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Extra resources for Logic-Based Program Synthesis and Transformation: 16th International Symposium, LOPSTR 2006, Venice, Italy, July 12-14, 2006, Revised Selected Papers
U ∈ AS(Q), ∃S ∈ AS(P1 ) and ∃T ∈ AS(P2 ) such that U ⊆ S and U ⊆ T . 2. ∀V ∈ AS(R), ∃S ∈ AS(P1 ) and ∃T ∈ AS(P2 ) such that V ⊆ S and V ⊆ T . 3. ∀S ∈ AS(P1 ) and ∀T ∈ AS(P2 ), ∃ U ∈ AS(Q) such that U ⊆ S and U ⊆ T . Proof. Since U = S ∩ T for some S ∈ AS(P1 ) and T ∈ AS(P2 ), U ⊆ S and U ⊆ T hold. Thus, 1 and 2 hold. As U is a minimal element of cons(P1 , P2 ), the result 3 follows. 3 asserts that a result of minimal/maximal consensus reflects a part of beliefs included in an answer set of every program.
Proc. AAAI-04, pp. 293–298, MIT Press, 2004. 11. C. Sakama and H. Seki. Partial deduction in disjunctive logic programming. Journal of Logic Programming, 32(3):229–245, 1997. 12. C. Sakama and K. Inoue. Coordination between logical agents. Proceedings of the 5th International Workshop on Computational Logic in Multi-Agent Systems, Lecture Notes in Artificial Intelligence 3487, pp. 161–177, Springer, 2005. 13. C. Sakama and K. Inoue. Combining answer sets of nonmonotonic logic programs. Proceedings of the 6th International Workshop on Computational Logic in Multi-Agent Systems, Lecture Notes in Artificial Intelligence 3900, pp.
Among them, the intersection operation combines two programs by merging 40 C. Sakama and K. Inoue pair of rules with unifiable heads. For instance, given two programs: P1 : likes(x, y) ← not bitter(y), hates(x, y) ← sour(y), P2 : likes(Bob, y) ← sour(y), the program P1 ∩ P2 consists of the single rule: likes(Bob, y) ← not bitter(y), sour(y). The produced rule specifies information which is common to the original two programs. However, the operation is performed on individual rules, so that resulting rules do not always produce common conclusions.