We present the first class of mathematically rigorous, general, fully self-referential, self-improving, optimally efficient problem solvers. Inspired by Kurt Goedel's celebrated self-referential formulas (1931), such a problem solver rewrites any part of its own code as soon as it has found a proof that the rewrite is useful, where the problem-dependent utility function and the hardware and the entire initial code are described by axioms encoded in an initial proof searcher which is also part of the initial code. The searcher systematically and efficiently tests computable proof techniques (programs whose outputs are proofs) until it finds a provably useful, computable self-rewrite. We show that such a self-rewrite is globally optimal - no local maxima! - since the code first had to prove that it is not useful to continue the proof search for alternative self-rewrites. Unlike previous non-self-referential methods based on hardwired proof searchers, ours not only boasts an optimal order of complexity but can optimally reduce any slowdowns hidden by the O()-notation, provided the utility of such speed-ups is provable at all.

The axiom scheme of Extensionality states that whenever two predicates or relations are coextensive they must have the same propertie s: XY ( null x(Xnull x Ynull x) Z (ZX ZY)) (1) Historically Extensionality has always been problematic, the main problem being that in many areas of application, though not perhaps in t he foundations of mathematics, the statement is simply false. This was reco gnized by Whitehead and Russell in Principia Mathematica [32], where intensional functions such as ' A believes that p ' or'it is a strange coincidence that p ' are discussed at length. However, in the introduction to the second edition ( 1927) of the Prin-cipia Whitehead and Russell (influenced by Wittgenstein's Tractatus) already entertain the possibility that "all functions of functions are extensional". Thirteen years later, in Church's [6] canonical formulation of t he Theory of Types, it is observed that axioms of Extensionality should be adopt ed "[i]n order to obtain classical real number theory (analysis)", a wording that does not seem to rule out the option of not adopting them. Church's formula tion of type theory was completely syntactic and axioms could be adopted or d ropped at will, The Journal of Symbolic Logic, to appear.

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.

We present tableau calculi for some logics of nonmonotonic reasoning, as defined by Kraus, Lehmann and Magidor. We give a tableau proof procedure for all KLM logics, namely preferential, loop-cumulative, cumulative and rational logics. Our calculi are obtained by introducing suitable modalities to interpret conditional assertions. We provide a decision procedure for the logics considered, and we study their complexity.

INRA Toulouse, France Abstract Weighted Max-SA T is the optimization version of SA T and many important problems can be naturally encoded as such. Solving weighted Max-SA T is an important problem from both a theoretical and a practical point of view. In recent ye ars, there has been considerable interest in finding efficient solving techniques. Most of thi s work focus on the computation of good quality lower bounds to be used within a branch and bou nd DPLL-like algorithm. Most often, these lower bounds are described in a procedural way. Because of that, it is difficult to realize the logic that is behind. In this paper we introduce an original framework for Max-SA T that stresses the parallelism with classical SA T. Then, we extend the two basic SA T s olving techniques: search and inference. We show that many algorithmic tricks used in state-of-the-art Max-SA T solvers are easily expressable in logic terms with our framework in a unified manner. Besides, we introduce an original search algorithm that per forms a restricted amount of weighted resolution at each visited node. We empirically compare our algorithm w ith a variety of solving alternatives on several benchmarks. Our experiments, which constitute to the best of our knowledge the most comprehensive Max-sat eva luation ever reported, show that our algorithm is generally orders of magnitude faster t han any competitor. Preprint submitted to Elsevier Science 11 September 2018 1 Introduction Weighted Max-SA T is the optimization version of the SA T prob lem and many important problems can be naturally expressed as such. In recent years, there has been a considerable effort in finding efficient exact algorithms. A common drawback of all these alg orithms is that albeit the close relationship between SA T and Max-SA T, they cannot be easily described with logic terminology. For instance, the contributions of [11,12,13,14] are good quality lower bounds to be incorporated into a depth-first branch and bound procedure. These lower bounds are mostly defined in a procedural way and it is very difficult to see the logic that is behind the execution of the procedure. This is in contrast with SA T algorithms where the solving process can b e easily decomposed into atomic logical steps. In this paper we introduce an original framework for (weight ed) Max-SA T in which the notions of upper and lower bound are incorporated into the problem definition. Under this framework classical SA T is just a particular case of Max-SA T, and the main SA T solving techniques can be naturally extended. In pa rticular, we extend the basic simplification rules (for example, idempotency, absorption, unit clause reduction, etc) and introduce a new one, hardening, that does not make sense in the SA T context.

