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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Vydáno v:arXiv.org
Hlavní autoři: Charalambidis, Angelos, Rondogiannis, Panos, Symeonidou, Ioanna
Médium: Paper
Jazyk:angličtina
Vydáno: Ithaca Cornell University Library, arXiv.org 23.04.2018
Témata:
Approximation
Graphs
Iterative methods
Logic programming
Logic programs
Mathematical analysis
Mathematical models
Semantics
ISSN:2331-8422
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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. This paper is under consideration for acceptance in TPLP.
AbstractList 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. This paper is under consideration for acceptance in TPLP.
Author Symeonidou, Ioanna
Charalambidis, Angelos
Rondogiannis, Panos
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SubjectTerms Approximation
Graphs
Iterative methods
Logic programming
Logic programs
Mathematical analysis
Mathematical models
Semantics
Title Approximation Fixpoint Theory and the Well-Founded Semantics of Higher-Order Logic Programs
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