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steps toward a Rule Markup Language (RuleML), for forward and backward chaining in XML, but in 2004, there were an XML-only RuleML, an XMLRDF RuleML, and an RDF-only RuleML. Complementary efforts include Java-based rule engines such as Mandarax, RuleML, and XSB-RDF RuleML, with DTDs for basic RuleML sublanguages. As shown from the examples, embeddable expert system shells like JESS enable forward and backward chaining within a KB for reasoning and goaldirected inference in AACR use cases. Backward chaining can be more ef cient if rules are expressed as logical axioms, as in PROLOG. 8.4.2 PROLOG PROLOG is the logic-programming language for reasoning with closed-world knowledge. In a closed world, the inability to nd an assertion is treated as de facto proof that the assertion is not true. Horn clauses are an ef cient form of FOPC. In Horn clause logic, facts are atomic and conditional inference is expressed as a conjunctive clause with a single negative conjunct [204]. In the PROLOG implementation of the Horn clause representation, facts are expressed as predicates, such as Allocated (27.790, Army). For the logic enthusiast, the following six expressions are equivalent. The last logic form is a Horn clause. A implies B If A then B B if A Not (A) or B ( A B) . . . ( (A B))
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Most practical logic can be expressed in FOPC as Horn clauses and interpreted by the PROLOG language [205]. As with Jess, PROLOG facts are atomic:
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Allocated (27.790, Forest Products ) Allocated (27.790, Army)
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As a logic programming language, PROLOG statements imply existential ( ) or universal ( ) quanti cation. The statement Allocated (x, Army) means there exists a frequency x that is allocated to the Army. Implications are universal, however. So the following statement means for any and all frequencies, if the frequency is busy, then we can t use it.
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Cant-use (frequency) :- Busy (frequency)
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(PROLOG variables traditionally are single capital letters like A or X. For clarity, verbose variables are in bold.) The statement is read Can t use frequency if the frequency is busy. Placing the conclusion rst is one of the features of Horn-clause logic that if then rule programmers have to get used to. Conjunctive conditions are expressed on the right-hand side of the rule.
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Use (<Self>, frequency) :- Allocated (frequency, user), equals(user, <Self/>))
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PROLOG can backward-chain to establish a plan more ef ciently than Jess. Some versions of PROLOG include built-in numerical functions that return the value in the last argument. For example, the statement -*(10, 3, A) asserts A = 30, the product of 10 and 3. Since PROLOG is compact, one must read expressions carefully. PROLOG engines from universities are designed to teach logic programming. PROLOG sometimes requires one to rethink a use case in ways not necessarily intuitive to a C, C++, or Java programmer. For example, it may take a Java programmer some practice to get used to the PROLOG cut operator (!), similar to the Jess unique ag for lists. There are also industrial strength PROLOG engines like BinProlog [206], a high performance Internet-oriented PROLOG compiler with the ability to generate C/C++ code and stand-alone executables. BinProlog includes high level networking with remote predicate calls, blackboards, mobile code, multithreaded execution on Windows NT and Solaris and secure Internet programming with CGI scripting, multiuser server side databases, and rule-based reasoning. PROLOG utilities that make BinProlog more like conventional languages include dynamic clauses, a metainterpreter with tracing facility, sort, set-of, dynamic operators, oating point operations, and function de nition. Its mobile code, user interfaces, 3D graphics, client/server, dynamic databases, and make-facility are summarized in the companion CDROM. Other commercial PROLOG systems include Quintus and SICstus PROLOG.
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The previous sections surveyed current technology embeddable for the control of any SDR. To the degree that these techniques are expressed in a standard RXML, they facilitate AACR collaboration. This section sketches research ideas that may not be realized for some time. During the 1980s powerful machine learning technologies were invented. One of the most interesting was AM [320]. Although many of the concepts of the early research were re ned and improved, several pioneering contributions have yet to be fully realized, even in intelligent agent technology of 2005, yet are relevant to iCR. Speci cally, AM pioneered the multifaceted concept autonomously evolved by rich heuristics, the inspiration for the radio knowledge object (RKO) of this section. 8.5.1 The AM Concept Data Structure
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AM automated the discovery of data structures that express <Interesting/> mathematical expressions. Simple radio skills may be based on embedded
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HashMaps and expert system shells, but the autonomous extension of these skills by iCR is a technology challenge not unlike that of autonomously deriving principles of mathematics from set theory. Radio-use rules de ned by regulatory authorities are not unlike axioms of logic. Laws of physics are not unlike laws of mathematics. Rules of the previous sections were expressed in RXML for autonomous extension by AM-class AML. AM employed 115 initial concepts like Set and Set-Union, Object, List, Compose, and Truth-value. From these plus heuristics for instantiating new concepts, it generated and evaluated as <Interesting/> ( discovered ) data structures corresponding to Perfect-squares and Peano s axioms. AM used a very large state space of concepts and 242 heuristic rules for lling-in concept slots, checking intermediate results, suggesting search directions, and calculating interest. Mathematics is a big, open domain not unlike the radio and user domains of AACR. What Lenat called a concept might be called a knowledge template, or knowledge object (KO), a named data structure where knowledge is brought together (adapting Lenat s original language): 1. Name(s): A string to which a person or agent may refer to the KO. 2. Computational De nitions: Metalevel methods for evaluating a concept. (a) Domain: List of sets over which the KO is de ned. (b) Range: List of sets to which the KO can map or be mapped. (c) Lambda ( ) expressions: Anonymous functions attached to the KO, akin to methods of object-oriented systems. These functions are typically Boolean, testing instances for degrees of conformance to the KO. (d) Slots: Lambda expressions that contain data used by the KO. 3. Algorithms: Named expressions attached to the KO. These are KOdomain functions that implement some aspect of the KO, such as mapping domain to range. 4. Generalizations: More abstract KOs from which this KO may inherit properties. KOs form inheritance networks (heterarchy not hierarchy), rarely inheriting all properties, so rarely are generalizations strictly less constrained than a given KO. 5. IsA: KOs, the de nitions of which this KO satis es. 6. Views: A view of some other class of KO as if it were this KO. (a) Intuitions: An abstract analogy for this KO. (b) Analogies: Similarities drawn between this KO and other KOs. (c) Conjectures: Unproven theorems (hypotheses) about this KO. 7. Specializations (a) Derivative KOs: AM s heuristics could create virtually new KOs from one or more existing KOs, so that the new KO inherited very little from the base KOs.
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