An important problem to be addr essed within Event-Driven Architecture (EDA) is how to correctly and efficiently capture and process the event/action-based logic. This paper endeavors to bridge the gap between the Knowledge Representation (KR) approaches based on durable events/actions and such formalisms as event calculus, on one hand, and event-condition-action (ECA) reaction rules extending the approach of active databases that view events as instantaneous occurrences and/or sequences of events, on the other. We propose formalism based on reaction rules (ECA rules) and a novel interval-based event logic and present concrete RuleML-based syntax, semantics and implementation. We further evaluate this approach theoretically, experimentally and on an example derived from common industry use cases and illustrate its benefits.

We are developing a system that aims to perf orm the same inferences as a human reader, on car-crash reports. More precisely, we expect it to determine the causes of the accident as they appear from the text. We describe the genera l semantic framework in which our study takes place, the linguistic and semantic levels of analysis, and the inference rules used by the system.

Event-driven reactive functionalities are an urgent need in nowadays distributed service-oriented applications and (Semantic) Web-based environments. An important problem to be addressed is how to correctly and efficiently capture and process the event-based behavioral, reactive logic represented as ECA rules in combination with other conditional decision logic which is represented as derivation rules. In this paper we elaborate on a homogeneous integration approach which combines derivation rules, reaction rules (ECA rules) and other rule types such as integrity constraint into the general framework of logic programming. The developed ECA-LP language provides expressive features such as ID-based updates with support for external and self-updates of the intensional and extensional knowledge, transactions including integrity testing and an event algebra to define and process complex events and actions based on a novel interval-based Event Calculus variant.

Doctoral Symposium of MATES'06 Abstract: Automated management and monitoring of service contracts like Service Level Agreements (SLAs) or higher-level policies is vital for efficient and reliable distributed se rvice-oriented architectures (SOA) with high quality of service (QoS) levels. IT service provider need to manage, exec ute 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. I propose a novel rule-based knowledge representation (KR) for SLA rules and a respective rule-based service level management (RBSLM) framework. My rule-based approach based on logic programming pr ovides several advantages including automated rule chaining allowing for compact knowledge representation and high levels of automation as well as flexibility to adapt to rapidly changing business requirements. Therewith, I address an urgent need service-oriented businesses do have nowadays which is to dynamically change their business and contractual logic in order to adapt to rapidly changing business environments and to overcome the restricting nature of slow change cycles.

We show that the unification problem `is there a substitution instance of a given formula that is provable in a given logic?' is undecidable for basic modal logics K and K4 extended with the universal modality. It follows that the admissibility problem for inference rules is undecidable for these logics as well. These are the first examples of standard decidable modal logics for which the unification and admissibility problems are undecidable. We also prove undecidability of the unification and admissibility problems for K and K4 with at least two modal operators and nominals (instead of the universal modality), thereby showing that these problems are undecidable for basic hybrid logics. Recently, unification has been introduced as an important reasoning service for description logics. The undecidability proof for K with nominals can be used to show the undecidability of unification for boolean description logics with nominals (such as ALCO and SHIQO). The undecidability proof for K with the universal modality can be used to show that the unification problem relative to role boxes is undecidable for Boolean description logic with transitive roles, inverse roles, and role hierarchies (such as SHI and SHIQ).