Approximation Fixpoint Theory and the Well-Founded Semantics of Higher-Order Logic Programs. Issue 3 (10th August 2018)

• Record Type: Journal Article
• Authors: CHARALAMBIDIS, ANGELOS; RONDOGIANNIS, PANOS; SYMEONIDOU, IOANNA
• Editors: Dal Palu, Alessandro; Tarau, Paul
• Is Part Of: Theory and practice of logic programming. Volume 18:Issue 3/4(2018)
• Page Start: 421
• Page End: 437
• Publication Date: 2018-08-10
• Subjects: Higher-Order Logic Programming, -- Negation in Logic Programming, -- Approximation Fixpoint Theory; Logic programming -- Periodicals; Artificial intelligence -- Computer programs -- Periodicals; Constraint programming (Computer science) -- Periodicals; 005.115
• DOI: 10.1017/S1471068418000108
• Languages: English
• ISSNs: 1471-0684

Abstract

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 an appealing formulation for capturing the well-founded semantics for higher-order logic programs .