Answer Set Programming (ASP) is a generic problem modeling and solving framework with a strong focus on knowledge representation and a rapid growth of industrial applications. So far, the study of complexity resulted in characterizing hardness and determining their sources, fine-grained insights in the form of dichotomy-style results, as well as detailed parameterized complexity landscapes. Unfortunately, for the well-known parameter treewidth disjunctive programs require double-exponential runtime under reasonable complexity assumptions. This quickly becomes out of reach. We deal with the classification of structural parameters for disjunctive ASP on the program's rule structure (incidence graph). First, we provide a polynomial kernel to obtain single-exponential runtime in terms of vertex cover size, despite subset-minimization being not represented in the program's structure. Then we turn our attention to strictly better structural parameters between vertex cover size and treewidth. Here, we provide double-exponential lower bounds for the most prominent parameters in that range: treedepth, feedback vertex size, and cliquewidth. Based on this, we argue that unfortunately our options beyond vertex cover size are limited. Our results provide an in-depth hardness study, relying on a novel reduction from normal to disjunctive programs, trading the increase of complexity for an exponential parameter compression.

Forgetting - or variable elimination - is an operation that allows the removal, from a knowledge base, of middle variables no longer deemed relevant. In recent years, many different approaches for forgetting in Answer Set Programming have been proposed, in the form of specific operators, or classes of such operators, commonly following different principles and obeying different properties. Each such approach was developed to somehow address some particular view on forgetting, aimed at obeying a specific set of properties deemed desirable in such view, but a comprehensive and uniform overview of all the existing operators and properties is missing. In this paper, we thoroughly examine existing properties and (classes of) operators for forgetting in Answer Set Programming, drawing a complete picture of the landscape of these classes of forgetting operators, which includes many novel results on relations between properties and operators, including considerations on concrete operators to compute results of forgetting and computational complexity. Our goal is to provide guidance to help users in choosing the operator most adequate for their application requirements.

Programming by example (PBE) systems allow end users to easily create programs by providing a few input-output examples to specify their intended task. The system attempts to generate a program in a domain specific language (DSL) that satisfies the given examples. However, a key challenge faced by existing PBE techniques is to ensure the robustness of the programs that are synthesized from a small number of examples, as these programs often fail when applied to new inputs. This is because there can be many possible programs satisfying a small number of examples, and the PBE system has to somehow rank between these candidates and choose the correct one without any further information from the user. In this work we present a different approach to PBE in which the system avoids making a ranking decision at the synthesis stage, by instead synthesizing a disjunctive program that includes the many top-ranked programs as possible alternatives and selects between these different choices upon execution on a new input. This delayed choice brings the important benefit of comparing the possible outputs produced by the different disjuncts on a given input at execution time. We present a generic framework for synthesizing such disjunctive programs in arbitrary DSLs, and describe two concrete implementations of disjunctive synthesis in the practical domains of data extraction from plain text and HTML documents. We present an evaluation showing the significant increase in robustness achieved with our disjunctive approach, as illustrated by an increase from 59% to 93% of tasks for which correct programs can be learnt from a single example.

Many approaches for forgetting in Answer Set Programming (ASP) have been proposed in recent years, in the form of specific operators, or classes of operators, following different principles and obeying different properties. Whereas each approach was developed to somehow address some particular view on forgetting, thus aimed at obeying a specific set of properties deemed adequate for such view, we are lacking a comprehensive and uniform overview of existing operators and properties. We aim at overcoming this by thoroughly examining existing properties and (classes of) operators for forgetting in ASP, drawing a complete picture, which includes many novel (even surprising) results on relations between properties and operators. Our goal is to provide a guide to help users in choosing the most adequate operator for their application requirements.

