Answer Set Planning refers to the use of Answer Set Programming (ASP) to compute plans, i.e., solutions to planning problems, that transform a given state of the world to another state. The development of efficient and scalable answer set solvers has provided a significant boost to the development of ASP-based planning systems. This paper surveys the progress made during the last two and a half decades in the area of answer set planning, from its foundations to its use in challenging planning domains. The survey explores the advantages and disadvantages of answer set planning. It also discusses typical applications of answer set planning and presents a set of challenges for future research.

We take up an idea from the folklore of Answer Set Programming, namely that choices, integrity constraints along with a restricted rule format is sufficient for Answer Set Programming. We elaborate upon the foundations of this idea in the context of the logic of Here-and-There and show how it can be derived from the logical principle of extension by definition. We then provide an austere form of logic programs that may serve as a normalform for logic programs similar to conjunctive normalform in classical logic. Finally, we take the key ideas and propose a modeling methodology for ASP beginners and illustrate how it can be used.

We explore different ways of implementing temporal constraints expressed in an extension of Answer Set Programming (ASP) with language constructs from dynamic logic. Foremost, we investigate how automata can be used for enforcing such constraints. The idea is to transform a dynamic constraint into an automaton expressed in terms of a logic program that enforces the satisfaction of the original constraint. What makes this approach attractive is its independence of time stamps and the potential to detect unsatisfiability. On the one hand, we elaborate upon a transformation of dynamic formulas into alternating automata that relies on meta-programming in ASP. This is the first application of reification applied to theory expressions in gringo. On the other hand, we propose two transformations of dynamic formulas into monadic second-order formulas. These can then be used by off-the-shelf tools to construct the corresponding automata. We contrast both approaches empirically with the one of the temporal ASP solver telingo that directly maps dynamic constraints to logic programs. Since this preliminary study is restricted to dynamic formulas in integrity constraints, its implementations and (empirical) results readily apply to conventional linear dynamic logic, too.

We present a general approach to planning with incomplete information in Answer Set Programming (ASP). More precisely, we consider the problems of conformant and conditional planning with sensing actions and assumptions. We represent planning problems using a simple formalism where logic programs describe the transition function between states, the initial states and the goal states. For solving planning problems, we use Quantified Answer Set Programming (QASP), an extension of ASP with existential and universal quantifiers over atoms that is analogous to Quantified Boolean Formulas (QBFs). We define the language of quantified logic programs and use it to represent the solutions to different variants of conformant and conditional planning. On the practical side, we present a translation-based QASP solver that converts quantified logic programs into QBFs and then executes a QBF solver, and we evaluate experimentally the approach on conformant and conditional planning benchmarks.

We provide a comprehensive elaboration of the theoretical foundations of variable instantiation, or grounding, in Answer Set Programming (ASP). Building on the semantics of ASP's modeling language, we introduce a formal characterization of grounding algorithms in terms of (fixed point) operators. A major role is played by dedicated well-founded operators whose associated models provide semantic guidance for delineating the result of grounding along with on-the-fly simplifications. We address an expressive class of logic programs that incorporates recursive aggregates and thus amounts to the scope of existing ASP modeling languages. This is accompanied with a plain algorithmic framework detailing the grounding of recursive aggregates. The given algorithms correspond essentially to the ones used in the ASP grounder gringo.

Over the last decades the development of ASP has brought about an expressive modeling language powered by highly performant systems. At the same time, it gets more and more difficult to provide semantic underpinnings capturing the resulting constructs and inferences. This is even more severe when it comes to hybrid ASP languages and systems that are often needed to handle real-world applications. We address this challenge and introduce the concept of abstract and structured theories that allow us to formally elaborate upon their integration with ASP. We then use this concept to make precise the semantic characterization of CLINGO's theory-reasoning framework and establish its correspondence to the logic of Here-and-there with constraints. This provides us with a formal framework in which we can elaborate formal properties of existing hybridizations of CLINGO such as CLINGCON, CLINGOM[DL], and CLINGO[LP].

We present an overview on Temporal Logic Programming under the perspective of its application for Knowledge Representation and declarative problem solving. Such programs are the result of combining usual rules with temporal modal operators, as in Linear-time Temporal Logic (LTL). We focus on recent results of the non-monotonic formalism called Temporal Equilibrium Logic (TEL) that is defined for the full syntax of LTL, but performs a model selection criterion based on Equilibrium Logic, a well known logical characterization of Answer Set Programming (ASP). We obtain a proper extension of the stable models semantics for the general case of arbitrary temporal formulas. We recall the basic definitions for TEL and its monotonic basis, the temporal logic of Here-and-There (THT), and study the differences between infinite and finite traces. We also provide other useful results, such as the translation into other formalisms like Quantified Equilibrium Logic or Second-order LTL, and some techniques for computing temporal stable models based on automata. In a second part, we focus on practical aspects, defining a syntactic fragment called temporal logic programs closer to ASP, and explain how this has been exploited in the construction of the solver TELINGO.

Answer Set Programming (ASP) has become a popular and quite sophisticated approach to declarative problem solving. This is arguably due to its attractive modeling-grounding-solving workflow that provides an easy approach to problem solving, even for laypersons outside computer science. Unlike this, the high degree of sophistication of the underlying technology makes it increasingly hard for ASP experts to put ideas into practice. For addressing this issue, this tutorial aims at enabling users to build their own ASP-based systems. More precisely, we show how the ASP system CLINGO can be used for extending ASP and for implementing customized special-purpose systems. To this end, we propose two alternatives. We begin with a traditional AI technique and show how meta programming can be used for extending ASP. This is a rather light approach that relies on CLINGO's reification feature to use ASP itself for expressing new functionalities. Unlike this, the major part of this tutorial uses traditional programming (in PYTHON) for manipulating CLINGO via its application programming interface. This approach allows for changing and controlling the entire model-ground-solve workflow of ASP. Central to this is CLINGO's new Application class that allows us to draw on CLINGO's infrastructure by customizing processes similar to the one in CLINGO. For instance, we may engage manipulations to programs' abstract syntax trees, control various forms of multi-shot solving, and set up theory propagators for foreign inferences. Another cross-sectional structure, spanning meta as well as application programming, is CLINGO's intermediate format, ASPIF, that specifies the interface among the underlying grounder and solver. We illustrate the aforementioned concepts and techniques throughout this tutorial by means of examples and several non-trivial case-studies.

This paper continues the line of research aimed at investigating the relationship between logic programs and first-order theories. We extend the definition of program completion to programs with input and output in a subset of the input language of the ASP grounder gringo, study the relationship between stable models and completion in this context, and describe preliminary experiments with the use of two software tools, anthem and vampire, for verifying the correctness of programs with input and output. Proofs of theorems are based on a lemma that relates the semantics of programs studied in this paper to stable models of first-order formulas. This paper is under consideration for acceptance in Theory and Practice of Logic Programming.

We elaborate upon the theoretical foundations of a metric temporal extension of Answer Set Programming. In analogy to previous extensions of ASP with constructs from Linear Temporal and Dynamic Logic, we accomplish this in the setting of the logic of Here-and-There and its nonmonotonic extension, called Equilibrium Logic. More precisely, we develop our logic on the same semantic underpinnings as its predecessors and thus use a simple time domain of bounded time steps. This allows us to compare all variants in a uniform framework and ultimately combine them in a common implementation. This article is under consideration for acceptance in TPLP.