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

Published online by Cambridge University Press:  10 August 2018

ANGELOS CHARALAMBIDIS ,
PANOS RONDOGIANNIS  and
IOANNA SYMEONIDOU
ANGELOS CHARALAMBIDIS
Affiliation:
Department of Informatics and Telecommunications, University of Athens, Greece (e-mail: [email protected], [email protected], [email protected])
PANOS RONDOGIANNIS
Affiliation:
Department of Informatics and Telecommunications, University of Athens, Greece (e-mail: [email protected], [email protected], [email protected])
IOANNA SYMEONIDOU
Affiliation:
Department of Informatics and Telecommunications, University of Athens, Greece (e-mail: [email protected], [email protected], [email protected])
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Abstract

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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.

Keywords

Higher-Order Logic ProgrammingNegation in Logic ProgrammingApproximation Fixpoint Theory
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 18 , Special Issue 3-4: 34th International Conference on Logic Programming , July 2018 , pp. 421 - 437
Copyright
Copyright © Cambridge University Press 2018 

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