The symmetric maximum, denoted by a"<, is an extension of the usual maximum a operation so that 0 is the neutral element, and -aEuro parts per thousand x is the symmetric (or inverse) of x, i.e., x a"<...
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The symmetric maximum, denoted by a"<, is an extension of the usual maximum a operation so that 0 is the neutral element, and -aEuro parts per thousand x is the symmetric (or inverse) of x, i.e., x a"< aEuro parts per thousand( -aEuro parts per thousand x) = 0. However, such an extension does not preserve the associativity of a. This fact asks for systematic ways of parenthesing (or bracketing) terms of a sequence (with more than two arguments) when using such an extended maximum. We refer to such systematic (predefined) ways of parenthesing as computation rules. As it turns out there are infinitely many computation rules, each of which corresponds to a systematic way of bracketing arguments of sequences. Essentially, computation rules reduce to deleting terms of sequences based on the condition x a"< aEuro parts per thousand( -aEuro parts per thousand x) = 0. This observation gives raise to a quasi-order on the set of such computation rules: say that rule 1 is below rule 2 if for all sequences of numbers, rule 1 deletes more terms of the sequence than rule 2. In this paper we present a study of this quasi-ordering of computation rules. In particular, we show that the induced poset of all equivalence classes of computation rules is uncountably infinite, has infinitely many maximal elements, has infinitely many atoms, and it embeds the powerset of natural numbers ordered by inclusion.
We understand that many logical problems cannot be solved by using logic programs. Logic programs have the limited capability of representation. We try to overcome this limitation by adopting KR-logic, an extension to...
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ISBN:
(纸本)9789897583827
We understand that many logical problems cannot be solved by using logic programs. Logic programs have the limited capability of representation. We try to overcome this limitation by adopting KR-logic, an extension to first-order logic. The extension includes function variables. In this paper, we take a problem which is well-described with function variables. We rely on Logical Problem Solving Framework (LPSF) to formalize our problem as a Model-intersection problem. Then we develop a solver for MI problems by adding five new transformation rules concerning function variables. Correctness of each rule is proved.i.e., each rule is an equivalent tranformation (ET) rule. Since each rule is correct, all ET rules can be used together without modification and combinational cost. Thus, the invented rules can be safely reused in other LPSF-based solvers.
The computational complexity properties of a hierarchy of classes of subrecursive schemata are investigated. The schemata are derived from the multiple recursive operators of Peter. Concrete complexity measures based ...
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The computational complexity properties of a hierarchy of classes of subrecursive schemata are investigated. The schemata are derived from the multiple recursive operators of Peter. Concrete complexity measures based on specific computation rules and an underlying random-access stored-program machine (RASP) model are defined and the complexity properties induced by certain structural features are studied.
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