The Intricacies of 3-Valued Extensional Semantics for Higher-Order Logic Programs

@inproceedings{Rondogiannis2018TheIO,
  title={The Intricacies of 3-Valued Extensional Semantics for Higher-Order Logic Programs},
  author={Panos Rondogiannis and Ioanna Symeonidou},
  booktitle={IJCAI},
  year={2018}
}
In this paper we examine the problem of providing a purely extensional three-valued semantics for higher-order logic programs with negation. We demonstrate that a technique that was proposed by M. Bezem for providing extensional semantics to positive higher-order logic programs, fails when applied to higher-order logic programs with negation. On the positive side, we demonstrate that for stratified higher-order logic programs, extensionality is indeed achieved by the technique. We analyze the… 
1 Citations
The intricacies of three-valued extensional semantics for higher-order logic programs
TLDR
It is demonstrated that the well-founded extension of Bezem's technique can be extended to higher-order logic programs with negation, retaining its extensional properties, provided that it is interpreted under a logic with an infinite number of truth values.

References

SHOWING 1-10 OF 37 REFERENCES
The intricacies of three-valued extensional semantics for higher-order logic programs
TLDR
It is demonstrated that the well-founded extension of Bezem's technique can be extended to higher-order logic programs with negation, retaining its extensional properties, provided that it is interpreted under a logic with an infinite number of truth values.
Extensional Semantics for Higher-Order Logic Programs with Negation
TLDR
It is demonstrated that for stratified and locally stratified higher-order logic programs, the proposed semantics never assigns the unknown truth value.
Minimum Model Semantics for Extensional Higher-order Logic Programming with Negation*
TLDR
It is demonstrated that every higher-order logic program with negation has a unique minimum infinite-valued model, which is the first purely model-theoretic semantics for negation in extensional higher- order logic programming.
An Improved Extensionality Criterion for Higher-Order Logic Programs
TLDR
A decidable extensionality criterion for simply typed logic programs is given, improving both on Wadge's definitional programs from [9] and on the authors' good programs from[2].
Equivalence of two fixed-point semantics for definitional higher-order logic programs
TLDR
For a very broad class of programs, namely the class of definitional programs introduced by W. W. Wadge, the two approaches for assigning a purely extensional semantics to higher-order logic programming coincide (with respect to ground atoms that involve symbols of the program).
Extensional Higher-Order Logic Programming
TLDR
A purely extensional theoretical framework for higher-order logic programming which generalizes the familiar theory of classical (first-order) logic programming and proposes an SLD-resolution proof system which is proven sound and complete with respect to the minimum Herbrand model semantics.
Higher-Order Horn Logic Programming
TLDR
A fragment of higher-order Horn logic is described which allows the programmer to axiomatize predicates of predicates and operations on predicates, and is in fact a subset of HiLog—a “pure” subset with simple semantics and a straightforward implementation.
Approximation Fixpoint Theory and the Well-Founded Semantics of Higher-Order Logic Programs
TLDR
A novel, extensional, three-valued semantics for higher-order logic programs with negation is defined, and it is proved 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 antimonot One-Monotone.
Extensional Higher-Order Datalog ?
TLDR
A higher-order extension of Datalog based on the Horn fragment of higher- order logic introduced in [Wad91] is defined, which retains all the basic principles of first-order logic programming.
Extensionality of Simply Typed Logic Programs
TLDR
It is shown that the initial model of a simply typed logic program, in case the program is extensional, collapses into a simple, set-theoretic representation.
...
...