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

EasyChair Preprint no. 193

Abstract

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 a serious candidate for the title of the well-founded semantics for higher-order logic programs.

Keyphrases: Approximation Fixpoint Theory, higher-order logic programming, Negation in Logic Programming

@Booklet{EasyChair:193,
  author = {Angelos Charalambidis and Panos Rondogiannis and Ioanna Symeonidou},
  title = {Approximation Fixpoint Theory and the Well-Founded Semantics of Higher-Order Logic  Programs},
  howpublished = {EasyChair Preprint no. 193},
  doi = {10.29007/4n46},
  year = {EasyChair, 2018}}