Tabling for non‐monotonic programming

@article{Swift2004TablingFN,
  title={Tabling for non‐monotonic programming},
  author={T. Swift},
  journal={Annals of Mathematics and Artificial Intelligence},
  year={2004},
  volume={25},
  pages={201-240}
}
  • T. Swift
  • Published 10 February 1999
  • Computer Science
  • Annals of Mathematics and Artificial Intelligence
Non‐monotonic extensions add power to logic programs. However, the main logic programming language, Prolog, is widely recognized as inadequate to implement these extensions due to its weak termination and complexity properties. By extending Prolog’s SLD resolution with tabling, Prolog can be improved in several ways. Tabling can allow a logic programming system to compute the well‐founded semantics for programs with bounded term depth, and to do so with polynomial data complexity. By exploiting… 
XSB: Extending Prolog with Tabled Logic Programming
TLDR
A survey of TLP and its applications as implemented in the XSB Prolog, along with discussion of how XSB supports tabling with dynamically changing code, and in a multi-threaded environment is provided.
Efficient Implementation of an Extended Semantics for Logic Programs with Annotated Disjunctions
TLDR
This paper presents the algorithm “Probabilistic Inference with Tabling and Answer subsumption” (PITA) for computing the probability of queries to programs according to the extended semantics and shows that the semantics is well-defined for a large class of programs.
Extending Tabled Logic Programming with Multi-Threading : A Systems Perspective
TLDR
The approach to MT-TLP taken by XSB Prolog, a leading open-source Prolog whose tabling engine has recently been extended for multi-threading, is presented, which supports a wide variety of TLP features, including tabled negation, tabled constraints, call subsumption, answer subsumption and incremental recomputation.
An Extended Semantics for Logic Programs with Annotated Disjunctions and its Efficient Implementation
TLDR
This paper presents the algorithm “Probabilistic Inference with Tabling and Answer subsumption” (PITA) for computing the probability of queries to programs according to the extended semantics and shows that the semantics is well-defined for a large class of programs.
Stable versus Layered Logic Program Semantics
TLDR
A new 2-valued semantics for NLPs — the Layer Supported Models semantics — is presented, which conservatively extends the SM semantics, enjoys relevance and cumulativity, guarantees model existence, and respects the Well-Founded Model.
Tabling with Sound Answer Subsumption
TLDR
It is shown that the different implementations indeed fail to produce least fixed points for some programs, and a formal framework is provided that generalises the existing approaches and a soundness criterion is established that explains for which programs the approach is sound.
Tabling with Answer Subsumption: Implementation, Applications and Performance
TLDR
The semantics and implementation ofanswer subsumption in XSB is discussed, and performance and scalability of answer subsumption on a variety of problems are discussed.
Stabel Model Implementation of Layer Supported Models by Program Transformation
TLDR
This paper exhibits a space and time linearly complex transformation, TR, from one propositional NLP into another, whose Layer Supported Models are precisely the Stable Models of the transform, which can then be computed by extant Stable Model implementations, providing a tool for the immediate generalized use of the new semantics and its applications.
...
...

References

SHOWING 1-10 OF 87 REFERENCES
An abstract machine for tabled execution of fixed-order stratified logic programs
TLDR
This article describes the architecture of the SLG-WAM for a powerful class of programs, the class of fixed-order dynamically stratified programs, and offers a detailed description of the algorithms, data structures, and instructions that the WAM adds, and a performance analysis of engine overhead due to the extensions.
Semantics-based program analysis for logic-based languages using XSB
TLDR
This article describes a simple and efficient way of using a logic programming language with builtin tabulation for general purpose semantics-based program analysis using XSB, and demonstrates that this approach competitively compares with most of the existing special purpose abstract interpretation tools for logic programs.
A logic programming system for nonmonotonic reasoning
TLDR
This paper presents and exploits a SLDNF-like derivation procedure, SLX, for programs with explicit negation under well-founded semantics (WFSX) and proves its soundness and completeness and introduces a paraconsistent version of WFSX that allows contradictions and for which the SLX top-down procedure is proven correct as well.
A New Formulation of Tabled Resolution with Delay
TLDR
The usefulness of the forest of trees paradigm for motivating tabling optimizations is shown by formalizing the concept of relevance within a tabled evaluation.
Practical program analysis using general purpose logic programming systems—a case study
TLDR
It is found that such declarative formulations can indeed be used in practical systems, when combined with the appropriate tool for evaluation, and experimental evidence that the resultant groundness and strictness analysis systems are practical in terms of both time and space is given.
Eecient Model Checking Using Tabled Resolution ?
TLDR
XMC, an XSB-based local model checker for a CCS-like value-passing language and the alternation-free fragment of the modal mu-calculus is presented and shows promise in its comparison with SPIN.
The limits of fixed-order computation
TLDR
SLGstrat is introduced, a variant of SLG resolution that uses a fixed-order computation rule, and it is proved that it correctly evaluates ground left-to-right dynamically stratified programs.
Well-founded Abduction via Tabled Dual Programs
TLDR
This paper shows how to use tabled logic programming to evaluate queries to abductive frameworks with integrity constraints when these frameworks contain both default and explicit negation.
An Abstract Machine for Computing the Well-Founded Semantics
TLDR
This paper presents an implementation of the well-founded semantics in the SLG-WAM of XSB, and presents a theorem that bounds the need for delay to those literals which are not dynamically strati ed for a xed-order computation.
...
...