A Ruleset is a set of RIF rules. Rules are generated by the Implies production, with optional Forall-quantification. Var, COMPOUND, and CONDITION were defined as part of the syntax for positive conditions in Section EBNF for RIF-BLD Condition Language. Note that COMPOUND terms are treated as rules with an empty condition part -- they are usually called facts. Note that, by a definition in Section Formulas, atomic formulas that correspond to builtin predicates (i.e., formulas with signature bi_atomic) are not allowed in the conclusion part of a rule. This restriction is not reflected in the EBNF syntax.

The document RIF Use Cases and Requirements includes a use case "Negotiating eBusiness Contracts Across Rule Platforms", which discusses a business rule slightly modified here:

```If an item is perishable and it is delivered to John more than 10 days after the
scheduled delivery date then the item will be rejected by him.
```

In the Presentation EBNF Syntax used throughout this document, this rule can be written in one of these two equivalent ways:

```Example 2 (RIF-BLD rules)
Here we use the prefix ppl as an abbreviation for http://example.com/people#.
The prefix op is used for a yet-to-be-determined IRI, which will be used for
RIF builtin predicates.

a. Universal form:

Forall ?item ?deliverydate ?scheduledate ?diffduration ?diffdays
(
reject^^rif:local(ppl:John^^rif:iri ?item) :-
And(perishable^^rif:local(?item)
delivered^^rif:local(?item ?deliverydate ppl:John^^rif:iri)
scheduled^^rif:local(?item ?scheduledate)
fn:subtract-dateTimes-yielding-dayTimeDuration(?deliverydate ?scheduledate ?diffduration)
fn:get-days-from-dayTimeDuration(?diffduration ?diffdays)
op:numeric-greater-than(?diffdays 10))
)

b. Universal-existential form:

Forall ?item
(
reject^^rif:local(ppl#John^^rif:iri ?item ) :-
Exists ?deliverydate ?scheduledate ?diffduration ?diffdays
(
And(perishable^^rif:local(?item)
delivered^^rif:local(?item ?deliverydate ppl:John^^rif:iri)
scheduled^^rif:local(?item ?scheduledate)
fn:subtract-dateTimes-yielding-dayTimeDuration(?deliverydate ?scheduledate ?diffduration)
fn:get-days-from-dayTimeDuration(?diffduration ?diffdays)
op:numeric-greater-than(?diffdays 10))
)
)
```

### XML Serialization for the Interchange of RIF-BLD

The XML serialization for RIF-BLD presentation syntax given in this section is alternating or fully striped (e.g., Alternating Normal Form). Positional information is optionally exploited only for the arg role elements. For example, role elements (declare and formula) are explicit within the Exists element. Following the examples of Java and RDF, we use capitalized names for class elements and names that start with lowercase for role elements.

The all-uppercase classes in the presentation syntax, such as CONDITION, become XML entities. They act like macros and are not visible in instance markup. The other classes as well as non-terminals and symbols (such as Exists or =) become XML elements with optional attributes, as shown below.

#### XML for RIF-BLD Condition Language

We now serialize the syntax of Section EBNF for RIF-BLD Condition Language in XML.

```Classes, roles and their intended meaning

- And       (conjunction)
- Or        (disjunction)
- Exists    (quantified formula for 'Exists', containing declare and formula roles)
- declare   (declare role, containing a Var)
- formula   (formula role, containing a CONDITION formula)
- Uniterm   (term or atomic formula, positional or with named arguments)
- Member    (member formula)
- Subclass  (subclass formula)
- Frame     (Frame formula)
- object    (Member/Frame role containing a TERM or an object description)
- op        (Uniterm role for predicates/functions as operations)
- arg       (argument role)
- upper     (Member/Subclass upper class role)
- lower     (Member/Subclass lower instance/class role)
- slot      (Uniterm/Frame slot role, prefix version of slot infix ' -> ')
- Equal     (prefix version of term equation '=')
- side      (Equal left-hand side and right-hand side role)
- Const     (slot, individual, function, or predicate symbol, with optional 'type' attribute)
- Var       (logic variable)
```

For the XML Schema Definition (XSD) of the RIF-BLD condition language see Appendix Specification.

The XML syntax for symbol spaces utilizes the type attribute associated with XML term elements such as Const. For instance, a literal in the xsd:dateTime data type can be represented as <Const type="xsd:dateTime">2007-11-23T03:55:44-02:30</Const>.

