Disjunctive Logic Programming (DLP) is an advanced formalism for knowledge representation and reasoning, which is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is decidable in the complexity class ΣP 2 (NPNP). Thus, under widely believed assumptions, DLP is strictly more expressive than normal (disjunction-free) logic programming, whose expressiveness is limited to properties decidable in NP. Importantly, apart from enlarging the class of applications which can be encoded in the language, disjunction often allows for representing problems of lower complexity in a simpler and more natural fashion. This paper presents the DLV system, which is widely considered the state-of-the-art implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel language, function-free disjunctive logic programs (also known as disjunctive datalog), extended by weak constraints, which are a powerful tool to express optimization problems. We then illustrate the usage of DLV as a tool for knowledge representation and reasoning, describing a new declarative programming methodology which allows one to encode complex problems (up to ∆P 3-complete problems) in a declarative fashion. On the foundational side, we provide a detailed analysis of the computational complexity of the language of

In Part I of this series of papers, we have proposed a new logic-based planning language, called K. This language facilitates the description of transitions between states of knowledge and it is well suited for planning under incomplete knowledge. Nonetheless, K also supports the representation of transitions between states of the world (i.e., states of complete knowledge) as a special case, proving to be very flexible. In the present Part II, we describe the DLV planning system, which implements K on top of the disjunctive logic programming system DLV. This novel planning system allows for solving hard planning problems, including secure planning under incomplete initial states (often called conformant planning in the literature), which cannot be solved at all by other logic-based planning systems such as traditional satisfiability planners. We present a detailed comparison of the system to several state-of-the-art conformant planning systems, both at the level of system features and on benchmark problems. Our results indicate that, thanks to the power of knowledge-state problem encoding, the DLV system is competitive even with special purpose conformant planning systems, and it often supplies a more natural and simple representation of the planning problems.

Recently, planning based on answer set programming has been proposed as an approach towards realizing declarative planning systems. In this paper, we present the language K extends the declarative planning language K by action costs. K provides the notion of admissible and optimal plans, which are plans whose overall action costs are within a given limit resp.

We describe the elds of disjunctive logic programming and disjunctive deductive databases from the time of their inception to the current time. Contributions with respect to semantics, implementations and applications are surveyed.

The extended answer set semantics for logic programs allows for the defeat of rules to resolve contradictions. We propose a refinement of these semantics based on a preference relation on extended literals. This relation, a strict partial order, induces a partial order on extended answer sets. The preferred answer sets, i.e. those that are minimal w.r.t. the induced order, represent the solutions that best comply with the stated preference on extended literals. In a further extension, we propose linearly ordered programs that are equipped with a linear hierarchy of preference relations. The resulting formalism is rather expressive and essentially covers the polynomial hierarchy. E.g. the membership problem for a program with a hierarchy of height n is # n+1 -complete. We illustrate an application of the approach by showing how it can easily express hierarchically structured weak constraints, i.e. a layering of "desirable" constraints, such that one tries to minimize the set of violated constraints on lower levels, regardless of the violation of constraints on higher levels.

Abstract. We describe an approach to modelling biological networks by action languages via answer set programming. To this end, we propose an action language for modelling biological networks, building on previous work by Baral et al. We introduce its syntax and semantics along with a translation into answer set programming. Finally, we describe one of its applications, namely, the sulfur starvation response-pathway of the model plant Arabidopsis thaliana and sketch the functionality of our system and its usage. 1

Abstract. We introduce the logic-based planning language K c as an extension of K [5]. K c has two advantages upon K. First, the introduction of external function calls in the rules of a planning description allows the knowledge engineer to describe certain planning domains, e.g. involving complex action effects, in a more intuitive fashion then is possible in K. Secondly, in contrast to the conformant planning framework K, K c is formalized as a conditional planning system, which enables K c to solve planning problems that are impossible to express in K, e.g. involving sensing actions. A prototype implementation of conditional planning with K c is build on top of the DLV K system, and we illustrate its use by some small examples. 1

This thesis presents the Planning System DLV , which supports the novel Planning Language K. The language allows to represent AI planning problems in a declarative way and is capable of representing incomplete knowledge as well as nondeterministic eects of actions. After explaining some basics, the syntax and semantics of this language will be formally described and some results on the computational complexity of our language will be given, proving that K is capable of expressing hard planning problems, possibly involving incomplete knowledge or uncertainty, such as secure (conformant) planning.

We describe the design of the OLPS system, an implementation of the preferred answer set semantics for ordered logic programs. The basic algorithm we propose computes the extended answer sets of a simple program using an intuitive 9-valued lattice, called T9 . During the computation, this lattice is employed to keep track of the status of the literals and the rules while evolving to a solution. It turns out that the basic algorithm needs little modification in order to be able to compute the preferred answer sets of an ordered logic program. We illustrate the system using an example from diagnostic reasoning and we present some preliminary benchmark results comparing OLPS with existing answer set solvers such as SMODELS and DLV.

This thesis presents the Planning System DLV^K, which supports the novel Planning Language K. The language allows to represent AI planning problems in a declarative way and is capable of representing incomplete knowledge as well as nondeterministic effects of actions. After explaining some basics, the syntax and semantics of this language will be formally described and some results on the computational complexity of our language will be given, proving that K is capable of expressing hard planning problems, possibly involving incomplete knowledge or uncertainty, such as secure (conformant) planning. A translation