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CNF and DNF considered harmful for computing prime implicants/implicates

JOURNAL OF AUTOMATED REASONING 1997年第3期18卷 337-356页

作者： Ramesh, A Becker, G Murray, NV SUNY ALBANY INST PROGRAMMING & LOG DEPT COMP SCI ALBANY NY 12222 USA INTEL CORP CHANDLER AZ 85226 USA

Several methods to compute the prime implicants and the prime implicates of a negation normal form (NNF) formula are developed and implemented. An algorithm PI is introduced that is an extension to negation normal form of an algorithm given by Jackson and Pais. ir. correctness proof of the PI algorithm is given. The PI algorithm alone is sufficient in a computational sense, However, it can be combined with path dissolution, and it is shown empirically that this is often an advantage. None of these variations rely on conjunct ive normal form or on disjunctive normal form. A class of formulas is described for which reliance on CNF or on DNF results in ar. exponential increase in the time required to compute prime implicants/implicates. The possibility of avoiding this problem with efficient structure preserving clause form translations is examined briefly and appears unfavorable.

关键词： solution prime implicants/implicates

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Simplification of many-valued logic formulas using anti-links

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JOURNAL OF LOGIC AND COMPUTATION 1998年第4期8卷 569-587页

作者： Beckert, B Hahnle, R Escalada-Imaz, G Univ Karlsruhe Inst Log Komplexitat & Dedukt Syst D-76128 Karlsruhe Germany Inst Invest Intel Ligencia Arificial E-08193 Barcelona Spain

The theoretical foundations of the many-valued generalization of a technique for simplifying large non-clausal formulas in propositional logic, called removal of anti-links are presented. Possible applications include computation of prime implicates of large non-clausal formulas as required, for example, in diagnosis. With the anti-link technique, one does not compute any normal form of a given formula;rather, one removes certain forms of redundancy from formulas in negation normal form (NNF). Its main advantage is that no clausal normal form has to be computed in order to remove redundant parts of a formula. An anti-link operation on a generic language is defined for expressing many-valued logic formulas called signed NNF and it is shown that all interesting properties of two-valued anti-links generalize to the many-valued setting, although in a non-trivial way.

关键词： many-valued logic subsumption prime implicants/implicates

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A New Class of Explanations for Classifiers with Non-binary Features 18th

A New Class of Explanations for Classifiers with Non-binary ...

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18th European Conference on Logics in Artificial Intelligence (JELIA)

作者： Ji, Chunxi Darwiche, Adnan Univ Calif Los Angeles Los Angeles CA 90095 USA

ISBN: (纸本)9783031436185;9783031436192

Two types of explanations have been receiving increased attention in the literature when analyzing the decisions made by classifiers. The first type explains why a decision was made and is known as a sufficient reason for the decision, also an abductive explanation or a PI-explanation. The second type explains why some other decision was not made and is known as a necessary reason for the decision, also a contrastive or counterfactual explanation. These explanations were defined for classifiers with binary, discrete and, in some cases, continuous features. We show that these explanations can be significantly improved in the presence of non-binary features, leading to a new class of explanations that relay more information about decisions and the underlying classifiers. Necessary and sufficient reasons were also shown to be the prime implicates and implicants of the complete reason for a decision, which can be obtained using a quantification operator. We show that our improved notions of necessary and sufficient reasons are also prime implicates and implicants but for an improved notion of complete reason obtained by a new quantification operator that we also define and study.

关键词： Explainable AI Decision Graphs prime implicants/implicates

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