The following example illustrates XML serialization of RIF conditions.

```Example 3 (A RIF condition and its XML serialization):
We use the prefix bks as an abbreviation for http://example.com/books#
and curr for http://example.com/currencies#

a. RIF condition

?Seller
book^^rif:local ( ?Author bks:LeRif^^rif:iri )
curr:USD^^rif:iri ( 49^^xsd:integer ) )
?Seller=?Author )

b. XML serialization

<And>
<formula>
<Exists>
<formula>
<Uniterm>
<op><Const type="rif:local">purchase</Const></op>
<arg><Var>Seller</Var></arg>
<arg>
<Uniterm>
<op><Const type="rif:local">book</Const></op>
<arg><Var>Author</Var></arg>
<arg><Const type="rif:iri">bks:LeRif</Const></arg>
</Uniterm>
</arg>
<arg>
<Uniterm>
<op><Const type="rif:iri">curr:USD</Const></op>
<arg><Const type="xsd:integer">49</Const></arg>
</Uniterm>
</arg>
</Uniterm>
</formula>
</Exists>
</formula>
<formula>
<Equal>
<side><Var>Seller</Var></side>
<side><Var>Author</Var></side>
</Equal>
</formula>
</And>
```

The following example illustrates XML serialization of RIF conditions that involve terms with named arguments.

```Example 4 (A RIF condition and its XML serialization):
We use the prefix bks to abbreviate http://example.com/books#,
the prefix auth for http://example.com/authors#, and
curr for http://example.com/currencies#,

a. RIF condition:

And ( Exists ?Buyer ?P ( ?P # purchase^^rif:local [
seller^^rif:local -> ?Seller
item^^rif:local -> book^^rif:local ( author^^rif:local -> ?Author
title^^rif:local -> bks:LeRif^^rif:iri )
price^^rif:local -> 49^^xsd:integer
currency^^rif:local -> curr:USD^^rif:iri ] )
?Seller=?Author )

b. XML serialization:

<And>
<formula>
<Exists>
<declare><Var>P</Var></declare>
<formula>
<Frame>
<object>
<Member>
<lower><Var>P</Var></lower>
<upper><Const type="rif:local">purchase</Const></upper>
</Member>
</object>
<slot><Const type="rif:local">seller</Const><Var>Seller</Var></slot>
<slot>
<Const type="rif:local">item</Const>
<Uniterm>
<op><Const type="rif:local">book</Const></op>
<slot><Const type="rif:local">author</Const><Var>Author</Var></slot>
<slot><Const type="rif:local">title</Const><Const type="rif:iri">bks:LeRif</Const></slot>
</Uniterm>
</slot>
<slot><Const type="rif:local">price</Const><Const type="xsd:integer">49</Const></slot>
<slot><Const type="rif:local">currency</Const><Const type="rif:iri">curr:USD</Const></slot>
</Frame>
</formula>
</Exists>
</formula>
<formula>
<Equal>
<side><Var>Seller</Var></side>
<side><Var>Author</Var></side>
</Equal>
</formula>
</And>
```

#### XML for RIF-BLD Rule Language

The following extends the XML syntax in Section XML for RIF-BLD Condition Language, by serializing the syntax of Section EBNF for RIF-BLD Rule Language in XML. The Forall element contains the role elements declare and formula, which were earlier used within the Exists element in Section XML for RIF-BLD Condition Language. The Implies element contains the role elements if and then to designate these two parts of a rule.

```Classes, roles and their intended meaning

- Ruleset (rule collection, containing rule roles)
- Forall  (quantified formula for 'Forall', containing declare and formula roles)
- Implies (implication, containing if and then roles)
- if      (antecedent role, containing CONDITION)
- then    (consequent role, containing a Uniterm, Equal, or Frame)
```

For the XML Schema Definition (XSD) of the RIF-BLD Horn rule language see Appendix Specification.

For instance, the rule in Example 5a can be serialized in XML as shown below as the first element of a rule set whose second element is a business rule for Fred.

```Example 5 (A RIF rule set in XML syntax)

<Ruleset>
<rule>
<Forall>
<declare><Var>item</Var></declare>
<declare><Var>deliverydate</Var></declare>
<declare><Var>scheduledate</Var></declare>
<declare><Var>diffduration</Var></declare>
<declare><Var>diffdays</Var></declare>
<formula>
<Implies>
<if>
<And>
<formula>
<Uniterm>
<op><Const type="rif:local">perishable</Const></op>
<arg><Var>item</Var></arg>
</Uniterm>
</formula>
<formula>
<Uniterm>
<op><Const type="rif:local">delivered</Const></op>
<arg><Var>item</Var></arg>
<arg><Var>deliverydate</Var></arg>
<arg><Const type="rif:iri">ppl:John</Const></arg>
</Uniterm>
</formula>
<formula>
<Uniterm>
<op><Const type="rif:local">scheduled</Const></op>
<arg><Var>item</Var></arg>
<arg><Var>scheduledate</Var></arg>
</Uniterm>
</formula>
<formula>
<Uniterm>
<op><Const type="rif:local">fn:subtract-dateTimes-yielding-dayTimeDuration</Const></op>
<arg><Var>deliverydate</Var></arg>
<arg><Var>scheduledate</Var></arg>
<arg><Var>diffduration</Var></arg>
</Uniterm>
</formula>
<formula>
<Uniterm>
<op><Const type="rif:local">fn:get-days-from-dayTimeDuration</Const></op>
<arg><Var>diffduration</Var></arg>
<arg><Var>diffdays</Var></arg>
</Uniterm>
</formula>
<formula>
<Uniterm>
<op><Const type="rif:iri">op:numeric-greater-than</Const></op>
<arg><Var>diffdays</Var></arg>
<arg><Const type="xsd:long">10</Const></arg>
</Uniterm>
</formula>
</And>
</if>
<then>
<Uniterm>
<op><Const type="xsd:long">reject</Const></op>
<arg><Const type="rif:iri">ppl:John</Const></arg>
<arg><Var>item</Var></arg>
</Uniterm>
</then>
</Implies>
</formula>
</Forall>
</rule>
<rule>
<Forall>
<declare><Var>item</Var></declare>
<formula>
<Implies>
<if>
<Uniterm>
<op><Const type="rif:local">unsolicited</Const></op>
<arg><Var>item</Var></arg>
</Uniterm>
</if>
<then>
<Uniterm>
<op><Const type="rif:local">reject</Const></op>
<arg><Const type="rif:iri">ppl:Fred</Const></arg>
<arg><Var>item</Var></arg>
</Uniterm>
</then>
</Implies>
</formula>
</Forall>
</rule>
</Ruleset>
```

