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International audience; In this article we propose a decision process integrating Non-Monotonic Reasoning (NMR), embedded in a deliberative architecture. The NMR process uses Default Logic to implement goal reasoning, managing partially observable or incomplete information, allowing the design of default behaviours completed by the handling of specific situations, in order to manage the current mission objective as well as safety rules. We illustrate our approach through an application of an underwater robot performing a marine biology mission.

Urban route planning is important for smart cities and intelligent transportation systems. Most of the exiting methods of urban route planning are either graph based search algorithms or optimization methods, however they show many weaknesses in real-world applications due to their high computational complexities and needs for global information of urban environments. To solve this problem, we propose a novel Recurrent Neural Network (RNN) based default logic for route planning. The proposed method is composed of three parts. The first part is the default theory of route planning, forcing no loops in the generated routes. The second part is the RNN based default reasoning to recommend default rules. The RNN outputs the probability distribution of the defaults used next, so the proposed method is a probabilistic method. The third part is the update algorithm of map models to improve the accuracy of default reasoning in dynamic environments. Training the proposed RNN is simple because no statistic computation is required for training. The time complexity of the proposed method during testing is just O(ρ2), where ρ is the length of the optimal route for two given nodes. To evaluate the proposed method, we build a new map model named BJ simulating the complex urban environments of the Beijing city, China. Extensive experiments on the BJ map model in both static and dynamic environments show the effectiveness and accuracy of the proposed method.

In this paper, we propose a computational model of human behavior events analysis that integrates perceptual causality. Design and establish a causal rule representation method based on default logic, which provides a concise syntax and semantic formal tool for potential causality. Through the analysis of the internal structure of the event, the technical framework of causality with the smallest action unit as the entity is established, which makes the traditional different entities, objects, events, states and actions naturally interrelated. By establishing the perceptual causal relationship between human goals and objects, events, reasoning the intention of human goals, and predicting their behavior, it can effectively solve the problem of human action occlusion and action error detection. The effectiveness of this method is evaluated on a new video dataset.

A brief idea

In nonmonotonic reasoning there are the problems of inconsistency and incoherence in general, and in default reasoning there may be only one trivial extension or no extension in special. We propose the restricted semantics of four-valued logic for default reasoning to resolve the problems of inconsistency and incoherence and in the meantime retain classical extensions in the presence of consistency and coherency. The restricted semantics can maintain both the expressiveness and reasoning ability of default logic. We provide a transformation approach to compute the restricted extensions by reducing them into classical ones.

In inductive learning of a broad concept, an algorithm should be able to distinguish concept examples from exceptions and noisy data. An approach through recursively finding patterns in exceptions turns out to correspond to the problem of learning default theories. Default logic is what humans employ in common-sense reasoning. Therefore, learned default theories are better understood by humans. In this paper, we present new algorithms to learn default theories in the form of non-monotonic logic programs. Experiments reported in this paper show that our algorithms are a significant improvement over traditional approaches based on inductive logic programming., Comment: Paper presented at the 33rd International Conference on Logic Programming (ICLP 2017), Melbourne, Australia, August 28 to September 1, 2017 16 pages, LaTeX, 3 PDF figures (arXiv:YYMM.NNNNN)

