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By Wolfgang Bibel (auth.)

ISBN-10: 3322901009

ISBN-13: 9783322901002

ISBN-10: 3528085207

ISBN-13: 9783528085209

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0. For two matrices obtained frOil (F , F) E F F, F -F in normal form we say by reduction , in symbols r- MULT U r- PURE U I- TAUT U I- SUBS U I- UNIT r- RED F F o is , if o • In other words, reduction means any of the previous five kinds of reductions. Note that strictly decreases in trix F with m a to the number of occurring literals reduction step. Therefore if a occurring literals may be reduced to reduction only, i. e. valid with the F r- RED T , then F maT by turns out to be n

For any matrix F and any set W of connections in F, the pair (F, W) is called a connection graph or connection aatrix . o In our two-dimensional display connections are exposed by connecting its two literals with an arc as in the matrix The two connections in this matrix are not spanning since none of them is contained in the path {K,M,L}, Le. this matrix is not complementary. The word "spanning" has its origin in the imagination of the paths being the basic constructing parts, fixed in themselves.

U In p. 3 The reader is encouraged always to imagine or even to draw such a picture whenever paths are the topic of discussion. Usually, we will not draw the barriers and their gates explicitly, rather we will use the following simpler way of illustration. It should now be clear how this generalizes to arbitrary matrices in normal form, where there may be more clauses, each with an arbitrary number of literals. Perhaps we should mention the special case in (p3) where Fm+i = 0. Since there is no matrix Ei, hence no path Pi, a path through the whole matrix cannot be given.

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Automated Theorem Proving by Wolfgang Bibel (auth.)

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