Properties of algorithmic operators
We consider operators working on lattices of interpretations of logic programs. Operators defined by programs are called algorithmic. Some properties of algorithmic operators, such as monotonicity and compactness, are used to define fix-point semantics. But what are necessary and sufficient conditions for such operators? The main result of this paper may be formulated, roughly speaking, as follows: an operator is algorithmic, iff its result on a given interpretation is the sum of its results on finite and restricted parts of this interpretation, i.e., is in essence defined by a certain algebra. This condition, which we called as n,k-truncateness of an operator, may be divided into several simpler conditions dealing with the generalisation of the notion of monotonicity and with the “breadth” n (the maximum number of terms) and the “height” k (the maximum height of terms) of subsystems which form the result of the operator.
Unable to display preview. Download preview PDF.
- Borshchev, V.B. and Khomyakov, M.V. (1972) Schemes for Functions and Relations. Workshop on Automatic Processing of Texts of Natural Languages. Yerevan, (The same text in Investigations in formalized languages and nonclassical logics, Moscow, Nauka 1974, 23–49). (in Russian).Google Scholar
- Borshchev, V.B. and Khomyakov, M.V. (1976) Club systems. Nauchno-Tekhnicheskaya Informatsia, Seriya 2, 8, 3–6 (in Russian).Google Scholar
- Colmerauer A., Kanoui H., van Caneghem M. (1983) Prolog, bases theoriques et developpements actuels. Technique et Science Informatiques, 4. 277–311.Google Scholar
- Kolmogerov, A.N. and Uspenskl, V.A. (1957) To the Definition of Algorithm. Uspekhi Matematicheskikh Nauk., 13, 4 3–28, (in Russian).Google Scholar
- Lloyd J.W. (1984) Foundations of logic programming. Springer Verlag, 124p.Google Scholar
- Turing, A.M. (1936) On Computable Numbers, with an Application to the Entsheidungproblem. Proc. London Math. Soc. Ser. 2, 42, 3–4 230–265.Google Scholar