This thesis presents a resilient model to pilot an aircraft based on a non-monotonic logic. This model is capable of handling solutions from incomplete, contradictory information and exceptions. This is a very well known problem in the field of Artificial Intelligence, which has been studied for more than 40 years. To do this, we use default logic to formalise the situation and find possible actions. Thanks to this logic we can transform the piloting rules to defaults. Then, when we calculate the solutions, several options could result. At this point an opportunistic deci- sion criteria takes place to choose the better solution. The control of the system is done via the property of resilience, we redefine this property as the integration of the non-monotonic logic in the Minsky’s model. As a result, it is shown that the proposed resilient model could be generalised to systems that incorporate a knowledge of the world that contains situations, objectives and actions. Finally, we present the experimental results and conclusion of the thesis discussing the prospects and challenges that exist for future directions. Different applications in other fields are taken into account for the interest of the model’s behavior.; Esta tesis presenta un modelo resistente para pilotar un avión basado en una lógica no monótona. Este modelo es capaz de manejar soluciones a partir de informaciones incompletas, contradictorias y excepciones. Este es un problema muy conocido en campo de la Inteligencia Artificial, que se ha estudiado durante más de 40 años. Para hacer esto, usamos la lógica por defectos para formalizar la situación y encontrar posibles acciones. Gracias a esta lógica, podemos transformar las reglas de pilotaje en defectos. Luego, cuando calculamos las soluciones, pueden surgir varias opciones. En este punto, tiene lugar un criterio de decisión oportunista para elegir la mejor solución. El control del sistema se realiza a través de la propiedad de resiliencia. Redefinimos esta propiedad como la integración de la lógica no monótona en el modelo de Minsky. Como resultado, se muestra que el modelo resistente propuesto podría generalizarse a sistemas que incorporan un conocimiento del mundo que contiene situaciones, objetivos y acciones. Finalmente, presentamos los resultados experimentales y la conclusión de la tesis sobre las perspectivas y los desafíos que existen para futuras direcciones. Se tienen en cuenta diferentes aplicaciones en otros campos para el interés del comportamiento del modelo.; Cette thèse présente un modèle résilient pour piloter un avion basé sur une logique non monotone. Ce modèle est capable de gérer des solutions à partir d’informations incomplètes, contradictoires et des exceptions. C’est un problème très connu dans le domaine de l’Intelligence Artificielle, qui est étudié depuis plus de 40 ans. Pour ce faire, nous utilisons la logique des défauts pour formaliser la situation et trouver des actions possibles. Grâce à cette logique, nous pouvons transformer les règles de pilotage en défauts. Ensuite, lorsque nous calculons les solutions, plusieurs options peuvent en résulter. À ce stade, il existe un critère de décision opportuniste pour choisir la meilleure solution. Le contrôle du système se fait via la propriété de résilience. Nous redéfinissons cette propriété comme l’intégration de la logique non-monotone dans le modèle de Minsky. En conséquence, il est démontré que le modèle de résilience proposé pourrait être généralisé aux systèmes intégrant une connaissance du monde contenant des situations, des objectifs et des actions. Enfin, nous présentons les résultats expérimentaux et la conclusion de la thèse en discutant des perspectives et des défis pour les orientations futures. Différentes applications dans d’autres domaines sont prises en compte pour l’intérêt du comportement du modèle.

This paper put forward constrained epistemic action model logic (EAML), which extended the action modal logic and reason epistemic default logic in the dynamic epistemic theory framework. In this paper, the constrained epistemic default logic and action model logic was combined to model the dynamic cognitive update process by introducing a cognitive operator. As constrained epistemic default logic restricts the current possible epistemic state and action model logic can describe epistemic actions, the new proposed logic can better portray the cognitive operations and the restriction of the corresponding accessibility relations. The description of the logic framework was given in this study, and the related theorems were proved to show the interpretation of the constrained epistemic action model logic.

Human non-conscious reasoning is one of the most successful procedures developed to solve everyday problems in an efficient way. This is why the field of artificial intelligence should analyze, formalize and emulate the multiple ways of non-conscious reasoning with the purpose of applying them in knowledge based systems, neurocomputers and similar devices for aiding people in the problem-solving process. In this paper, a framework for those non-conscious ways of reasoning is presented based on object-oriented representations, fuzzy sets and multivalued logic.

Formal semantic theories are designed to explain how it is possible to produce and understand an infinite number of sentences on the basis of a finite lexicon and a finite number of composition rules. According to this architecture, language comprehension completely proceeds in a bottom-up fashion only driven by linear linguistic input thereby leaving no room for a predictive component which allows to make expectations about upcoming words. This is in stark contrast to neurophysiological research in the past decades on online semantic processing which has provided ample evidence that prediction plays indeed an indispensable role in language comprehension the brain as a prediction machine, [Ber10]. In this article, we present an extension of formal semantic theory that allows to make predictions of upcoming words. The basic intuition is: predictions are based on incomplete information. Drawing defeasible conclusions based on such information can be modeled by default reasoning. Since predictions can go wrong, a second strategy for retracting wrong guesses is needed in order to integrate unexpected words into the prior context. This is modeled by belief revision. We model both processing stages, making predictions about upcoming words and integrating them into the prior context, and relate the models to the empirical findings in neurophysiological research.

Brewka's Cumulative Default Logic (CDL), a new version of Reiter's default logic, puts emphasis on the joint consistency among the justifications of all applied defaults to obtain cumulativity. In this paper, a finite characterization of CDL extensions using sets of generating defaults is given. From this characterization we derive new algorithms for various reasoning tasks in CDL. Moreover, we show that (propositional) cumulative default reasoning has the same complexity as classical default reasoning.