In this paper, we study the expressive power of first-order disjunctive logic programming (DLP) and normal logic programming (NLP) under the stable model semantics. We show that, unlike the propositional case, first-order DLP is strictly more expressive than NLP. This result still holds even if auxiliary predicates are allowed, assuming that NP not equals to coNP. On the other side, we propose a partial translation from first-order DLP to NLP via unfolding and shifting, which suggests a sound yet incomplete approach to implement DLP via NLP solvers. We also identify some NLP definable subclasses, and conjecture to exactly capture NLP definability by unfolding and shifting.

A Forgetting is an operation for eliminating variables from a semantic theory of forgetting for normal logic programs knowledge base (Lin and Reiter 1994; Lang, Liberatore, and under answer set semantics is introduced in (Wang, Sattar, Marquis 2003). It constitutes a reduction in an agent's language and Su 2005), in which a sound and complete algorithm or, more accurately, the agent's signature. It has also is developed based on a series of program transformations; been studied under different names, such as variable elimination, this theory is further developed and extended uniform interpolation and relevance (Subramanian, to disjunctive logic programs in (Eiter and Wang 2006; Greiner, and Pearl 1997). Forgetting has various possible 2008). However, this theory of forgetting is defined in terms applications in a reasoning system. For example, in query of answer sets rather than SE models, and so again is not answering, if one can determine what is relevant to a query, syntax-independent.

We study the problem of rewriting a disjunctive datalog program into plain datalog. We show that a disjunctive program is rewritable if and only if it is equivalent to a linear disjunctive program, thus providing a novel characterisation of datalog rewritability. Motivated by this result, we propose weakly linear disjunctive datalog -- a novel rule-based KR language that extends both datalog and linear disjunctive datalog and for which reasoning is tractable in data complexity. We then explore applications of weakly linear programs to ontology reasoning and propose a tractable extension of OWL 2 RL with disjunctive axioms. Our empirical results suggest that many non-Horn ontologies can be reduced to weakly linear programs and that query answering over such ontologies using a datalog engine is feasible in practice.

Answer Set Programming (ASP) is a popular framework for modeling combinatorial problems. However, ASP cannot easily be used for reasoning about uncertain information. Possibilistic ASP (PASP) is an extension of ASP that combines possibilistic logic and ASP. In PASP a weight is associated with each rule, where this weight is interpreted as the certainty with which the conclusion can be established when the body is known to hold. As such, it allows us to model and reason about uncertain information in an intuitive way. In this paper we present new semantics for PASP, in which rules are interpreted as constraints on possibility distributions. Special models of these constraints are then identified as possibilistic answer sets. In addition, since ASP is a special case of PASP in which all the rules are entirely certain, we obtain a new characterization of ASP in terms of constraints on possibility distributions. This allows us to uncover a new form of disjunction, called weak disjunction, that has not been previously considered in the literature. In addition to introducing and motivating the semantics of weak disjunction, we also pinpoint its computational complexity. In particular, while the complexity of most reasoning tasks coincides with standard disjunctive ASP, we find that brave reasoning for programs with weak disjunctions is easier.

We provide reformulations and generalizations of both the semantics of logic programs by Faber, Leone and Pfeifer and its extension to arbitrary propositional formulas by Truszczynski. Unlike the previous definitions, our generalizations refer neither to grounding nor to fixpoints, and apply to first-order formulas containing aggregate expressions. In the same spirit as the first-order stable model semantics proposed by Ferraris, Lee and Lifschitz, the semantics proposed here are based on syntactic transformations that are similar to circumscription. The reformulations provide useful insights into the FLP semantics and its relationship to circumscription and the first-order stable model semantics.

We provide reformulations and generalizations of both the semantics of logic programs by Faber, Leone and Pfeifer and its extension to arbitrary propositional formulas by Truszczynski. Unlike the previous definitions, our generalizations refer neither to grounding nor to fixpoints, and apply to first-order formulas containing aggregate expressions. Similar to the first-order stable model semantics by Ferraris, Lee and Lifschitz, the reformulations presented here are based on syntactic transformations that are similar to circumscription. The reformulations provide useful insights into the FLP semantics and its relationship to circumscription and the first-order stable model semantics.