Temporal Answer Set Programming

Answer Set Programming (ASP) has become a popular way for representing different kinds of scenarios from knowledge representation in Artificial Intelligence. Frequently, these scenarios involve a temporal component which must be considered. In ASP, time is usually represented as a variable whose values are defined by an extensional predicate with a finite domain. Dealing with a finite temporal interval has some disadvantages. First, checking the existence of a plan is not possible and second, it also makes difficult to decide whether two programs are strongly equivalent. If we extend the syntax of Answer Set Programming by using temporal operators from temporal modal logics, then infinite time can be considered, so the aforementioned disadvantages can be overcome. This extension constitutes, in fact, a formalism called Temporal Equilibrium Logic, which is based on Equilibrium Logic (a logical characterisation of ASP). Although recent contributions have shown promising results, Temporal Equilibrium Logic is still a novel paradigm and there are many gaps to fill. Our goal is to keep developing this paradigm, filling those gaps and turning it into a suitable framework for temporal reasoning

Paving the Way for Temporal Grounding

In this paper we consider the problem of introducing variables in temporal logic programs under the formalism of Temporal Equilibrium Logic (TEL), an extension of Answer Set Programming (ASP) for dealing with linear-time modal operators. We provide several fundamental contributions that pave the way for the implementation of a grounding process, that is, a method that allows replacing variables by ground instances in all the possible (or better, relevant) ways

Past-present temporal programs over finite traces

Extensions of Answer Set Programming with language constructs from temporal logics, such as temporal equilibrium logic over finite traces (TELf), provide an expressive computational framework for modeling dynamic applications. In this paper, we study the so-called past-present syntactic subclass, which consists of a set of logic programming rules whose body references to the past and head to the present. Such restriction ensures that the past remains independent of the future, which is the case in most dynamic domains. We extend the definitions of completion and loop formulas to the case of past-present formulas, which allows capturing the temporal stable models of a set of past-present temporal programs by means of an LTLf expression

Metric Dynamic Equilibrium Logic

In temporal extensions of Answer Set Programming (ASP) based on linear-time, the behavior of dynamic systems is captured by sequences of states. While this representation reflects their relative order, it abstracts away the specific times associated with each state. In many applications, however, timing constraints are important like, for instance, when planning and scheduling go hand in hand. We address this by developing a metric extension of linear-time Dynamic Equilibrium Logic, in which dynamic operators are constrained by intervals over integers. The resulting Metric Dynamic Equilibrium Logic provides the foundation of an ASP-based approach for specifying qualitative and quantitative dynamic constraints. As such, it constitutes the most general among a whole spectrum of temporal extensions of Equilibrium Logic. In detail, we show that it encompasses Temporal, Dynamic, Metric, and regular Equilibrium Logic, as well as its classic counterparts once the law of the excluded middle is added.Comment: arXiv admin note: text overlap with arXiv:2304.1477

Towards Metric Temporal Answer Set 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 non-monotonic 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.Comment: Paper presented at the 36th International Conference on Logic Programming (ICLP 2019), University Of Calabria, Rende (CS), Italy, September 2020, 28 page

Linear-Time Temporal Answer Set Programming

[Abstract]: In this survey, we present an overview on (Modal) Temporal Logic Programming in view of its application to Knowledge Representation and Declarative Problem Solving. The syntax of this extension of logic programs is the result of combining usual rules with temporal modal operators, as in Linear-time Temporal Logic (LTL). In the paper, we focus on the main recent results of the non-monotonic formalism called Temporal Equilibrium Logic (TEL) that is defined for the full syntax of LTL but involves a model selection criterion based on Equilibrium Logic, a well known logical characterization of Answer Set Programming (ASP). As a result, we obtain a proper extension of the stable models semantics for the general case of temporal formulas in the syntax of LTL. We recall the basic definitions for TEL and its monotonic basis, the temporal logic of Here-and-There (THT), and study the differences between finite and infinite trace length. We also provide further useful results, such as the translation into other formalisms like Quantified Equilibrium Logic and Second-order LTL, and some techniques for computing temporal stable models based on automata constructions. In the remainder of the paper, we focus on practical aspects, defining a syntactic fragment called (modal) temporal logic programs closer to ASP, and explaining how this has been exploited in the construction of the solver telingo, a temporal extension of the well-known ASP solver clingo that uses its incremental solving capabilities.Xunta de Galicia; ED431B 2019/03We are thankful to the anonymous reviewers for their thorough work and their useful suggestions that have helped to improve the paper. A special thanks goes to Mirosaw Truszczy´nski for his support in improving the quality of our paper. We are especially grateful to David Pearce, whose help and collaboration on Equilibrium Logic was the seed for a great part of the current paper. This work was partially supported by MICINN, Spain, grant PID2020-116201GB-I00, Xunta de Galicia, Spain (GPC ED431B 2019/03), R´egion Pays de la Loire, France, (projects EL4HC and etoiles montantes CTASP), European Union COST action CA-17124, and DFG grants SCHA 550/11 and 15, Germany