Research in NMR has focused largely on the idea of representing knowledge about the world via rules that are generally true but can be defeated. Even if relational databases are nowadays the main tool for storing very large sets of data, the approach of using non-monotonic formalisms as relational database query languages has been investigated to a much smaller extent. In this work we propose a novel application of default logic by introducing a default query language (DQL) for finite relational databases, which is based on default rules. The main result of this paper is that DQL is as expressive as SO∃∀, the existential universal fragment of second order logic. This result is not only of theoretical importance: We show queries -which are useful in practice- that can be expressed with DQL and cannot with other query languages based on non-monotonic logics such as DATALOGstable Another result in this paper concerns the combined complexity of DQL, i.e., when it is assumed that the query is part of the input; for this problem, NEXPTIMENP-completeness is shown.

Since Konolige's translation of default logic into strongly grounded autoepistemic logic, several other variants of Moore's original autoepistemic logic that embody default logic have been studied. All these logics differ significantly from Moore's autoepistemic logic (standard AEL) in that expansions are subject to additional groundedness-conditions. Hence, the question naturally arises whether default logic can be translated into standard AEL at all. We show that a modular translation is not possible. However, we are able to construct a faithful polynomial-time translation from default logic into standard AEL, which is nonmodular. Our translation exploits the self-referentiality of AEL. It uses as an important intermediate step an embedding of Marek's and Truszczyn´ski's nonmonotonic logic N into standard AEL. It follows from our results that the expressive power of standard AEL is strictly greater than that of default logic.

If we reason about propositions in AI systems which are based on classic logic, we use only two possible logic values, i.e., true and false. However, in the case of reasoning about the real (physical) world such a two-valued evaluation is inadequate, because of the aspect of uncertainty

This paper presents an adaptive logic enhancement of conditional logics of normality that allows for defeasible applications of Modus Ponens to conditionals. In addition to the possibilities these logics already offer in terms of reasoning about conditionals, this way they are enriched by the ability to perform default inferencing. The idea is to apply Modus Ponens defeasibly to a conditional and a fact on the condition that it is ‘safe' to do so concerning the factual and conditional knowledge at hand. It is for instance not safe if the given information describes exceptional circumstances: although birds usually fly, penguins are exceptional to this rule. The two adaptive standard strategies are shown to correspond to different intuitions, a skeptical and a credulous reasoning type, which manifest themselves in the handling of so-called floating conclusions.

Within agent-based Ambient Intelligence applications agents react to humans based on information obtained by sensoring and their knowledge about human functioning. Appropriate types of reactions depend on the extent to which an agent understands the human and is able to interpret the available information (which is often incomplete, and hence multi-interpretable) in order to create a more complete internal image of the environment, including humans. Such an understanding requires that the agent has knowledge to a certain depth about the human's physiological and mental processes in the form of an explicitly represented model of the causal and dynamic relations describing these processes. In addition, given such a model representation, the agent needs reasoning methods to derive conclusions from the model and interpret the (partial) information available by sensoring. This paper presents the development of a toolbox that can be used by a modeller to design Ambient Intelligence applications. This toolbox contains a number of model-based reasoning methods and approaches to control such reasoning methods. Formal specifications in an executable temporal format are offered, which allows for simulation of reasoning processes and automated verification of the resulting reasoning traces in a dedicated software environment. A number of such simulation experiments and their formal analysis are described. The main contribution of this paper is that the reasoning methods in the toolbox have the possibility to reason using both quantitative and qualitative aspects in combination with a temporal dimension, and the possibility to perform focused reasoning based upon certain heuristic information. © 2011 Elsevier B.V. All rights reserved.

In this article, I present a dynamic logic game for defeasible reasoning. I argue that, as far as defeasible reasoning is concerned, one should distinguish between practical and ideal rationality. Starting from the adaptive logic framework, I formalize both rationality notions by means of logic games. The presented adaptive logic games are based on (i) standard logic games on the one hand and (ii) dynamic proof procedures for adaptive logic on the other hand. The games are similar to standard logic games, but have the extra property that some moves are revisable. This is handled by means of a main control game, which starts different standard logic games. I argue that the adaptive logic games form intuitive reasoning models for rationality in defeasible reasoning contexts. Moreover, I will also demonstrate that the games give a good insight in the computational complexity of defeasible reasoning forms.

