Logic Programming and Logarithmic Space

We present an algebraic view on logic programming, related to proof theory and more specifically linear logic and geometry of interaction. Within this construction, a characterization of logspace (deterministic and non-deterministic) computation is given via a synctactic restriction, using an encoding of words that derives from proof theory. We show that the acceptance of a word by an observation (the counterpart of a program in the encoding) can be decided within logarithmic space, by reducing this problem to the acyclicity of a graph. We show moreover that observations are as expressive as two-ways multi-heads finite automata, a kind of pointer machines that is a standard model of logarithmic space computation

Unifying Reasoning and Core-Guided Search for Maximum Satisfiability

A central algorithmic paradigm in maximum satisfiability solving geared towards real-world optimization problems is the core-guided approach. Furthermore, recent progress on preprocessing techniques is bringing in additional reasoning techniques to MaxSAT solving. Towards realizing their combined potential, understanding formal underpinnings of interleavings of preprocessing-style reasoning and core-guided algorithms is important. It turns out that earlier proposed notions for establishing correctness of core-guided algorithms and preprocessing, respectively, are not enough for capturing correctness of interleavings of the techniques. We provide an in-depth analysis of these and related MaxSAT instance transformations, and propose correction set reducibility as a notion that captures inprocessing MaxSAT solving within a state-transition style abstract MaxSAT solving framework. Furthermore, we establish a general theorem of correctness for applications of SAT-based preprocessing techniques in MaxSAT. The results pave way for generic techniques for arguing about the formal correctness of MaxSAT algorithms.Peer reviewe

Abstract Solvers for Quantified Boolean Formulas and their Applications

none2norestrictedBrochenin, Remi; Maratea, MarcoBrochenin, Remi; Maratea, Marc

Reasoning about the state change of authorization policies

Reasoning about authorization policies has been a prominent issue in information security research. In a complex information sharing and exchange environment, a user’s request may initiate a sequence of executions of authorization commands in order to decide whether such request should be granted or denied. Becker and Nanz’s logic of State- Modifying Policies (SMP) is a formal system addressing such problem in access control. In this paper, we provide a declarative semantics for SMP through a translation from SMP to Answer Set Programming (ASP). We show that our translation is sound and complete for bounded SMP reasoning. With this translation, we are able not only to directly compute users’ authorization query answers, but also to specifically extract information of how users’ authorization states change in relation to the underlying query answering. In this way, we eventually avoid SMP’s tedious proof system and significantly simply the SMP reasoning process. Furthermore, we argue that the proposed ASP translation of SMP also provides a flexibility to enhance SMP’s capacity for accommodating more complex authorization reasoning problems that the current SMP lacks

Архитектура приложения Text2ALM для семантической обработки языка

In this work we design a narrative understanding tool TEXT2ALM. This tool uses an action language ALM to perform inferences on complex interactions of events described in narratives. The methodology used to implement the TEXT2ALM system was originally outlined by Lierler, Inclezan, and Gelfond [11] via a manual process of converting a narrative to an ALM model. It relies on a conglomeration of resources and techniques from two distinct fields of artificial intelligence, namely, natural language processing and knowledge representation and reasoning. The effectiveness of system TEXT2ALM is measured by its ability to correctly answer questions from the bAbI tasks by Facebook Research in 2015. This tool matched or exceeded the performance of state-of-the-art machine learning methods in six of the seven tested tasks. Приложения Text2ALM ориентируется на семантическую обработку текста с глаголами действия. Эта система использует язык программирования действий под названием ALM для выполнения выводов о сложных взаимодействиях событий, описанных в тексте. Система опирается на ресурсы и методы из двух различных областей искусственного интеллекта, а именно: обработка естественного языка и представление знаний. Эффективность приложения Text2ALM измеряется по ее способности правильно отвечать на вопросы из задач babi (Facebook Research, 2015). Text2ALM соответствовал или превышал производительность современных методов машинного обучения в шести из семи протестированных заданий

Abstract solvers for dung’s argumentation frameworks

none5sirestrictedBrochenin, Rémi; Linsbichler, Thomas; Maratea, Marco; Wallner, Johannes Peter; Woltran, StefanBrochenin, Remi; Linsbichler, Thomas; Maratea, Marco; Wallner, Johannes Peter; Woltran, Stefa

On the interaction of existential rules and equality constraints in ontology querying

Ontological query processing is an exciting research topic in database theory, knowledge representation, and logic programming. In many cases, ontological constraints are expressed over an extensional database by extending traditional Datalog rules to allow existential quantification and equality atoms in the head. The unrestricted use of these features causes undecidability of query answering and, therefore, their interaction must be controlled. This work provides a tutorial-like introduction to the problem of query answering under existential and equality constraints. We survey the most notable (semantic and syntactic) restrictions to such constraints ensuring decidability of query answering, and we discuss their practical application to conceptual modelling