Approximation Fixpoint Theory and the Well-Founded Semantics of Higher-Order Logic Programs

We define a novel, extensional, three-valued semantics for higher-order logic programs with negation. The new semantics is based on interpreting the types of the source language as three-valued Fitting-monotonic functions at all levels of the type hierarchy. We prove that there exists a bijection be...

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Bibliographic Details
Published in:Theory and practice of logic programming Vol. 18; no. 3-4; pp. 421 - 437
Main Authors: CHARALAMBIDIS, ANGELOS, RONDOGIANNIS, PANOS, SYMEONIDOU, IOANNA
Format: Journal Article
Language:English
Published: Cambridge, UK Cambridge University Press 01.07.2018
Subjects:
Approximation
Graphs
Iterative methods
Logic programming
Logic programs
Mathematical analysis
Mathematical models
Original Article
Semantics
Negation in Logic Programming
Approximation Fixpoint Theory
Higher-Order Logic Programming
ISSN:1471-0684, 1475-3081
Online Access:Get full text
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Summary:We define a novel, extensional, three-valued semantics for higher-order logic programs with negation. The new semantics is based on interpreting the types of the source language as three-valued Fitting-monotonic functions at all levels of the type hierarchy. We prove that there exists a bijection between such Fitting-monotonic functions and pairs of two-valued-result functions where the first member of the pair is monotone-antimonotone and the second member is antimonotone-monotone. By deriving an extension of consistent approximation fixpoint theory (Denecker et al. 2004) and utilizing the above bijection, we define an iterative procedure that produces for any given higher-order logic program a distinguished extensional model. We demonstrate that this model is actually a minimal one. Moreover, we prove that our construction generalizes the familiar well-founded semantics for classical logic programs, making in this way our proposal an appealing formulation for capturing the well-founded semantics for higher-order logic programs.
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ISSN:1471-0684
1475-3081
DOI:10.1017/S1471068418000108