In this article we make sdrt’s glue logic for computing logical form dynamic. This allows us to model a dialogue agent’s understanding of what the update of the semantic representation of the dialogue would be after his next contribution, including the effects of the rhetorical moves that he is contemplating performing next. This is a pre-requisite for developing a model of how agents reason about what to say next. We make the glue logic dynamic by using a dynamic public announcement logic (pal). We extend pal with a particular variety of default reasoning suited to reasoning about discourse—this default reasoning being an essential component of inferring the pragmatic effects of one’s dialogue moves. We add to the pal language a new type of announcement, known as ceteris paribus announcement, and this is used to model how an agent anticipates the (default) pragmatic effects of his next dialogue move. Our extended pal validates certain intuitive patterns of default inference that existing pals for practical reasoning do not. We prove that the dynamic glue logic has a pspace validity problem, and as such is no more complex than pal with multiple \({\square}\) operators.

In this paper we explore the use of dynamic epistemic default logic to offer a natural way of communication policies for the management of inter-agent exchanges in the multi-agent systems. We firstly focus on the acquisition of the extension in the dynamic epistemic theory based multi-agent system when its background set absorbing new information constantly, then we add the constrained default sets to restrict the agent's inference behavior and manage to obtain the extension of constrained epistemic default logic theory via default reasoning. We also discuss the characteristic of the dynamic updating when agent meets incompatible knowledge in the logical framework of multi-agent systems and finally we proved the related theorem for knowledge updating.

PurposeThe importance of fuzzy logic (FL) in approximate reasoning, and that of default logic (DL) in reasoning with incomplete information, is well established. Also, the need for a commonsense reasoning framework that handles both these aspects has been widely anticipated. The purpose of this paper is to show that fuzzyfied default logic (FDL) is an attempt at creating such a framework.Design/methodology/approachThe basic syntax, semantics, unique characteristics and examples of its complex reasoning abilities have been presented in this paper.FindingsInterestingly, FDL turns out to be a generalization of traditional DL, with even better support for non‐monotonic reasoning.Originality/valueThe paper presents a generalized tool for commonsense reasoning which can be used for inference under incomplete information.

Default reasoning can provide a means of deriving plausible semantic conclusion under imprecise and contradictory information in forensic visual surveillance. In such reasoning under uncertainty, proper uncertainty handling formalism is required. A discrete species of Bilattice for multivalued default logic demonstrated default reasoning in visual surveillance. In this article, the authors present an approach to default reasoning using subjective logic that acts in a continuous space. As an uncertainty representation and handling formalism, subjective logic bridges Dempster Shafer belief theory and second order Bayesian, thereby making it attractive tool for artificial reasoning. For the verification of the proposed approach, the authors extend the inference scheme on the bilattice for multivalued default logic to L-fuzzy set based logics that can be modeled with continuous species of bilattice structures. The authors present some illustrative case studies in visual surveillance scenarios to contrast the proposed approach with L-fuzzy set based approaches.

One way to allocate tasks to agents is by ascribing them obligations. From obligations to be, agents are able to infer what are the forbidden, permitted and obligatory actions they may perform, by using the well-known Meyer’s reduction from obligations to be to obligations to do. However, we show through an example that this method is not completely adequate to guide agents’ decisions. We then propose a solution using, instead of obligations, the concept of ‘responsibility’. To formalise responsibility we use a multiagent extension of propositional dynamic logic as framework, and then we define some basic concepts, such as ‘agent ability’, also briefly discussing the problem of uniform strategies and a possible solution. In the last part, we show that our framework can be used in the specification of normative multiagent systems, by presenting an extensive running example.

In this paper we address dynamic assumption-based reasoning in open agent systems, where, unavoidably, agents have incomplete knowledge about their environment and about other agents. The interactions among agents in such systems are typically subject to norms, which stipulate what each agent is obliged, permitted, prohibited, empowered etc. to do, while it participates in the system. In such environments agents need to resort to assumptions, in order to establish what actions are appropriate to perform, and they need to do so dynamically, since the environment, the agents that exist in it, the information that is exchanged between them, and the normative relations between them change over time. In earlier work, we had proposed Default Theory construction to support dynamic assumption-based reasoning. We argued that in this way, agents could perform both assumption identification and employment dynamically, contrary to other approaches to assumption-based reasoning, which catered for either one or the other. A shortcoming of this early proposal of ours, though, is that Default Theory construction seems to require proof, which is notably computationally expensive. In this paper we present a computational technique that can be used for this construction in an incremental manner that does not depend on proof, and a prototype tool that we developed for experimentation. In a nutshell, depending on their current knowledge at any given time, agents can identify appropriate candidate assumptions in an ad hoc manner. When such choices need to be revised, agents can reconstruct their view of the possible world in which they find themselves, and establish their revised assumption requirements at run-time. This paper is an extended version of the work presented at the 2008 IEEE/WI/ACM Int. Conf. on Intelligent Agent Technology, 9-12 December, Sydney, Australia.

