Answer Set Programming (ASP) [13, 12, 4] is a successful paradigm for Knowledge Representation and problem solving. Under this paradigm, the programmer represents a problem as a logic program formed by a set of rules and obtains solutions to that problem in terms of models of the program called answer sets. Thanks to the availability of efficient solvers, ASP is nowadays applied in a wide variety of areas including robotics, bioinformatics, music composition [7, 5, 3], and many more. An ASP program does not contain information about the method to obtain the answer sets, something that is completely delegated to the ASP solver. This, of course, has the advantage of making ASP a fully declarative language, where the programmer must concentrate on specification rather than on design of search algorithms.

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.

In this paper, we study the problem of formal verification for Answer Set Programming (ASP), namely, obtaining a formal proof showing that the answer sets of a given (non-ground) logic program P correctly correspond to the solutions to the problem encoded by P, regardless of the problem instance. To this aim, we use a formal specification language based on ASP modules, so that each module can be proved to capture some informal aspect of the problem in an isolated way. This specification language relies on a novel definition of (possibly nested, first order) program modules that may incorporate local hidden atoms at different levels. Then, verifying the logic program P amounts to prove some kind of equivalence between P and its modular specification.

We describe eclingo, a solver for epistemic logic programs under Gelfond 1991 semantics built upon the Answer Set Programming system clingo. The input language of eclingo uses the syntax extension capabilities of clingo to define subjective literals that, as usual in epistemic logic programs, allow for checking the truth of a regular literal in all or in some of the answer sets of a program. The eclingo solving process follows a guess and check strategy. It first generates potential truth values for subjective literals and, in a second step, it checks the obtained result with respect to the cautious and brave consequences of the program. This process is implemented using the multi-shot functionalities of clingo. We have also implemented some optimisations, aiming at reducing the search space and, therefore, increasing eclingo's efficiency in some scenarios. Finally, we compare the efficiency of eclingo with two state-of-the-art solvers for epistemic logic programs on a pair of benchmark scenarios and show that eclingo generally outperforms their obtained results. Under consideration for acceptance in TPLP.

It is well-know that deciding consistency for normal answer set programs (ASP) is NP-complete, thus, as hard as the satisfaction problem for classical propositional logic (SAT). The best algorithms to solve these problems take exponential time in the worst case. The exponential time hypothesis (ETH) implies that this result is tight for SAT, that is, SAT cannot be solved in subexponential time. This immediately establishes that the result is also tight for the consistency problem for ASP. However, accounting for the treewidth of the problem, the consistency problem for ASP is slightly harder than SAT: while SAT can be solved by an algorithm that runs in exponential time in the treewidth k, it was recently shown that ASP requires exponential time in k \cdot log(k). This extra cost is due checking that there are no self-supported true atoms due to positive cycles in the program. In this paper, we refine the above result and show that the consistency problem for ASP can be solved in exponential time in k \cdot log({\lambda}) where {\lambda} is the minimum between the treewidth and the size of the largest strongly-connected component in the positive dependency graph of the program. We provide a dynamic programming algorithm that solves the problem and a treewidth-aware reduction from ASP to SAT that adhere to the above limit.

The Weak Completion Semantics (WCS) is a computational cognitive theory that has shown to be successful in modeling episodes of human reasoning. As the WCS is a recently developed logic programming approach, this paper investigates the correspondence of the WCS with respect to the well-established Answer Set Semantics (ASP). The underlying three-valued logic of both semantics is different and their models are evaluated with respect to different program transformations. We first illustrate these differences by the formal representation of some examples of a well-known psychological experiment, the suppression task. After that, we will provide a translation from logic programs understood under the WCS into logic programs understood under the ASP. In particular, we will show that logic programs under the WCS can be represented as logic programs under the ASP by means of a definition completion, where all defined atoms in a program must be false when their definitions are false.

One of the current problems in decision support from Artifici al Intelligence systems is the lack of explanations. When a system is making decisions in critical co ntexts and those decisions may have an impact on people's life like in the medical or legal domains, then explanations turn to be crucial, especially if we expect that a domain expert relies on the obtaine d answers. One of these situations from the medical domain where explanations have a crucial role is the process of donor-patient matching in an organ transplantation unit. This process starts when a new o rgan is received and consists in selecting a patient among those included in a waiting list for transplan tation. The transplantation unit is expected to follow an objective policy that takes into account medica l parameters and is experimentally supported by the existing records, but more importantly, this decisio n must be easily reproducible and explicable in a comprehensible way for other agents potentially involved, since it may have life-critical consequences at personal, medical and legal levels. Typically, this deci sion is taken in terms of a set of numerical weights (the impact of weights variation is studied in [7]). Although different classification systems based on Artificial Neural Networks (ANNs) are being propose d (see for instance [2] for the case of liver transplantation) their decisions rely on a black box whose b ehaviour is not explicable in human terms. In this paper, we present a rule interpreter, web-liver, designed for assisting the medical experts in the donor-patient matching of a liver transplantation un it, using the case scenario from the Digestive F. Aguado et al.

A common feature in Answer Set Programming is the use of a seco nd negation, stronger than default negation and sometimes called explicit, strong or classica l negation. This explicit negation is normally used in front of atoms, rather than allowing its use as a regular op erator. In this paper we consider the arbitrary combination of explicit negation with nested expressions, as those defined by Lifschitz, Tang and Turner. We extend the concept of reduct for this new syntax and then pr ove that it can be captured by an extension of Equilibrium Logic with this second negation. We study som e properties of this variant and compare to the already known combination of Equilibrium Logic with Nel son's strong negation.

In a recent line of research, two familiar concepts from logic programming semantics (unfounded sets and splitting) were extrapolated to the case of epistemic logic programs. The property of epistemic splitting provides a natural and modular way to understand programs without epistemic cycles but, surprisingly, was only fulfilled by Gelfond's original semantics (G91), among the many proposals in the literature. On the other hand, G91 may suffer from a kind of self-supported, unfounded derivations when epistemic cycles come into play. Recently, the absence of these derivations was also formalised as a property of epistemic semantics called foundedness. Moreover, a first semantics proved to satisfy foundedness was also proposed, the so-called Founded Autoepistemic Equilibrium Logic (FAEEL). In this paper, we prove that FAEEL also satisfies the epistemic splitting property something that, together with foundedness, was not fulfilled by any other approach up to date. To prove this result, we provide an alternative characterisation of FAEEL as a combination of G91 with a simpler logic we called Founded Epistemic Equilibrium Logic (FEEL), which is somehow an extrapolation of the stable model semantics to the modal logic S5.

Dynamic Epistemic Logic (DEL) is a family of multimodal logics that has proved to be very successful for epistemic reasoning in planning tasks. In this logic, the agent's knowledge is captured by modal epistemic operators whereas the system evolution is described in terms of (some subset of) dynamic logic modalities in which actions are usually represented as semantic objects called event models. In this paper, we study a variant of DEL, that wecall DEL[ASP], where actions are syntactically described by using an Answer Set Programming (ASP) representation instead of event models. This representation directly inherits high level expressive features like indirect effects, qualifications, state constraints, defaults, or recursive fluents that are common in ASP descriptions of action domains. Besides, we illustrate how this approach can be applied for obtaining conditional plans in single-agent, partially observable domains where knowledge acquisition may be represented as indirect effects of actions.