Implementing Default and Autoepistemic Logics via the Logic of GK

The logic of knowledge and justified assumptions, also known as logic of grounded knowledge (GK), was proposed by Lin and Shoham as a general logic for nonmonotonic reasoning. To date, it has been used to embed in it default logic (propositional case), autoepistemic logic, Turner's logic of universal causation, and general logic programming under stable model semantics. Besides showing the generality of GK as a logic for nonmonotonic reasoning, these embeddings shed light on the relationships among these other logics. In this paper, for the first time, we show how the logic of GK can be embedded into disjunctive logic programming in a polynomial but non-modular translation with new variables. The result can then be used to compute the extension/expansion semantics of default logic, autoepistemic logic and Turner's logic of universal causation by disjunctive ASP solvers such as claspD(-2), DLV, GNT and cmodels.Comment: Proceedings of the 15th International Workshop on Non-Monotonic Reasoning (NMR 2014

Modularity in answer set programs

Answer set programming (ASP) is an approach to rule-based constraint programming allowing flexible knowledge representation in variety of application areas. The declarative nature of ASP is reflected in problem solving. First, a programmer writes down a logic program the answer sets of which correspond to the solutions of the problem. The answer sets of the program are then computed using a special purpose search engine, an ASP solver. The development of efficient ASP solvers has enabled the use of answer set programming in various application domains such as planning, product configuration, computer aided verification, and bioinformatics. The topic of this thesis is modularity in answer set programming. While modern programming languages typically provide means to exploit modularity in a number of ways to govern the complexity of programs and their development process, relatively little attention has been paid to modularity in ASP. When designing a module architecture for ASP, it is essential to establish full compositionality of the semantics with respect to the module system. A balance is sought between introducing restrictions that guarantee the compositionality of the semantics and enforce a good programming style in ASP, and avoiding restrictions on the module hierarchy for the sake of flexibility of knowledge representation. To justify a replacement of a module with another, that is, to be able to guarantee that changes made on the level of modules do not alter the semantics of the program when seen as an entity, a notion of equivalence for modules is provided. In close connection with the development of the compositional module architecture, a transformation from verification of equivalence to search for answer sets is developed. The translation-based approach makes it unnecessary to develop a dedicated tool for the equivalence verification task by allowing the direct use of existing ASP solvers. Translations and transformations between different problems, program classes, and formalisms are another central theme in the thesis. To guarantee efficiency and soundness of the translation-based approach, certain syntactical and semantical properties of transformations are desirable, in terms of translation time, solution correspondence between the original and the transformed problem, and locality/globality of a particular transformation. In certain cases a more refined notion of minimality than that inherent in ASP can make program encodings more intuitive. Lifschitz' parallel and prioritized circumscription offer a solution in which certain atoms are allowed to vary or to have fixed values while others are falsified as far as possible according to priority classes. In this thesis a linear and faithful transformation embedding parallel and prioritized circumscription into ASP is provided. This enhances the knowledge representation capabilities of answer set programming by allowing the use of existing ASP solvers for computing parallel and prioritized circumscription

Counterexample Guided Abstraction Refinement Algorithm for Propositional Circumscription

Circumscription is a representative example of a nonmonotonic reasoning inference technique. Circumscription has often been studied for first order theories, but its propositional version has also been the subject of extensive research, having been shown equivalent to extended closed world assumption (ECWA). Moreover, entailment in propositional circumscription is a well-known example of a decision problem in the second level of the polynomial hierarchy. This paper proposes a new Boolean Satisfiability (SAT)-based algorithm for entailment in propositional circumscription that explores the relationship of propositional circumscription to minimal models. The new algorithm is inspired by ideas commonly used in SAT-based model checking, namely counterexample guided abstraction refinement. In addition, the new algorithm is refined to compute the theory closure for generalized close world assumption (GCWA). Experimental results show that the new algorithm can solve problem instances that other solutions are unable to solve

05171 Abstracts Collection -- Nonmonotonic Reasoning, Answer Set Programming and Constraints

From 24.04.05 to 29.04.05, the Dagstuhl Seminar 05171 ``Nonmonotonic Reasoning, Answer Set Programming and Constraints\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Space Efficiency of Propositional Knowledge Representation Formalisms

We investigate the space efficiency of a Propositional Knowledge Representation (PKR) formalism. Intuitively, the space efficiency of a formalism F in representing a certain piece of knowledge A, is the size of the shortest formula of F that represents A. In this paper we assume that knowledge is either a set of propositional interpretations (models) or a set of propositional formulae (theorems). We provide a formal way of talking about the relative ability of PKR formalisms to compactly represent a set of models or a set of theorems. We introduce two new compactness measures, the corresponding classes, and show that the relative space efficiency of a PKR formalism in representing models/theorems is directly related to such classes. In particular, we consider formalisms for nonmonotonic reasoning, such as circumscription and default logic, as well as belief revision operators and the stable model semantics for logic programs with negation. One interesting result is that formalisms with the same time complexity do not necessarily belong to the same space efficiency class

Epistemic Reasoning in OWL 2 DL

We extend the description logic SROIQ (OWL 2 DL) with the epistemic operator K and argue that unintended effects occur when imposing the semantics traditionally employed. Consequently, we identify the most expressive DL for which the traditional approach can still be adapted. For the epistemic extension of SROIQ and alike expressive DLs, we suggest a revised semantics that behaves more intuitively in these cases and coincides with the traditional semantics on less expressive DLs

Reasoning about Action: An Argumentation - Theoretic Approach

We present a uniform non-monotonic solution to the problems of reasoning about action on the basis of an argumentation-theoretic approach. Our theory is provably correct relative to a sensible minimisation policy introduced on top of a temporal propositional logic. Sophisticated problem domains can be formalised in our framework. As much attention of researchers in the field has been paid to the traditional and basic problems in reasoning about actions such as the frame, the qualification and the ramification problems, approaches to these problems within our formalisation lie at heart of the expositions presented in this paper