Sato, T., On the Consistency of First Order Logic Programs, Technical Report 87-12, Electrotechnical Laboratory, Ibarki, Japan, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....for nonstrati ed programs. In Example 5.2.3, P is G strati ed, G(P ) f p; r :p z; z rg keeps heads. GH = G; f (z) j 2 GH g = fzg, and we can compute that the standard model of G(P ) is fpg. So P j= SM :z. Similarly, P j= SM :r. Before closing this section, we remark that the results in [22], 9] and [14] do not imply Theorem 5.2.3 and 5.2.4, or vise visa. Clearly, in Example 5.2.2, P [ fr g isn t strict strati ed, However, P is G hierarchical. On the other hand, for P = f:p n ng; 17 P [ f:p g is strict strati ed. But the only symmetric group associated with P is trivial. P ....

Sato, T., On the Consistency of First Order Logic Programs, Technical Report 87-12, Electrotechnical Laboratory, Ibarki, Japan, 1987.

....Example 2.1 is stratified and therefore has only one stable model. Existence of stable models was further studied in [Fag90, Cav89, Dun92, Prz88a] The following result, due to Fages [Fag90] is representative of this direction of research. A general logic program is said to be call consistent [Kun89, Sat87] if its dependency graph does not have a cycle with an odd number of negative edges. Theorem 2.3 [Fag90] A call consistent logic program whose dependency graph does not have a cycle with only positive edges has at least one stable model. 2 In our further discussion we will need the following ....

T. Sato. On the consistency of first-order logic programs. Technical report, ETL, TR-87-12, 1987.

....take a look at quasi strati ed programs. By Theorem 4.6, we have the following Theorem 6.2.4 If P is quasi strati ed, then Comp(P ) is consistent. This theorem extends the result that Comp(P ) is consistent for strati ed programs. The latter result was ever generalized to call consistent programs[24]. We remark that it doesn t cover Theorem 6.2.4, or vise visa. Let s consider P = f:p :z n; n :z p; p :n zg: P is quasi strati ed. But it isn t call consistent. On the other hand, P = f:p n n; n p pg is call consistent. However, it isn t quasi strati ed. 36 Though a ....

Sato, T., On the Consistency of First Order Logic Programs, Technical Report 87-12, Electrotechnical Laboratory, Ibarki, Japan, 1987.

....Example 2.1 is stratified and therefore has only one stable model. Existence of stable models was further studied in [Fag90, Cav89, Dun92, Prz88a] The following result, due to Fages [Fag90] is representative of this direction of research. A general logic program is said to be call consistent [Kun89, Sat87] if its dependency graph does not have a cycle with an odd number of negative edges. Theorem 2.3 [Fag90] A call consistent logic program whose dependency graph does not have a cycle with only positive edges has at least one stable model. 2 In our further discussion we will need the following ....

T. Sato. On the consistency of first-order logic programs. Technical report, ETL, TR-87-12, 1987.

....conditions for the existence of stable models for positive order consistent programs. Then we show that a negative cycle free program can have no stable model if it is not positive order consistent, but that order consistency alone [17] 2] this condition generalizes call consistency [10] [18], it is independent of positive order consistency) is sufficient to ensure the existence of a stable model. The last result is based on a characterization of stable models due to [5] and on a generalization of the result of [17] on the consistency of Clark s completion to infinite logic programs. ....

.... Gamma q. We say q depends positively on p, denoted p 0 q, if there is a non empty path from p to q with all edges positive (this definition differs from [2] A logic program Pi is stratified [1] 21] if no node depends on itself through at least one negative edge. Pi is call consistent [10] [18] if no node depends 3 oddly on itself, i.e. Gamma is irreflexive. For example the logic program f:a b; b ag is call consistent but not stratified. 2.1. Theorem [9] 22] If Pi is stratified then the stratified model of Pi (see [1] is the unique stable model of Pi. 2.2. Theorem [18] ....

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T. Sato, On the consistency of first-order logic programs, ETL technical report TR-87-12, (1987).

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