Equivalence of two Fixed-Point Semantics for Definitional Higher-Order Logic Programs

Two distinct research approaches have been proposed for assigning a purely extensional semantics to higher-order logic programming. The former approach uses classical domain theoretic tools while the latter builds on a fixed-point construction defined on a syntactic instantiation of the source progr...

Full description

Saved in:
Bibliographic Details
Published in:Electronic proceedings in theoretical computer science Vol. 191; no. Proc. FICS 2015; pp. 18 - 32
Main Authors: Charalambidis, Angelos, Rondogiannis, Panos, Symeonidou, Ioanna
Format: Journal Article
Language:English
Published: Open Publishing Association 09.09.2015
ISSN:2075-2180, 2075-2180
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Two distinct research approaches have been proposed for assigning a purely extensional semantics to higher-order logic programming. The former approach uses classical domain theoretic tools while the latter builds on a fixed-point construction defined on a syntactic instantiation of the source program. The relationships between these two approaches had not been investigated until now. In this paper we demonstrate that for a very broad class of programs, namely the class of definitional programs introduced by W. W. Wadge, the two approaches coincide (with respect to ground atoms that involve symbols of the program). On the other hand, we argue that if existential higher-order variables are allowed to appear in the bodies of program rules, the two approaches are in general different. The results of the paper contribute to a better understanding of the semantics of higher-order logic programming.
ISSN:2075-2180
2075-2180
DOI:10.4204/EPTCS.191.4