In this paper, we propose a new nonmonotonic logic called general default logic. On the one hand, it generalizes Reiter's default logic by adding to it rule-like operators used in logic programming. On the other hand, it extends logic programming by allowing arbitrary propositional formulas. We show that with this new logic, one can formalize naturally rule constraints, generalized closed world assumptions, and conditional defaults. We show that under a notion of strong equivalence, sentences of this new logic can be converted to a normal form. We also investigate the computational complexity of various reasoning tasks in the logic, and relate it to some other nonmonotonic formalisms such as Lin and Shoham's logic of GK and Moore's autoepistemic logic.

Handling exceptions represents one of the most important problems in Artificial Intelligence. Several approaches have been proposed for reasoning on default theories. This paper focuses on a possibilistic approach, and more precisely on the MSP-entailment (where MSP stands for Minimum Specificity Principle) from default theories which is equivalent to System P augmented by rational monotony. In order to make this entailment tractable from a computational point of view, we propose here a compilation of default theories with respect to a target compilation language. This allows us to provide polynomial algorithms to derive efficiently the MSP-conclusions of a compiled default theory. Moreover, the proposed compilation is qualified to be flexible since it efficiently takes advantage of any classical compiler and generally provides a low recompilation cost when updating a compiled default theory.

Inductive Logic Programming (ILP) is concerned with the task of generalising sets of positive and negative examples with respect to background knowledge expressed as logic programs. Negation as Failure (NAF) is a key feature of logic programming which provides a means for nonmonotonic commonsense reasoning under incomplete information. But, so far, most ILP research has been aimed at Horn programs which exclude NAF, and has failed to exploit the full potential of normal programs that allow NAF. By contrast, Abductive Logic Programming (ALP), a related task concerned with explaining observations with respect to a prior theory, has been well studied and applied in the context of normal logic programs. This paper shows how ALP can be used to provide a semantics and proof procedure for nonmonotonic ILP that utilises practical methods of language and search bias to reduce the search space. This is done by lifting an existing method called Hybrid Abductive Inductive Learning (HAIL) from Horn clauses to normal logic programs. To demonstrate its potential benefits, the resulting system, called XHAIL, is applied to a process modelling case study involving a nonmonotonic temporal Event Calculus (EC).

Fixpoint semantics are provided for ambiguity blocking and propagating variants of Nute’s defeasible logic. The semantics are based upon the well-founded semantics for logic programs. It is shown that the logics are sound with respect to their counterpart semantics and complete for locally finite theories. Unlike some other nonmonotonic reasoning formalisms such as Reiter’s default logic, the two defeasible logics are directly skeptical and so reject floating conclusions. For defeasible theories with transitive priorities on defeasible rules, the logics are shown to satisfy versions of Cut and Cautious Monotony. For theories with either conflict sets closed under strict rules or strict rules closed under transposition, a form of Consistency Preservation is shown to hold. The differences between the two logics and other variants of defeasible logic—specifically those presented by Billington, Antoniou, Governatori, and Maher—are discussed.

Most solutions to the sorites reject its major premise, i.e. the quantified conditional\({\forall{i}(P(ai) \rightarrow {P(ai+))}}\) . This rejection appears to imply a discrimination between two elements that are supposed to be indiscriminable. Thus, the puzzle of the sorites involves in a fundamental way the notion of indiscriminability. This paper analyzes this relation and formalizes it, in a way that makes the rejection of the major premise more palatable.

Default logics are usually used to describe the regular behavior and normal properties of domain elements. In this paper we suggest, conversely, that the framework of default logics can be exploited for detecting outliers. Outliers are observations expressed by sets of literals that feature unexpected semantical characteristics. These sets of literals are selected among those explicitly embodied in the given knowledge base. Hence, essentially we perceive outlier detection as a knowledge discovery technique. This paper defines the notion of outlier in two related formalisms for specifying defaults: Reiter's default logic and extended disjunctive logic programs. For each of the two formalisms, we show that finding outliers is quite complex. Indeed, we prove that several versions of the outlier detection problem lie over the second level of the polynomial hierarchy. We believe that a thorough complexity analysis, as done here, is a useful preliminary step towards developing effective heuristics and exploring tractable subsets of outlier detection problems.

