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Magically Constraining the Inverse Method Using Dynamic Polarity Assignment
, 2010
"... Abstract. Given a logic program that is terminating and modecorrect in an idealized Prolog interpreter (i.e., in a topdown logic programming engine), a bottomup logic programming engine can be used to compute exactly the same set of answers as the topdown engine for a given modecorrect query by ..."
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Abstract. Given a logic program that is terminating and modecorrect in an idealized Prolog interpreter (i.e., in a topdown logic programming engine), a bottomup logic programming engine can be used to compute exactly the same set of answers as the topdown engine for a given modecorrect query by rewriting the program and the query using the Magic Sets Transformation (MST). In previous work, we have shown that focusing can logically characterize the standard notion of bottomup logic programming if atomic formulas are statically given a certain polarity assignment. In an analogous manner, dynamically assigning polarities can characterize the effect of MST without needing to transform the program or the query. This gives us a new proof of the completeness of MST in purely logical terms, by using the general completeness theorem for focusing. As the dynamic assignment is done in a general logic, the essence of MST can potentially be generalized to larger fragments of logic. 1
Magically Constraining the Inverse Method with Dynamic Polarity Assignment 3:
"... Abstract. Given a logic program that is terminating and modecorrect in an idealised Prolog interpreter (i.e., in a topdown logic programming engine), a bottomup logic programming engine can be used to compute exactly the same set of answers as the topdown engine for a given modecorrect query by ..."
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Abstract. Given a logic program that is terminating and modecorrect in an idealised Prolog interpreter (i.e., in a topdown logic programming engine), a bottomup logic programming engine can be used to compute exactly the same set of answers as the topdown engine for a given modecorrect query by rewriting the program and the query using the Magic Sets Transformation (MST). In previous work, we have shown that focusing can logically characterise the standard notion of bottomup logic programming if atomic formulas are statically given a certain polarity assignment. In an analogous manner, dynamically assigning polarities can characterise the effect of MST without needing to transform the program or the query. This gives us a new proof of the completeness of MST in purely logical terms, by using the general completeness theorem for focusing. As the dynamic assignment is done in a general logic, the essence of MST can potentially be generalised to larger fragments of logic.
ON NESTED SEQUENTS FOR CONSTRUCTIVE MODAL LOGICS
"... Abstract. We present deductive systems for various modal logics that can be obtained from the constructive variant of the normal modal logic CK by adding combinations of the axioms d, t, b, 4, and 5. This includes the constructive variants of the standard modal logics K4, S4, and S5. We use for our ..."
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Abstract. We present deductive systems for various modal logics that can be obtained from the constructive variant of the normal modal logic CK by adding combinations of the axioms d, t, b, 4, and 5. This includes the constructive variants of the standard modal logics K4, S4, and S5. We use for our presentation the formalism of nested sequents and give a syntactic proof of cut elimination. 1.