By Jair Minoro Abe
This ebook offers the various most modern purposes of recent theories in line with the idea that of paraconsistency and correlated issues in informatics, reminiscent of trend attractiveness (bioinformatics), robotics, decision-making topics, and pattern measurement. every one bankruptcy is self-contained, and an introductory bankruptcy masking the good judgment theoretical foundation is usually incorporated. the purpose of the textual content is twofold: to function an introductory textual content at the theories and functions of latest common sense, and as a textbook for undergraduate or graduate-level classes in AI.
Today AI often has to deal with difficulties of vagueness, incomplete and conflicting (inconsistent) info. some of the most amazing formal theories for addressing them is paraconsistent (paracomplete and non-alethic) common sense.
Read or Download Paraconsistent Intelligent-Based Systems: New Trends in the Applications of Paraconsistency PDF
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Additional info for Paraconsistent Intelligent-Based Systems: New Trends in the Applications of Paraconsistency
Consider the following knowledge base KB1. KB1 ¼ fA; :B; A ! B; B ! Cg Here, we assume that the base logic is classical logic. From KB1, we should conclude C using modus ponens. But, it is impossible in classical logic, since KB1 produces inconsistency. In fact, both ‘KB1 B and ‘KB1 :B. However, in classical logic C, B ^ :B ‘C D, where D denotes an arbitrary formula. In other words, the knowledge base KB1 is trivial and it is not of use as a knowledge base in that no useful information is derivable.
E. C ‘A ) CA. Now, we give a completeness proof. e. e. e. :d A 62 CÃ iff $ :d A2 CÃ . Here, discursiveness is needed to capture the property of discursive negation. Lemma 3 For any mntdt C and any formula A; B the following hold: (1) (2) (3) (4) (5) (6) (7) (8) (9) A ^ B2 C iff A 2 Cand B 2 C A _ B 2 C iff A 2 C or B 2 C A ! B 2 C iff 8DðCD and A2D ) B2DÞ :d A2C iff 8DðCD ) A 62 DÞ $ ðA ^ BÞ2C iff $ A2C or $ B2C $ ðA _ BÞ2C iff $ A2C and $ B2C $ ðA ! BÞ2C iff A 2 C and $ B2C $ $ A2C iff A 2 C $ :d A2C iff 9DðCD and A2DÞ.
H The next lemma is a truth lemma. Constructive Discursive Logic: Paraconsistency in Constructivism 33 Lemma 4 (truth lemma) For any mntdt C and any A, we have the following: VðA; CÞ ¼ 1 iff A2C VðA; CÞ ¼ 0 iff $ A2C Proof It sufﬁces Vð:d B; CÞ ¼ 1 ðIH Þ ðLemma 4 ð4ÞÞ to check the case A ¼ :d B. iff 8D 2 CÃ ðCD ) VðB; DÞ 6¼ 1Þ iff 8D 2 CÃ ðCD ) B 62 DÞ iff :d B 2 C Vð:d B; CÞ ¼ 0 ðIH Þ ðLemma 4 ð9ÞÞ iff 9D 2 CÃ ðCD and VðB; DÞ ¼ 1Þ iff 9D 2 CÃ ðCD and B 2 DÞ iff $ :d B 2 C h Then, we can state the (strong) completeness of CDLSN as follows: Theorem 2 (completeness).