Knowledge Representation Concepts for Automated SLA Management

Outsourcing of complex IT infrastructure to IT service providers has increased substantially during the past years. IT service providers must be able to fulfil their service-quality commitments based upon predefined Service Level Agreements (SLAs) with the service customer. They need to manage, execute and maintain thousands of SLAs for different customers and different types of services, which needs new levels of flexibility and automation not available with the current technology. The complexity of contractual logic in SLAs requires new forms of knowledge representation to automatically draw inferences and execute contractual agreements. A logic-based approach provides several advantages including automated rule chaining allowing for compact knowledge representation as well as flexibility to adapt to rapidly changing business requirements. We suggest adequate logical formalisms for representation and enforcement of SLA rules and describe a proof-of-concept implementation. The article describes selected formalisms of the ContractLog KR and their adequacy for automated SLA management and presents results of experiments to demonstrate flexibility and scalability of the approach.Comment: Paschke, A. and Bichler, M.: Knowledge Representation Concepts for Automated SLA Management, Int. Journal of Decision Support Systems (DSS), submitted 19th March 200

Reasoning about Minimal Belief and Negation as Failure

We investigate the problem of reasoning in the propositional fragment of MBNF, the logic of minimal belief and negation as failure introduced by Lifschitz, which can be considered as a unifying framework for several nonmonotonic formalisms, including default logic, autoepistemic logic, circumscription, epistemic queries, and logic programming. We characterize the complexity and provide algorithms for reasoning in propositional MBNF. In particular, we show that entailment in propositional MBNF lies at the third level of the polynomial hierarchy, hence it is harder than reasoning in all the above mentioned propositional formalisms for nonmonotonic reasoning. We also prove the exact correspondence between negation as failure in MBNF and negative introspection in Moore's autoepistemic logic

A Goal-Directed Implementation of Query Answering for Hybrid MKNF Knowledge Bases

Ontologies and rules are usually loosely coupled in knowledge representation formalisms. In fact, ontologies use open-world reasoning while the leading semantics for rules use non-monotonic, closed-world reasoning. One exception is the tightly-coupled framework of Minimal Knowledge and Negation as Failure (MKNF), which allows statements about individuals to be jointly derived via entailment from an ontology and inferences from rules. Nonetheless, the practical usefulness of MKNF has not always been clear, although recent work has formalized a general resolution-based method for querying MKNF when rules are taken to have the well-founded semantics, and the ontology is modeled by a general oracle. That work leaves open what algorithms should be used to relate the entailments of the ontology and the inferences of rules. In this paper we provide such algorithms, and describe the implementation of a query-driven system, CDF-Rules, for hybrid knowledge bases combining both (non-monotonic) rules under the well-founded semantics and a (monotonic) ontology, represented by a CDF Type-1 (ALQ) theory. To appear in Theory and Practice of Logic Programming (TPLP

Logic Programs with Compiled Preferences

We describe an approach for compiling preferences into logic programs under the answer set semantics. An ordered logic program is an extended logic program in which rules are named by unique terms, and in which preferences among rules are given by a set of dedicated atoms. An ordered logic program is transformed into a second, regular, extended logic program wherein the preferences are respected, in that the answer sets obtained in the transformed theory correspond with the preferred answer sets of the original theory. Our approach allows both the specification of static orderings (as found in most previous work), in which preferences are external to a logic program, as well as orderings on sets of rules. In large part then, we are interested in describing a general methodology for uniformly incorporating preference information in a logic program. Since the result of our translation is an extended logic program, we can make use of existing implementations, such as dlv and smodels. To this end, we have developed a compiler, available on the web, as a front-end for these programming systems

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

Abduction in Well-Founded Semantics and Generalized Stable Models

Abductive logic programming offers a formalism to declaratively express and solve problems in areas such as diagnosis, planning, belief revision and hypothetical reasoning. Tabled logic programming offers a computational mechanism that provides a level of declarativity superior to that of Prolog, and which has supported successful applications in fields such as parsing, program analysis, and model checking. In this paper we show how to use tabled logic programming to evaluate queries to abductive frameworks with integrity constraints when these frameworks contain both default and explicit negation. The result is the ability to compute abduction over well-founded semantics with explicit negation and answer sets. Our approach consists of a transformation and an evaluation method. The transformation adjoins to each objective literal $O$ in a program, an objective literal $not(O)$ along with rules that ensure that $not(O)$ will be true if and only if $O$ is false. We call the resulting program a {\em dual} program. The evaluation method, \wfsmeth, then operates on the dual program. \wfsmeth{} is sound and complete for evaluating queries to abductive frameworks whose entailment method is based on either the well-founded semantics with explicit negation, or on answer sets. Further, \wfsmeth{} is asymptotically as efficient as any known method for either class of problems. In addition, when abduction is not desired, \wfsmeth{} operating on a dual program provides a novel tabling method for evaluating queries to ground extended programs whose complexity and termination properties are similar to those of the best tabling methods for the well-founded semantics. A publicly available meta-interpreter has been developed for \wfsmeth{} using the XSB system.Comment: 48 pages; To appear in Theory and Practice in Logic Programmin

Reason Maintenance - Conceptual Framework

This paper describes the conceptual framework for reason maintenance developed as part of WP2

Normality Operators and Classical Collapse

In this paper, we extend the expressive power of the logics K3, LP and FDE with anormality operator, which is able to express whether a for-mula is assigned a classical truth value or not. We then establish classical recapture theorems for the resulting logics. Finally, we compare the approach via normality operator with the classical collapse approach devisedby Jc Beall