4-Compound.html

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  <title>NARS Tutorial 4</title>
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<h3 align="center"><a href="http://www.mindmakers.org/documents/13">NARS Tutorial</a></h3>
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<h1 align="center">NAL-2 to NAL-4: Compound Term</h1>
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<p></p>
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<p>A traditional criticism of <a
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href="http://en.wikipedia.org/wiki/Term_logic">term logic</a> is on its limited expressive power. NAL solves this
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problem by introducing multiple copulas and compound terms, layer by layer. The
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ideas covered in these three layers mainly come from set theory. </p>
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<h2>1. NAL-2: Derivative copulas</h2>
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<i>Similarity</i> is defined as the symmetric variant of <i>inheritance</i>. In
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psychology, these two notions are sometimes called "symmetric similarity" and
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"asymmetric similarity", respectively. 
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<p>In IL-2, <i>similarity</i> means perfect (mutual) substitutability. </p>
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<p>The <i>instance</i>, <i>property</i>, and <i>instance-property</i> copula
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marks the end of transitivity in one or both directions in an inheritance
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chain, and represent "individual" and "feature". </p>
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<p>The <i>instance</i> and <i>property</i> copulas correspond to two ways to
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specify a set. A term can be a set, but not necessarily so. </p>
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<p>Valid syllogistic rules of NAL-2 include <i>resemblance</i>, <i>analogy</i>, and
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<i>comparison</i>, and they are variants of the syllogistic rules of NAL-1.</p>
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<h2>2. NAL-3: Intersection and Difference</h2>
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A compound term can be formed by taking the intersection or difference of the
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extensions or intensions of two existing terms. 
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<p>The inference rules of IL-3 come from the definitions of the related
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compound term, and may take one or two premises. The conclusion may contain new
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terms not included in the system's vocabulary. </p>
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<p>In a term logic, the compositional and structural rules can be seen as
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variants of the syllogistic rules. </p>
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<p>Intersection and union are dual operators, as in set theory, with respect to
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the extension and intension of a term. </p>
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<p>The inference rules of NAL-3 include <i>compositional</i>, <i>decompositional</i>, and
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<i>structural</i> rules, as well as a <i>choice</i> rule that takes simplicity into account.
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The rules defined in lower layers remain valid when a compound is used as a
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whole. </p>
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<h2>3. NAL-4: Product and Image</h2>
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A logic can have both "built-in" and "acquired" relations between terms. In
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IL/NAL, the former is either syntactic ("composed of", indicated by term
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connectors) or semantic ("used as", indicated by copulas), and the latter is
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represented by a term with a meaning learned from experience. 
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<p>In set theory, "relation" is defined similarly, except here in IL-NAL relation is not limited to sets
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defined extensionally. </p>
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<p>The inference rules of IL-4 come from the definitions of the related
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compound term. Each of them only takes one premise. </p>
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<p>Similarly, each inference rule of NAL-4 only takes one premise, and produce conclusions
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with the same truth-value, since the premise and the conclusions express the
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same content, though in different forms. </p>
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<h2>4. Meaning of concept</h2>
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Since in NARS each concept is named by a term, the meaning of a concept is
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basically defined in the same way as the meaning of a term, that is, by its relations with the other
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concepts. Some relations are syntactic (component-compound), and the others are
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semantic (subject-predicate). </p>
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<p>A semantic relation can be extensional, intensional, or both. The extension
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and intension of a concept mutually determines each other in IL, and their
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sizes change in the opposite direction. In NARS, they are defined differently
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from the <a
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href="http://www.britannica.com/EBchecked/topic/289860/intension-and-extension">conventional
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definition</a> (which presumes model-theoretic semantics), while still keep the
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same intuitive meaning. </p>
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<p>The cognitive processes usually called "recognition", "perception", and "categorization" can often be seen as answering a question of the form
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"<i>T</i> &rarr; ?" for a given term <i>T</i>, which can be a compound. There are often multiple answers that are not mutually
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exclusive, but form an inheritance hierarchy. The choice rule in NAL answers this type of questions by balancing the 
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expectation and simplicity of the candidates. Some control factors, such as familiarity and relevance, also plays important roles,
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since the system cannot consider all candidates. </p>
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<p>When deciding the degree of membership of T to a concept C in an inheritance hierarchy, there are two opposite tendencies:
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specificity (<a href="http://en.wikipedia.org/wiki/Representativeness_heuristic">representativeness</a>)
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and probability. The "<a href="http://en.wikipedia.org/wiki/Conjunction_fallacy">Conjunction Fallacy</a>" comes from the assumption that
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a concept is defined merely by its extension (instances). A compromise of the two tendencies: <a href="http://en.wikipedia.org/wiki/Prototype_theory#Basic_level_categories">basic
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level categories</a>. </p>
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<p>The meaning of a compound term is semi-compositional: it is determined
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partly by the syntactic relations, and partly by the semantic or acquired relations with
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the compound as a whole, which usually cannot be fully derived from the former.
