Logic & Formal Reasoning
Designing and Building Multimedia Cultural Stories Using Concepts of Film Theories and Logic Programming
Mele, Francesco (Institute of Cybernetics National Research Council Italy) | Sorgente, Antonio (Institute of Cybernetics National Research Council Italy) | Vettigli, Giuseppe (Institute of Cybernetics National Research Council Italy)
In this paper we propose a middleware to reuse multimedia resources in order to produce new types of multimedia artifacts. In this work we adopt some basic concepts of film theory, such as the notions of plot, fabula and, in particular, diegetic time. The techniques we use are located within the area of artificial intelligence, using an explicit representation of time. The middleware consists of several modules, some devoted to the semantic annotation of multimedia components, and others to their visualization. Some modules regard the analysis of temporal connectivity and consistency of events. From a methodological point of view, an important module of the middleware contains the representation of a story (time of the narration and time of the story) and the temporal reasoning services, which are both implemented using a logic programming language (Flora2). Finally, there is a module in the middleware that translates the logical representation (in Flora2 language) into SMIL language, which allows the use of the final composition by a standard player.
Multi-Agent Only-Knowing Revisited
Belle, Vaishak, Lakemeyer, Gerhard
Levesque introduced the notion of only-knowing to precisely capture the beliefs of a knowledge base. He also showed how only-knowing can be used to formalize non-monotonic behavior within a monotonic logic. Despite its appeal, all attempts to extend only-knowing to the many agent case have undesirable properties. A belief model by Halpern and Lakemeyer, for instance, appeals to proof-theoretic constructs in the semantics and needs to axiomatize validity as part of the logic. It is also not clear how to generalize their ideas to a first-order case. In this paper, we propose a new account of multi-agent only-knowing which, for the first time, has a natural possible-world semantics for a quantified language with equality. We then provide, for the propositional fragment, a sound and complete axiomatization that faithfully lifts Levesque's proof theory to the many agent case. We also discuss comparisons to the earlier approach by Halpern and Lakemeyer.
Progress in Computer-Assisted Inductive Theorem Proving by Human-Orientedness and Descente Infinie?
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.
A formalism for causal explanations with an Answer Set Programming translation
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.
Ultrametric and Generalized Ultrametric in Computational Logic and in Data Analysis
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.
A Homogeneous Reaction Rule Language for Complex Event Processing
Paschke, Adrian, Kozlenkov, Alexander, Boley, Harold
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.
A Program-Level Approach to Revising Logic Programs under the Answer Set Semantics
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.
Towards Closed World Reasoning in Dynamic Open Worlds (Extended Version)
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.
Testing and Debugging Techniques for Answer Set Solver Development
Brummayer, Robert, Järvisalo, Matti
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.