We analyze the relative expressiveness of the two-valued semantics of abstract argumentation frameworks, normal logic programs and abstract dialectical frameworks. By expressiveness we mean the ability to encode a desired set of two-valued interpretations over a given propositional vocabulary A using only atoms from A. While the computational complexity of the two-valued model existence problem for all these languages is (almost) the same, we show that the languages form a neat hierarchy with respect to their expressiveness. We then demonstrate that this hierarchy collapses once we allow to introduce a linear number of new vocabulary elements.

Broad application of answer set programming (ASP) for declarative problem solving requires the development of tools supporting the coding process. Program debugging is one of the crucial activities within this process. Modern ASP debugging approaches allow efficient computation of possible explanations of a fault. However, even for a small program a debugger might return a large number of possible explanations and selection of the correct one must be done manually. In this paper we present an interactive query-based ASP debugging method which extends previous approaches and finds the preferred explanation by means of observations. The system automatically generates a sequence of queries to a programmer asking whether a set of ground atoms must be true in all (cautiously) or some (bravely) answer sets of the program. Since some queries can be more informative than the others, we discuss query selection strategies which - given user's preferences for an explanation - can find the most informative query reducing the overall number of queries required for the identification of a preferred explanation.

A fundamental task in reasoning about action and change is projection, which refers to determining what holds after a number of actions have occurred. A powerful method for solving the projection problem is regression, which reduces reasoning about the future to reasoning about the initial state. In particular, regression has played an important role in the situation calculus and its epistemic extensions. Recently, a modal variant of the situation calculus was proposed, which allows an agent to revise its beliefs based on so-called belief conditionals as part of its knowledge base. In this paper, we show how regression can be extended to reduce beliefs about the future to initial beliefs in the presence of belief conditionals. Moreover, we show how any remaining belief operators can be eliminated as well, thus reducing the belief projection problem to ordinary first-order entailments.

Logic Programming and Argumentation Theory have been existing side by side as two separate, yet related, techniques in the field of Knowledge Representation and Reasoningfor many years.When Assumption-Based Argumentation (ABA) was first introduced in the nineties,the authors showed how a logic program can be encoded in an ABA framework andproved that the stable semantics of a logic program corresponds to the stable extension semantics of the ABA framework encoding this logic program.We revisit this initial work by provingthat the 3-valued stable semantics of a logic program coincides with the complete semantics of the encoding ABA framework,and that the L-stable semantics of this logic program coincides with the semi-stable semantics of the encoding ABA framework.Furthermore, we show how to graphically represent the structure of a logic program encoded in an ABA frameworkand that not only logic programming and ABA semanticsbut also Abstract Argumentation semantics can be easily applied to a logic program using these graphical representations.

Modularity is an essential aspect of knowledge representation theory and practice. It has received substantial attention. We introduce model-based modular systems, an abstract framework for modular knowledge representation formalisms, similar in scope to multi-context systems but employing a simpler information-flow mechanism. We establish the precise relationship between the two frameworks, showing that they can simulate each other. We demonstrate that recently introduced modular knowledge representation formalisms integrating logic programming with satisfiability and, more generally, with constraint satisfaction can be cast as modular systems in our sense. These results show that our formalism offers a simple unifying framework for studies of modularity in knowledge representation.

This paper proposes an alternative definition of elementary loops and extends the notion of proper loops for disjunctive logic programs. Different from normal logic programs, the computational complexities of recognizing elementary loops and proper loops for disjunctive programs are coNP-complete. To address this problem, we introduce weaker versions of both elementary loops and proper loops and provide polynomial time algorithms for identifying them respectively. On the other hand, based on the notion of elementary loops, the class of Head-Elementary-loop-Free (HEF) programs was presented, which can be turned into equivalent normal logic programs by shifting head atoms into bodies. However, the problem of recognizing an HEF program is coNP-complete. Then we present a subclass of HEF programs which generalizes the class of Head-Cycle-Free programs and provide a polynomial time algorithm to identify them. At last, some experiments show that both elementary loops and proper loops could be replaced by their weak versions in practice.

Lifschitz and Turner introduced the notion of the splitting set and provided a method to divide a logic program into two parts. They showed that the task of computing the answer sets of the program can be converted into the tasks of computing the answer sets of these parts. However, the empty set and the set of all atoms are the only two splitting sets for many programs, then these programs cannot be divided by the splitting method. In this paper, we extend Lifschitz and Turner's splitting set theorem to allow the program to be split by an arbitrary set of atoms, while some new atoms may be introduced in the process. To illustrate the usefulness of the result, we show that for some typical programs the splitting process is efficient and the program simplification problem can be investigated using the concept of splitting.

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.

In this paper we describe asprin, a general, flexible, and extensible framework for handling preferences among the stable models of a logic program. We show how complex preference relations can be specified through user-defined preference types and their arguments. We describe how preference specifications are handled internally by so-called preference programs, which are used for dominance testing. We also give algorithms for computing one, or all, optimal stable models of a logic program. Notably, our algorithms depend on the complexity of the dominance tests and make use of multi-shot answer set solving technology.

Algebraical fixpoint theory is an invaluable instrument for studying semantics of logics. For example, all major semantics of logic programming, autoepistemic logic, default logic and more recently, abstract argumentation have been shown to be induced by the different types of fixpoints defined in approximation fixpoint theory (AFT). In this paper, we add a new type of fixpoint to AFT: a grounded fixpoint of lattice operator O : L → L is defined as a lattice element x ∈ L such that O(x) = x and for all v ∈ L such that O(v ∧ x) ≤ v, it holds that x ≤ v. On the algebraical level, we show that all grounded fixpoints are minimal fixpoints approximated by the well-founded fixpoint and that all stable fixpoints are grounded. On the logical level, grounded fixpoints provide a new mathematically simple and compact type of semantics for any logic with a (possibly non-monotone) semantic operator. We explain the intuition underlying this semantics in the context of logic programming by pointing out that grounded fixpoints of the immediate consequence operator are interpretations that have no non-trivial unfounded sets. We also analyse the complexity of the induced semantics. Summarised, grounded fixpoint semantics is a new, probably the simplest and most compact, element in the family of semantics that capture basic intuitions and principles of various non-monotonic logics.