Sequence Domains and Fixpoint Semantics for Logic Programs

Susumu YAMASAKI

Sequence Domains and Fixpoint Semantics for Logic Programs

Susumu YAMASAKI

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There have been semantics for logic programs as sets of definite clauses over sequence domains in [2],[6]. The sequence of substitutions caused by resolutions for logic programs can be captured by a fixpoint of a functional [3],[16]. In [15], a functional is regarded as a behaviour of a dataflow network, the semantics over sequence domains induces dataflow computing for logic programs. Also it may provide a transformation of logic programs to functional programs[16]. Motivated by dataflow computing constructions for logic programming, this paper deals with fixpoint semantics over sequence domains for logic programs with equations and negations. A transformation, representing deductions caused by resolutions and narrowings, is associated with a logic program with equations, modified from the operator in [18], so that it may be represented by a continuous functional over a sequence domain, and its least fixpoint is well-defined. An explicit construction of such a continuous functional of sequence variables is necessary for dataflow computing, and we should prove that the functional of sequence variables can exactly represent the transformation concerned with sets. For a general logic program, a functional is constructed over a sequence domain so that it may reflect a consistency-preserving renewal function for the pair of atom sets on the basis of the 3-valued logic approach as in [7], and [11]. It is a problem to construct the domain for the functional representing a generation of atom sets interpreted as true and negation as failure in the generation, for general logic programs. The functional is monotonic over a complete partial order and its least fixpoint is well-defined, although the least fixpoint is not always obtained by the limit of finite computing, because of the functional being not necessarily continuous.

Publication: IEICE TRANSACTIONS on Information Vol.E79-D No.6 pp.840-854

Publication Date: 1996/06/25

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Type of Manuscript: PAPER

Category: Software Theory

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Susumu YAMASAKI, "Sequence Domains and Fixpoint Semantics for Logic Programs" in IEICE TRANSACTIONS on Information, vol. E79-D, no. 6, pp. 840-854, June 1996, doi: .
Abstract: There have been semantics for logic programs as sets of definite clauses over sequence domains in [2],[6]. The sequence of substitutions caused by resolutions for logic programs can be captured by a fixpoint of a functional [3],[16]. In [15], a functional is regarded as a behaviour of a dataflow network, the semantics over sequence domains induces dataflow computing for logic programs. Also it may provide a transformation of logic programs to functional programs[16]. Motivated by dataflow computing constructions for logic programming, this paper deals with fixpoint semantics over sequence domains for logic programs with equations and negations. A transformation, representing deductions caused by resolutions and narrowings, is associated with a logic program with equations, modified from the operator in [18], so that it may be represented by a continuous functional over a sequence domain, and its least fixpoint is well-defined. An explicit construction of such a continuous functional of sequence variables is necessary for dataflow computing, and we should prove that the functional of sequence variables can exactly represent the transformation concerned with sets. For a general logic program, a functional is constructed over a sequence domain so that it may reflect a consistency-preserving renewal function for the pair of atom sets on the basis of the 3-valued logic approach as in [7], and [11]. It is a problem to construct the domain for the functional representing a generation of atom sets interpreted as true and negation as failure in the generation, for general logic programs. The functional is monotonic over a complete partial order and its least fixpoint is well-defined, although the least fixpoint is not always obtained by the limit of finite computing, because of the functional being not necessarily continuous.
URL: https://global.ieice.org/en_transactions/information/10.1587/e79-d_6_840/_p

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@ARTICLE{e79-d_6_840,
author={Susumu YAMASAKI, },
journal={IEICE TRANSACTIONS on Information},
title={Sequence Domains and Fixpoint Semantics for Logic Programs},
year={1996},
volume={E79-D},
number={6},
pages={840-854},
abstract={There have been semantics for logic programs as sets of definite clauses over sequence domains in [2],[6]. The sequence of substitutions caused by resolutions for logic programs can be captured by a fixpoint of a functional [3],[16]. In [15], a functional is regarded as a behaviour of a dataflow network, the semantics over sequence domains induces dataflow computing for logic programs. Also it may provide a transformation of logic programs to functional programs[16]. Motivated by dataflow computing constructions for logic programming, this paper deals with fixpoint semantics over sequence domains for logic programs with equations and negations. A transformation, representing deductions caused by resolutions and narrowings, is associated with a logic program with equations, modified from the operator in [18], so that it may be represented by a continuous functional over a sequence domain, and its least fixpoint is well-defined. An explicit construction of such a continuous functional of sequence variables is necessary for dataflow computing, and we should prove that the functional of sequence variables can exactly represent the transformation concerned with sets. For a general logic program, a functional is constructed over a sequence domain so that it may reflect a consistency-preserving renewal function for the pair of atom sets on the basis of the 3-valued logic approach as in [7], and [11]. It is a problem to construct the domain for the functional representing a generation of atom sets interpreted as true and negation as failure in the generation, for general logic programs. The functional is monotonic over a complete partial order and its least fixpoint is well-defined, although the least fixpoint is not always obtained by the limit of finite computing, because of the functional being not necessarily continuous.},
keywords={},
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TY - JOUR
TI - Sequence Domains and Fixpoint Semantics for Logic Programs
T2 - IEICE TRANSACTIONS on Information
SP - 840
EP - 854
AU - Susumu YAMASAKI
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E79-D
IS - 6
JA - IEICE TRANSACTIONS on Information
Y1 - June 1996
AB - There have been semantics for logic programs as sets of definite clauses over sequence domains in [2],[6]. The sequence of substitutions caused by resolutions for logic programs can be captured by a fixpoint of a functional [3],[16]. In [15], a functional is regarded as a behaviour of a dataflow network, the semantics over sequence domains induces dataflow computing for logic programs. Also it may provide a transformation of logic programs to functional programs[16]. Motivated by dataflow computing constructions for logic programming, this paper deals with fixpoint semantics over sequence domains for logic programs with equations and negations. A transformation, representing deductions caused by resolutions and narrowings, is associated with a logic program with equations, modified from the operator in [18], so that it may be represented by a continuous functional over a sequence domain, and its least fixpoint is well-defined. An explicit construction of such a continuous functional of sequence variables is necessary for dataflow computing, and we should prove that the functional of sequence variables can exactly represent the transformation concerned with sets. For a general logic program, a functional is constructed over a sequence domain so that it may reflect a consistency-preserving renewal function for the pair of atom sets on the basis of the 3-valued logic approach as in [7], and [11]. It is a problem to construct the domain for the functional representing a generation of atom sets interpreted as true and negation as failure in the generation, for general logic programs. The functional is monotonic over a complete partial order and its least fixpoint is well-defined, although the least fixpoint is not always obtained by the limit of finite computing, because of the functional being not necessarily continuous.
ER -