Τίτλος:
Approximation Fixpoint Theory and the Well-Founded Semantics of Higher-Order Logic Programs
Γλώσσες Τεκμηρίου:
Αγγλικά
Περίληψη:
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. Copyright © Cambridge University Press 2018.
Συγγραφείς:
Charalambidis, A.
Rondogiannis, P.
Symeonidou, I.
Περιοδικό:
Theory and Practice of Logic Programming
Εκδότης:
Cambridge University Press
Λέξεις-κλειδιά:
Computer circuits; Formal logic; Semantics, Classical logic; Fixpoints; Higher order logic; Higher-order logic programming; Monotonic functions; Negation in logic programming; Type hierarchies; Well founded semantics, Logic programming
DOI:
10.1017/S1471068418000108
