Concept Representation in a Paraconsistent Logic with Higher-Order Elements

  • Stefan Wrobel


The discussion of psychological data on human concept formation in the preceding chapter (chapter 2) has enabled us to arrive at a number of minimal requirements that a knowledge representation should meet if it is to serve as the basis of a computational model of concepts and concept formation. As a central conclusion, we observed that a propositional formalism is insufficient to represent people’s knowledge about concepts, their features, and their relationships to other concepts.


Knowledge Representation Inference Rule Concept Formation Concept Representation Horn Clause 
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  1. 1.
    The inference engine offers additional “autoepistemic” predicates that are described in detail in [Emde, 1989]Google Scholar
  2. 3.
    See section 3.3.7 for an alternative, multi-valued semantics for ℜ.Google Scholar
  3. 4.
    In section 3.3.6, we will discuss why resolution cannot be chosen if the representation system is to tolerate inconsistencies gracefully.Google Scholar
  4. 7.
    Note that since the arity of predicates is at most A, and there are no function symbols, matching a premise against a fact can be regarded as a constant time operation.Google Scholar
  5. 10.
    Well-annotated means that only true and false are used as annotations. MOBAL’s inference engine actually uses a similar annotated format internally, i.e., stores only positive literals, and attaches an evidence point to each of them, see [Emde, 1991].Google Scholar
  6. 11.
    We omit the semantics for Ghp statements that do not correspond to statements in **R the complete semantics can be found in [Blair and Subrahmanian, 1989].Google Scholar
  7. 12.
    We should point out that MOBAL’s inference engine [Emde, 1989] also implements a mechanism that allows inferences with inconsistent statements to be blocked; this blocking roughly corresponds to requiring that I(F) =T G T to satisfy a fact, and leads to a non¬monotonic effect. At Universität Dortmund, work is presently under way to understand the exact interrelationship between blocking and the paraconsistent semantics presented here [Weber and Bell, 1994]. For our discussions in this and subsequent chapters, we assume blocking is not used.Google Scholar
  8. 13.
    Even though we have not actually defined the four-valued semantics for higher-order statements and metapredicates, the definitions given here can be extended in analogy to the path taken for the two-valued semantics.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  • Stefan Wrobel
    • 1
  1. 1.GMDSankt AugustinGermany

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