Temporal Answer Set Programming

[Abstract] Commonsense temporal reasoning is full of situations that require drawing default conclusions, since we rarely have all the information available. Unfortunately, most modal temporal logics cannot accommodate default reasoning, since they typically deal with a monotonic inference relation. On the other hand, non-monotonic approaches are very expensive and their treatment of time is not so well delimited and studied as in modal logic. Temporal Equilibrium Logic (TEL) is the first non-monotonic temporal logic which fully covers the syntax of some standard modal temporal approach without requiring further constructions. TEL shares the syntax of Linear-time Temporal Logic (LTL) (first proposed by Arthur Prior and later extended by Hans Kamp) which has become one of the simplest, most used and best known temporal logics in Theoretical Computer Science. Although TEL had been already defined, few results were known about its fundamental properties and nothing at all on potential computational methods that could be applied for practical purposes. This situation unfavourably contrasted with the huge body of knowledge available for LTL, both in well-known formal properties and in computing methods with practical implementations. In this thesis we have mostly filled this gap, following a research program that has systematically analysed different essential properties of TEL and, simultaneously, built computational tools for its practical application. As an overall, this thesis collects a corpus of results that constitutes a significant breakthrough in the knowledge about TEL.[Resumen] El razonamiento temporal del sentido común está lleno de situaciones que requieren suponer conclusiones por defecto, puesto que raramente contamos con toda la información disponible. Lamentablemente, la mayoría de lógicas modales temporales no permiten modelar este tipo de razonamiento por defecto debido a que, típicamente, se definen por medio de relaciones de inferencia monótonas. Por el contrario, las aproximaciones no monótonas existentes son típicamente muy costosas pero su manejo del tiempo no está tan bien delimitado como en lógica modal. Temporal Equilibrium Logic (TEL) es la primera lógica temporal no monótona que cubre totalmente la sintaxis de alguna de las lógicas modales tradicionales sin requerir el uso de más construcciones. TEL comparte la sintaxis de Linear-time Temporal Logic (LTL) (formalismo propuesto por Arthur Prior y posteriormente extendido por Hans Kamp), que es una de las lógicas más simples, utilizadas y mejor conocidas en Teoría de la Computación. Aunque TEL había sido definido, muy pocas propiedades eran conocidas, lo que contrastaba con el vasto conocimiento de LTL que está presente en el estado del arte. En esta tesis hemos estudiado diferentes aspectos de TEL, una novedosa combinación de lógica modal temporal y un formalismo no monótono. A grandes rasgos, esta tesis recoge un conjunto de resultados, tanto desde el punto de vista teórico como práctico, que constituye un gran avance en lo relativo al conocimiento sobre TEL.[Resumo] O razoamento do sentido común aplicado ao caso temporal está cheo de situacións que requiren supoñer conclusións por defecto, posto que raramente contamos con toda a información dispoñible. Lamentablemente a maioría de lóxicas modais temporáis non permiten modelar este tipo de razoamento por defecto debido a que, típicamente, están definidas por medio de relacións de inferencia monótonas. Pola contra, as aproximacións non monótonas existentes son moi costosos e o seu tratamento do tempo non está ben tan delimitado nin estudiado como nas lóxicas modais. Temporal Equilibrium Logic (TEL) é a primeira aproximación non monótona que cubre totalmente a sintaxe dalgunha das lóxicas modais traidicionáis sen requerir o uso de máis construccións. TEL comparte a sintaxe de Lineartime Temporal Logic (LTL) (formalismo proposto por Arthur Prior e extendido posteriormente por Hans Kamp), que é considerada unha das lóxicas modais máis simples, utilizadas e coñecidas dentro da Teoría da Computación. Aínda que TEL xa fora definido previamente, moi poucas das súas propiedades eran coñecidas, dato que contrasta co vasto coñecemento de LTL existente no estado da arte. Nesta tese, estudiamos diferentes aspectos de TEL, unha novidosa combinación de lóxica modal temporal e un formalimo non monótono. A grandes rasgos, esta tese recolle un conxunto de resultados, tanto dende o punto de vista teórico como práctico, que constitúe un gran avance no relativo ó coñecemento sobre o formalismo TEL