The Qualification Problem: A solution to the problem of anomalous models

AbstractIntelligent agents in open environments inevitably face the Qualification Problem: The executability of an action can never be predicted with absolute certainty; unexpected circumstances, albeit unlikely, may at any time prevent the successful performance of an action. Reasoning agents in real-world environments rely on a solution to the Qualification Problem in order to make useful predictions but also to explain and recover from unexpected action failures. Yet the main theoretical result known today in this context is a negative one: While a solution to the Qualification Problem requires to assume away by default abnormal qualifications of actions, straightforward minimization of abnormality falls prey to the production of anomalous models. We present an approach to the Qualification Problem which resolves this anomaly. Anomalous models are shown to arise from ignoring causality, and they are avoided by appealing to just this concept. Our theory builds on the established predicate logic formalism of the Fluent Calculus as a solution to the Frame Problem and to the Ramification Problem in reasoning about actions. The monotonic Fluent Calculus is enhanced by a default theory in order to obtain the nonmonotonic approach called for by the Qualification Problem. The approach has been implemented in an action programming language based on the Fluent Calculus and successfully applied to the high-level control of robots

Pseudo-contractions as Gentle Repairs

Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas

Lambda Calculus with Explicit Recursion

AbstractThis paper is concerned with the study ofλ-calculus with explicit recursion, namely of cyclicλ-graphs. The starting point is to treat aλ-graph as a system of recursion equations involvingλ-terms and to manipulate such systems in an unrestricted manner, using equational logic, just as is possible for first-order term rewriting. Surprisingly, now the confluence property breaks down in an essential way. Confluence can be restored by introducing a restraining mechanism on the substitution operation. This leads to a family ofλ-graph calculi, which can be seen as an extension of the family ofλσ-calculi (λ-calculi with explicit substitution). While theλσ-calculi treat the let-construct as a first-class citizen, our calculi support the letrec, a feature that is essential to reason about time and space behavior of functional languages and also about compilation and optimizations of program

Order-Sorted Equational Computation

The expressive power of many-sorted equational logic can be greatly enhanced by allowing for subsorts and multiple function declarations. In this paper we study some computational aspects of such a logic. We start with a self-contained introduction to order-sorted equational logic including initial algebra semantics and deduction rules. We then present a theory of order-sorted term rewriting and show that the key results for unsorted rewriting extend to sort decreasing rewriting. We continue with a review of order-sorted unification and prove the basic results. In the second part of the paper we study hierarchical order-sorted specifications with strict partial functions. We define the appropriate homomorphisms for strict algebras and show that every strict algebra is base isomorphic to a strict algebra with at most one error element. For strict specifications, we show that their categories of strict algebras have initial objects. We validate our approach to partial functions by proving that completely defined total functions can be defined as partial without changing the initial algebra semantics. Finally, we provide decidable sufficient criteria for the consistency and strictness of ground confluent rewriting systems

FluCaP: A Heuristic Search Planner for First-Order MDPs

We present a heuristic search algorithm for solving first-order Markov Decision Processes (FOMDPs). Our approach combines first-order state abstraction that avoids evaluating states individually, and heuristic search that avoids evaluating all states. Firstly, in contrast to existing systems, which start with propositionalizing the FOMDP and then perform state abstraction on its propositionalized version we apply state abstraction directly on the FOMDP avoiding propositionalization. This kind of abstraction is referred to as first-order state abstraction. Secondly, guided by an admissible heuristic, the search is restricted to those states that are reachable from the initial state. We demonstrate the usefulness of the above techniques for solving FOMDPs with a system, referred to as FluCaP (formerly, FCPlanner), that entered the probabilistic track of the 2004 International Planning Competition (IPC2004) and demonstrated an advantage over other planners on the problems represented in first-order terms

Verbmobil : translation of face-to-face dialogs

Verbmobil is a long-term project on the translation of spontaneous language in negotiation dialogs. We describe the goals of the project, the chosen discourse domains and the initial project schedule. We discuss some of the distinguishing features of Verbmobil and introduce the notion of translation on demand and variable depth of processing in speech translation. Finally, the role of anytime modules for efficient dialog translation in close to real time is described

Narrowing Based Inductive Proof Search

Premiere version en 2005, en l'honneur de Harald GanzingerVersion finale envoyé a SpringerWe present in this paper a narrowing-based proof search method for inductive theorems. It has the specificity to be grounded on deduction modulo and to yield a direct translation from a successful proof search derivation to a proof in the sequent calculus. The method is shown to be sound and refutationally correct in a proof theoretical way

Web Services Compositions Modelling and Choreographies Analysis

International audienceIn (Rouached, Godart and al. 2006; Rouached, Godart 2007), we have described the semantics of WSBPEL by way of mapping each of the WSBPEL (Arkin, Askary and al. 2004) constructs to the EC algebra and building a model of the process behaviour. With these mapping rules, we have described a modelling approach of a process defined for a single Web service composition. However, this modelling is limited to a local view and can only be used to model the behaviour of a single process. A series of compositions in Web service choreography need specific modelling activities that are not explicitly derived from an implementation. An elaboration of modelling is then required to represent the behaviour of interacting compositions across partnered processes. This elaboration provides a representation that enables us to perform analysis of service interaction for behaviour properties. The ability to perform verification and validation between execution and design, and within the process compositions themselves, is a key requirement of the Web services architecture specification. In this paper, we further the semantic mapping to include Web service composition interactions through modelling Web service conversations and their choreography. We describe this elaboration of models to support a view of interacting Web service compositions extending the mapping from WSBPEL to EC, and including Web service interfaces (WSDL) for use in modelling between services. The verification and validation techniques are also exposed. An automated induction-based theorem prover is used as verification back-end

Deductive synthesis of recursive plans in linear logic

Centre for Intelligent Systems and their ApplicationsConventionally, the problem of plan formation in Artificial Intelligence deals with the generation of plans in the form of a sequence of actions. This thesis describes an approach to extending the expressiveness of plans to include conditional branches and recursion. This allows problems to be solved at a higher level, such that a single plan in such a language is capable of solving a class of problems rather than a single problem instance. A plan of fixed size may solve arbitrarily large problem instances. To form such plans, we take a deductive planning approach, in which the formation of the plan goes hand-in-hand with the construction of the proof that the plan specification is realisable. The formalism used here for specifying and reasoning with planning problems is Girard's Institutionistic Linear Logic (ILL), which is attractive for planning problems because state change can be expressed directly as linear implication, with no need for frame axioms. We extract plans by means of the relationship between proofs in ILL and programs in the style of Abramsky. We extend the ILL proof rules to account for induction over inductively defined types, thereby allowing recursive plans to be synthesised. We also adapt Abramsky's framework to partially evaluate and execute the plans in the extended language. We give a proof search algorithm tailored towards the fragment of the ILL employed (excluding induction rule selection). A system implementation, Lino, comprises modules for proof checking, automated proof search, plan extraction and partial evaluation of plans. We demonstrate the encodings and solutions in our framework of various planning domains involving recursion. We compare the capabilities of our approach with the previous approaches of Manna and Waldinger, Ghassem-Sani and Steel, and Stephen and Biundo. We claim that our approach gives a good balance between coverage of problems that can be described and the tractability of proof search