Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

FLINGO -- Instilling ASP Expressiveness into Linear Integer Constraints

Jorge Fandinno, Pedro Cabalar, Philipp Wanko, Torsten Schaub

TL;DR

FLINGO addresses a gap in CASP by enabling ASP-like expressiveness—defaults, undefined attributes, non-determinism, and aggregates—within the numeric constraint layer. It builds on $HT_{c}$ to provide formal semantics and offers a translation to the clingcon backend, preserving foundedness for integer variables and enabling aggregates inside constraint atoms. The approach yields a more expressive and declarative modeling framework for real-world problems with partial information, accompanied by a concrete implementation that integrates with existing ASP tooling. The work thus broadens the applicability of CASP by reconciling high-level ASP constructs with efficient numeric solving, and the system is publicly available for experimentation.

Abstract

Constraint Answer Set Programming (CASP) is a hybrid paradigm that enriches Answer Set Programming (ASP) with numerical constraint processing, something required in many real-world applications. The usual specification of constraints in most CASP solvers is closer to the numerical back-end expressiveness and semantics, rather than to standard specification in ASP. In the latter, numerical attributes are represented with predicates and this allows declaring default values, leaving the attribute undefined, making non-deterministic assignments with choice rules or using aggregated values. In CASP, most (if not all) of these features are lost once we switch to a constraint-based representation of those same attributes. In this paper, we present the FLINGO language (and tool) that incorporates the aforementioned expressiveness inside the numerical constraints and we illustrate its use with several examples. Based on previous work that established its semantic foundations, we also present a translation from the newly introduced FLINGO syntax to regular CASP programs following the CLINGCON input format.

FLINGO -- Instilling ASP Expressiveness into Linear Integer Constraints

TL;DR

FLINGO addresses a gap in CASP by enabling ASP-like expressiveness—defaults, undefined attributes, non-determinism, and aggregates—within the numeric constraint layer. It builds on to provide formal semantics and offers a translation to the clingcon backend, preserving foundedness for integer variables and enabling aggregates inside constraint atoms. The approach yields a more expressive and declarative modeling framework for real-world problems with partial information, accompanied by a concrete implementation that integrates with existing ASP tooling. The work thus broadens the applicability of CASP by reconciling high-level ASP constructs with efficient numeric solving, and the system is publicly available for experimentation.

Abstract

Constraint Answer Set Programming (CASP) is a hybrid paradigm that enriches Answer Set Programming (ASP) with numerical constraint processing, something required in many real-world applications. The usual specification of constraints in most CASP solvers is closer to the numerical back-end expressiveness and semantics, rather than to standard specification in ASP. In the latter, numerical attributes are represented with predicates and this allows declaring default values, leaving the attribute undefined, making non-deterministic assignments with choice rules or using aggregated values. In CASP, most (if not all) of these features are lost once we switch to a constraint-based representation of those same attributes. In this paper, we present the FLINGO language (and tool) that incorporates the aforementioned expressiveness inside the numerical constraints and we illustrate its use with several examples. Based on previous work that established its semantic foundations, we also present a translation from the newly introduced FLINGO syntax to regular CASP programs following the CLINGCON input format.
Paper Structure (10 sections, 4 theorems, 41 equations)

This paper contains 10 sections, 4 theorems, 41 equations.

Table of Contents

  1. Introduction
  2. Background
  3. The Logic of Here-And-There with Constraints.
  4. ASP System clingo and CASP System clingcon.
  5. The flingo language
  6. Syntax.
  7. Semantics.
  8. The flingo system
  9. Conclusion
  10. Proofs

Key Result

Proposition 1

Let $c_1$ and $c_2$ stand for the flingo constraint atoms and let $\langle h,t \rangle$ be an ht-interpretation satisfying $\normalfont\texttt{\&int}(x)$ for each integer variable $x$ in $\mathit{vars}(c_1)$ and $\mathit{vars}(c_2)$. Then, $\langle h,t \rangle \models \mu c_1$ if and only if $\langle h,t \rangle \models \mu c_2$.

Theorems & Definitions (9)

  • Definition 1
  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Proposition 4
  • proof : Proof of Proposition \ref{['prop:sumf-susf']}.
  • proof : Proof of Proposition \ref{['prop:clingcon.ht.models.flingo']}.
  • proof : Proof of Proposition \ref{['prop:clingcon.as.flingo']}.
  • proof : Proof of Proposition \ref{['prop:clingcon-monotonicity']}.