### Translation Between the RIF-BLD Presentation and XML Syntaxes

We now show how to translate between the presentation and XML syntaxes of RIF-BLD.

#### Translation of RIF-BLD Condition Language

The translation between the presentation syntax and the XML syntax of the RIF-BLD Condition Language is given by a table as follows.

Presentation SyntaxXML Syntax
```And (
conjunct1
. . .
conjunctn
)```
```<And>
<formula>conjunct1</formula>
. . .
<formula>conjunctn</formula>
</And>```
```Or (
disjunct1
. . .
disjunctn
)```
```<Or>
<formula>disjunct1</formula>
. . .
<formula>disjunctn</formula>
</Or>```
```Exists
variable1
. . .
variablen (
body
)```
```<Exists>
<declare>variable1</declare>
. . .
<declare>variablen</declare>
<formula>body</formula>
</Exists>```
```predfunc (
argument1
. . .
argumentn
)```
```<Uniterm>
<op>predfunc</op>
<arg>argument1</arg>
. . .
<arg> argumentn</arg>
</Uniterm>```
```predfunc (
key1 -> filler1
. . .
keyn -> fillern
)```
```<Uniterm>
<op>predfunc</op>
<slot>key1 filler1</slot>
. . .
<slot>keyn fillern</slot>
</Uniterm>```
```inst [
key1 -> filler1
. . .
keyn -> fillern
]```
```<Frame>
<object>inst</object>
<slot>key1 filler1</slot>
. . .
<slot>keyn fillern</slot>
</Frame>```
```inst # class [
key1 -> filler1
. . .
keyn -> fillern
]```
```<Frame>
<object>
<Member>
<lower>inst</lower>
<upper>class</upper>
</Member>
</object>
<slot>key1 filler1</slot>
. . .
<slot>keyn fillern</slot>
</Frame>```
```sub ## super [
key1 -> filler1
. . .
keyn -> fillern
]```
```<Frame>
<object>
<Subclass>
<lower>sub</lower>
<upper>super</upper>
</Subclass>
</object>
<slot>key1 filler1</slot>
. . .
<slot>keyn fillern</slot>
</Frame>```
`inst # class`
```<Member>
<lower>inst</lower>
<upper>class</upper>
</Member>```
`sub ## super`
```<Subclass>
<lower>sub</lower>
<upper>super</upper>
</Subclass>```
`left = right`
```<Equal>
<side>left</side>
<side>right</side>
</Equal>```
`name^^space`
`<Const type="space">name</Const>`
`?name`
`<Var>name</Var>`

#### Translation of RIF-BLD Rule Language

The translation between the presentation syntax and the XML syntax of the RIF-BLD Rule Language is given by a table that extends the translation table of Section Translation of RIF-BLD Condition Language as follows.

Presentation SyntaxXML Syntax
```Ruleset (
clause1
. . .
clausen
)```
```<Ruleset>
<rule>clause1</rule>
. . .
<rule>clausen</rule>
</Ruleset>```
```Forall
variable1
. . .
variablen (
rule
)```
```<Forall>
<declare>variable1</declare>
. . .
<declare>variablen</declare>
<formula>rule</formula>
</Forall>```
`conclusion :- condition`
```<Implies>
<if>condition</if>
<then>conclusion</then>
</Implies>```

### Subdialects of RIF-BLD

 *** This is a proposal to specify RIF-CORE etc. by just removing syntactic constructs from RIF-BLD (hence, through The effect of the syntax, restricting the semantics). The point is that it makes more sense for most engines to support only some subdialects of BLD, and that subdialects and fragments of BLD are reused in the definition of other RIF dialects. ***

The syntactic structure of RIF-BLD suggests several useful subdialects:

• RIF-CORE. This subdialect is obtained from RIF-BLD by removing support for:

• equality formulas in the rule conclusions (while still allowing them in conditions)
• terms with named arguments
• ??? membership, subclass, and frame terms ???
• RIF-CORE+equality.

• This subdialect extends RIF-CORE by adding support for equality formulas in the rule conclusions.
• RIF-CORE+named arguments.

• This subdialect extends RIF-CORE by adding syntactic support for terms with named arguments.
 *** If frames are not included in RIF-CORE / RIF-CORECOND then extensions of RIF-CORE / RIF-CORECOND with frames are added here.