Concepción Vidal

Felicidad Aguado, Pedro Cabalar, Brais Muñiz et al.

In this paper, we compare four different semantics for disjunction in Answer Set Programming that, unlike stable models, do not adhere to the principle of model minimality. Two of these approaches, Cabalar and Muñiz' \emph{Justified Models} and Doherty and Szalas' \emph{Strongly Supported Models}, directly provide an alternative non-minimal semantics for disjunction. The other two, Aguado et al's \emph{Forks} and Shen and Eiter's \emph{Determining Inference} (DI) semantics, actually introduce a new disjunction connective, but are compared here as if they constituted new semantics for the standard disjunction operator. We are able to prove that three of these approaches (Forks, Justified Models and a reasonable relaxation of the DI semantics) actually coincide, constituting a common single approach under different definitions. Moreover, this common semantics always provides a superset of the stable models of a program (in fact, modulo any context) and is strictly stronger than the fourth approach (Strongly Supported Models), that actually treats disjunctions as in classical logic.

Felicidad Aguado, Pedro Cabalar, Martin Dieguez et al.

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.

Felicidad Aguado, Pedro Cabalar, Martín Diéguez et al.

In this note 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. To this aim, we provide a definition of a first-order version of TEL that shares the syntax of first-order Linear-time Temporal Logic (LTL) but has a different semantics, selecting some LTL models we call "temporal stable models". Then, we consider a subclass of theories (called "splittable temporal logic programs") that are close to usual logic programs but allowing a restricted use of temporal operators. In this setting, we provide a syntactic definition of "safe variables" that suffices to show the property of "domain independence" -- that is, addition of arbitrary elements in the universe does not vary the set of temporal stable models. Finally, we present a method for computing the derivable facts by constructing a non-temporal logic program with variables that is fed to a standard ASP grounder. The information provided by the grounder is then used to generate a subset of ground temporal rules which is equivalent to (and generally smaller than) the full program instantiation.