In this short position paper we briefly review the development history of automated inductive theorem proving and computer-assisted mathematical induction. We think that the current low expectations on progress in this field result from a faulty narrow-scope historical projection. Our main motivation is to explain--on an abstract but hopefully sufficiently descriptive level--why we believe that future progress in the field is to result from human-orientedness and descente infinie.

We examine the practicality for a user of using Answer Set Programming (ASP) for representing logical formalisms. Our example is a formalism aiming at capturing causal explanations from causal information. We show the naturalness and relative efficiency of this translation job. We are interested in the ease for writing an ASP program. Limitations of the earlier systems made that in practice, the ``declarative aspect'' was more theoretical than practical. We show how recent improvements in working ASP systems facilitate the translation.

Following a review of metric, ultrametric and generalized ultrametric, we review their application in data analysis. We show how they allow us to explore both geometry and topology of information, starting with measured data. Some themes are then developed based on the use of metric, ultrametric and generalized ultrametric in logic. In particular we study approximation chains in an ultrametric or generalized ultrametric context. Our aim in this work is to extend the scope of data analysis by facilitating reasoning based on the data analysis; and to show how quantitative and qualitative data analysis can be incorporated into logic programming.

The Logic Programming (LP) community, through the Association for Logic Programming (ALP) and its Executive Committee, decided to introduce for 2010 important changes in the way the main yearly results in LP and related areas are published. Whereas such results have appeared to date in standalone volumes of proceedings of the yearly International Conferences on Logic Programming (ICLP), and this method -fully in the tradition of Computer Science (CS)- has served the community well, it was felt that an effort needed to be made to achieve a higher level of compatibility with the publishing mechanisms of other fields outside CS. In order to achieve this goal without giving up the traditional CS conference format a different model has been adopted starting in 2010 in which the yearly ICLP call for submissions takes the form of a joint call for a) full papers to be considered for publication in a special issue of the journal, and b) shorter technical communications to be considered for publication in a separate, standalone volume, with both kinds of papers being presented by their authors at the conference. Together, the journal special issue and the volume of short technical communications constitute the proceedings of ICLP. This 26th International Conference on Logic Programming Special Issue is the first of a series of yearly special issues of Theory and Practice of Logic Programming (TPLP) putting this new model into practice.

Event-driven automation of reactive functionalities for complex event processing is an urgent need in today's distributed service-oriented architectures and Web-based event-driven environments. An important problem to be addressed is how to correctly and efficiently capture and process the event-based behavioral, reactive logic embodied in reaction rules, and combining this with other conditional decision logic embodied, e.g., in derivation rules. This paper elaborates a homogeneous integration approach that combines derivation rules, reaction rules and other rule types such as integrity constraints into the general framework of logic programming, the industrial-strength version of declarative programming. We describe syntax and semantics of the language, implement a distributed web-based middleware using enterprise service technologies and illustrate its adequacy in terms of expressiveness, efficiency and scalability through examples extracted from industrial use cases. The developed reaction rule language provides expressive features such as modular ID-based updates with support for external imports and self-updates of the intensional and extensional knowledge bases, transactions including integrity testing and roll-backs of update transition paths. It also supports distributed complex event processing, event messaging and event querying via efficient and scalable enterprise middleware technologies and event/action reasoning based on an event/action algebra implemented by an interval-based event calculus variant as a logic inference formalism.

An approach to the revision of logic programs under the answer set semantics is presented. For programs P and Q, the goal is to determine the answer sets that correspond to the revision of P by Q, denoted P * Q. A fundamental principle of classical (AGM) revision, and the one that guides the approach here, is the success postulate. In AGM revision, this stipulates that A is in K * A. By analogy with the success postulate, for programs P and Q, this means that the answer sets of Q will in some sense be contained in those of P * Q. The essential idea is that for P * Q, a three-valued answer set for Q, consisting of positive and negative literals, is first determined. The positive literals constitute a regular answer set, while the negated literals make up a minimal set of naf literals required to produce the answer set from Q. These literals are propagated to the program P, along with those rules of Q that are not decided by these literals. The approach differs from work in update logic programs in two main respects. First, we ensure that the revising logic program has higher priority, and so we satisfy the success postulate; second, for the preference implicit in a revision P * Q, the program Q as a whole takes precedence over P, unlike update logic programs, since answer sets of Q are propagated to P. We show that a core group of the AGM postulates are satisfied, as are the postulates that have been proposed for update logic programs.

The need for integration of ontologies with nonmonotonic rules has been gaining importance in a number of areas, such as the Semantic Web. A number of researchers addressed this problem by proposing a unified semantics for hybrid knowledge bases composed of both an ontology (expressed in a fragment of first-order logic) and nonmonotonic rules. These semantics have matured over the years, but only provide solutions for the static case when knowledge does not need to evolve. In this paper we take a first step towards addressing the dynamics of hybrid knowledge bases. We focus on knowledge updates and, considering the state of the art of belief update, ontology update and rule update, we show that current solutions are only partial and difficult to combine. Then we extend the existing work on ABox updates with rules, provide a semantics for such evolving hybrid knowledge bases and study its basic properties. To the best of our knowledge, this is the first time that an update operator is proposed for hybrid knowledge bases.

This paper develops automated testing and debugging techniques for answer set solver development. We describe a flexible grammar-based black-box ASP fuzz testing tool which is able to reveal various defects such as unsound and incomplete behavior, i.e. invalid answer sets and inability to find existing solutions, in state-of-the-art answer set solver implementations. Moreover, we develop delta debugging techniques for shrinking failure-inducing inputs on which solvers exhibit defective behavior. In particular, we develop a delta debugging algorithm in the context of answer set solving, and evaluate two different elimination strategies for the algorithm.

Answer Set Programming (ASP) has been deployed in many applications, thanks to the availability of efficient solvers. Most programs encountered in practice have an important property: Their predicate arities are bounded by a constant, and in this case it is known that the relevant computations can be done using polynomial space. However, all competitive ASP systems rely on grounding, due to which they may use exponential space for these programs. We present three evaluation methods that respect the polynomial space bound and a generic framework architecture for realization. Experimental results for a prototype implementation indicate that the methods are effective. They show not only benign space consumption, but interestingly also good runtime compared to some state of the art ASP solvers.

In this paper, we study the knowledge compilation task for propositional epistemic logic S5. We first extend many of the queries and transformations considered in the classical knowledge compilation map to S5. We then show that the notion of disjunctive normal form (DNF) can be profitably extended to the epistemic case; we prove that the DNF fragment of S5, when appropriately defined, satisfies essentially the same queries and transformations as its classical counterpart.