Meta-Programming for Linear-Time Temporal Answer Set Programming

Abstract The development of temporal extensions of Answer Set Programming (ASP) has led to the emergence of non-monotonic linear-time ( TEL <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:mtext>TEL</mml:mtext> </mml:mrow> </mml:math> $\textrm {TEL}$ ), dynamic ( DEL <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:mtext>DEL</mml:mtext> </mml:mrow> </mml:math> $\textrm {DEL}$ ), and metric ( MEL <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:mtext>MEL</mml:mtext> </mml:mrow> </mml:math> $\textrm {MEL}$ ) temporal equilibrium logics. However, the inherent rigidity of highly optimized ASP systems often hinders the rapid exploration and implementation of alternative logical designs. In this work, we propose a flexible meta-programming framework that operationalizes the semantics of varied temporal logics through a unified, declarative framework. Our approach extends standard ASP meta-programming by augmenting clingo ’s theory grammar with formal type specifications and nesting capabilities. To ensure semantic correctness, we introduce a transformation pipeline that protects nested modalities from stable-model-based simplifications during grounding. We demonstrate the extensibility of our framework by implementing meta-encodings for TEL <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:mtext>TEL</mml:mtext> </mml:mrow> </mml:math> $\textrm {TEL}$ , MEL <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:mtext>MEL</mml:mtext> </mml:mrow> </mml:math> $\textrm {MEL}$ , and DEL <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:mtext>DEL</mml:mtext> </mml:mrow> </mml:math> $\textrm {DEL}$ . We provide a comprehensive account of TEL <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:mtext>TEL</mml:mtext> </mml:mrow> </mml:math> $\textrm {TEL}$ and highlight the key features for managing the interval constraints of MEL <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:mtext>MEL</mml:mtext> </mml:mrow> </mml:math> $\textrm {MEL}$ and the Fischer–Ladner closure in <jats:alternative