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The meaning of a compound term is initially determined fully by the syntactic
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relations, but later more and more by the semantic and acquired relations, which usually
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cannot be derived from the former. </p>
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<p>Restricted by available resources, when processing a given task, each
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involved concept normally is used with partial meaning. Which part will be used
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is influenced by the priority distribution among beliefs, which depends on
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experience and context. For some concepts, there is a stable "core meaning", which correspond to its "essence" and "definition".
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When a concept is used with a meaning that differs from the norm, it corresponds to a "metaphorical" usage of the concept. </p>
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<p>A useful concept usually have relatively sharp and balanced extension and
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intension, such as <a
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href="http://en.wikipedia.org/wiki/Prototype_theory#Basic_level_categories">basic
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level categories</a> and <a
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href="http://plato.stanford.edu/entries/natural-kinds/">natural kinds</a>. </p>
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<p>The NARS categorization model takes the <a
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href="http://en.wikipedia.org/wiki/Categorization">existing categorization
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models</a> as special cases.</p>
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<h2>5. Learning as reasoning</h2>
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The empirical knowledge of NARS consists of explicit knowledge (as Narsese
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sentences and concepts) and implicit knowledge (as priority distributions). 
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<p>In NARS, all forms of empirical knowledge is producible and modifiable by
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experience (though can be implanted, too). At this level, learning is
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<i>complete</i>. </p>
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<p>On the other hand, the grammar rules, inference rules, and control
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mechanisms are defined at the meta-level, which are not acquired, but built-in.
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</p>
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<p>In NARS, learning and reasoning are basically two aspects of the same
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process. Learning is an open-ended process that does not follow any
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predetermined algorithm. This feature differs NARS from the conventional "<a
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href="http://en.wikipedia.org/wiki/Machine_learning">machine learning</a>" works,
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where "learning" is usually studied as following a fixed algorithm. </p>
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<p>New concepts appears in the system in three ways: <i>accepted</i>, <i>composed</i>,
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<i>altered</i>. The "original meaning" of a concept is not necessarily its "current"
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meaning. In general, there is no "correct", "true", or "ultimate" meaning for a
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concept, though concepts with stable and clear meaning are preferred. </p>
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<p>The leaning process selects useful concepts, based on repeatedly
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experienced patterns to summarize experience and to process tasks efficiently. The goal of learning is
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not "to know the world as it is", but "to adapt to the environment as the system needs".</p>
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<p></p>
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<hr>
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<h2>Reference</h2>
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<ul>
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  <li><i><a href="NAL-Wang.pdf">Non-Axiomatic Logic: A Model of Intelligent Reasoning</a></i>, Ch. 6-8</li>
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  <li><i><a href="http://code.google.com/p/open-nars/source/browse/trunk/nars-dist/Examples/Example-NAL2-edited.txt">Examples of NAL-2</a>, 
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  <i><a href="http://code.google.com/p/open-nars/source/browse/trunk/nars-dist/Examples/Example-NAL3-edited.txt">Examples of NAL-3</a>, 
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  <i><a href="http://code.google.com/p/open-nars/source/browse/trunk/nars-dist/Examples/Example-NAL4-edited.txt">Examples of NAL-4</a></i>
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  </li>
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</ul>
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