# Temporal Answer Set Programming on Finite Traces

@article{Cabalar2018TemporalAS, title={Temporal Answer Set Programming on Finite Traces}, author={Pedro Cabalar and Roland Kaminski and Torsten Schaub and Anna Schuhmann}, journal={Theory and Practice of Logic Programming}, year={2018}, volume={18}, pages={406 - 420} }

Abstract In this paper, we introduce an alternative approach to Temporal Answer Set Programming that relies on a variation of Temporal Equilibrium Logic (TEL) for finite traces. This approach allows us to even out the expressiveness of TEL over infinite traces with the computational capacity of (incremental) Answer Set Programming (ASP). Also, we argue that finite traces are more natural when reasoning about action and change. As a result, our approach is readily implementable via multi-shot…

## 28 Citations

### Linear-Time Temporal Answer Set Programming

- Computer ScienceTheory and Practice of Logic Programming
- 2021

This survey presents an overview on (Modal) Temporal Logic Programming in view of its application to Knowledge Representation and Declarative Problem Solving and obtains a proper extension of the stable models semantics for the general case of temporal formulas in the syntax of LTL.

### Implementing Dynamic Answer Set Programming

- Computer ScienceArXiv
- 2020

The reduction of dynamic formulas to temporal logic programs allows to extend ASP with both approaches in a uniform way and to implement both extensions via temporal ASP solvers such as telingo.

### Dynamic and Temporal Answer Set Programming on Linear Finite Traces

- Computer ScienceDatalog
- 2019

An expressive non-monotonic modal logic, which extends traditional temporal logic programming approaches to the general syntax of LTL and possesses a computational complexity beyond LTL (Bozzelli and Pearce, 2015).

### Quantitative and Stream Extensions of Answer Set Programming

- Computer ScienceICLP Technical Communications
- 2021

This work focuses on the Logic-based framework for Analytic Reasoning over Streams (LARS) and the input language was extended with operators like ♦, corresponding to existential quantification over time points.

### Automata for dynamic answer set solving: Preliminary report

- Computer ScienceICLP Workshops
- 2021

This preliminary study investigates different ways of implementing temporal constraints expressed in an extension of Answer Set Programming with language constructs from dynamic logic and proposes two transformations of dynamic formulas into monadic second-order formulas.

### Temporal Modalities in Answer Set Programming

- Computer Science
- 2020

A temporal extension of ASP called Temporal Equilibrium Logic (TEL) was proposed in and extensively studied later and is an expressive non-monotonic modal logic that shares the syntax of Linear-Time Temporal Logic but interprets temporal formulas under a non-Monotonic semantics that properly extends stable models.

### Towards Metric Temporal Answer Set Programming

- Computer ScienceTheory and Practice of Logic Programming
- 2020

This work develops the logic of Here-and-There and its non-monotonic extension, called Equilibrium Logic on the same semantic underpinnings as its predecessors and thus uses a simple time domain of bounded time steps.

### First-order Temporal Logic on Finite Traces: Semantic Properties, Decidable Fragments, and Applications

- Computer ScienceArXiv
- 2022

This paper investigates preservation of equivalences and satisfiability of formulas between finite and infinite traces, and provides a set of semantic and syntactic conditions to guarantee when the distinction between reasoning in the two cases can be blurred.

### telingo = ASP + Time

- Computer ScienceLPNMR
- 2019

Telingo is described, an extension of the ASP system clingo with temporal operators over finite linear time and insights into its implementation are provided and an empirical evaluation contrasting standard incremental ASP programs with their temporal counterparts in telingo’s input language is provided.

### Temporal Logic Programs with Temporal Description Logic Axioms

- PhilosophyDescription Logic, Theory Combination, and All That
- 2019

A combination of Answer Set Programming (ASP) and Description Logics (DL) on top of a modal temporal basis using connectives from Linear-time Temporal Logic (LTL), which actually interprets \(\mathcal{ALC}\) axioms in terms of their translation into first order sentences, so that the semantics of TEL is eventually used in the background.

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