We propose a combination of logic programming under the answer set semantics with the description logics SHIF (D) and SHOIN (D), which underly the Web ontology languages OWL Lite and OWL DL, respectively. To this end, we introduce description logic programs (or dl-programs), which consist of a description logic knowledge base L and a finite set P of description logic rules (or dl-rules). Such rules are similar to usual rules in nonmonotonic logic programs, but they may also contain queries to L, possibly under default negation, in their bodies. They allow for building rules on top of ontologies but also, to a limited extent, building ontologies on top of rules. We define a suite of semantics for various classes of dl-programs, which conservatively extend the standard semantics of the respective classes and coincide with it in absence of a description logic knowledge base. More concretely, we generalize positive, stratified, and arbitrary normal logic programs to dl-programs, and define a Herbrand model semantics for them. We show that they have similar properties as ordinary logic programs, and also provide fixpoint characterizations in terms of (iterated) consequence operators. For arbitrary dl-programs, we define answer sets by generalizing Gelfond and Lifschitz's notion of a transform, leading to a strong and a weak answer set semantics, which are based on reductions to the semantics of positive dl-programs and ordinary positive logic programs, respectively. We also show how the weak answer sets can be computed utilizing answer sets of ordinary normal logic programs. Furthermore, we show how some advanced reasoning tasks for the Semantic Web, including different forms of closed-world reasoning and default reasoning, as well as DL-safe rules, can be realized on top of dl-programs. Finally, we give a precise picture of the computational complexity of dl-programs, and we describe efficient algorithms and a prototype implementation of dl-programs which is available on the Web. © 2008 Elsevier B.V. All rights reserved.

We study a generalization of default logic obtained by extending its logical, monotonic basis to disjunctive (multiple-conclusion) rules. Special attention will be paid to the representation opportunities created by such rules, in particular to the use of default justifications in the heads of the rules. On the other hand, it will be shown that even the generalized default logic can be simplified to a formal system that involves only monotonic inference rules and unconditional (`supernormal') default assumptions.

We motivate and formalize the idea of sameness by default: two objects are considered the same if they cannot be proved to be different. This idea turns out to be useful for a number of widely different applications, including natural language processing, reasoning with incomplete information, and even philosophical paradoxes. We consider two formalizations of this notion, both of which are based on Reiter's Default Logic. The first formalization is a new relation of indistinguishability that is introduced by default. We prove that the corresponding default theory has a unique extension, in which every two objects are indistinguishable if and only if their non-equality cannot be proved from the known facts. We show that the indistinguishability relation has some desirable properties: it is reflexive, symmetric, and, while not transitive, it has a transitive "flavor." The second formalization is an extension (modification) of the ordinary language equality by a similar default: two objects are equal if and only if their non-equality cannot be proved from the known facts. It appears to be less elegant from a formal point of view. In particular, it gives rise to multiple extensions. However, this extended equality is better suited for most of the applications discussed in this paper.

This paper focuses on the role that social norms play in the selection of equilibrium points seen as social conventions under unforeseen contingencies — that is, their role in the emergence of regularities of behavior which are self-enforcing and effectively adhered to by bounded rational agents due to their self-policing incentives. Differently stated, given a set of game situations imperfectly described, we want to understand how general and abstract norms provide at least the starting point for a norm-based equilibrium selection reasoning procedure which in the end will be able to determine which equilibrium point, belonging to perfectly described games, will be played as the unique solution of each imperfectly described game. In order to solve such a problem we introduce a selection process based on the reformulation of default logic in terms of possibility theory.

Formal nonmonotonic systems try to model the phenomenon that common sense reasoners are able to “jump” in their reasoning from assumptions ∆ to conclusions C without their being any deductive chain from ∆ to C. Such jumps are done by various mechanisms which are strongly dependent on context and knowledge of how the actual world functions. Our aim is to motivate these jump rules as inference rules designed to optimise survival in an environment with scant resources of effort and time. We begin with a general discussion and quickly move to Section 3 where we introduce five resource principles. We show that these principles lead to some well known nonmonotonic systems such as Nute’s defeasible logic. We also give several examples of practical reasoning situations to illustrate our principles.

The sentences of deontic logic may be understood as describing what an agent ought to do when faced with a given set of norms. If these norms come into conflict, the best the agent can be expected to do is to follow a maximal subset of the norms. Intuitively, a priority ordering of the norms can be helpful in determining the relevant sets and resolve conflicts, but a formal resolution mechanism has been difficult to provide. In particular, reasoning about prioritized conditional imperatives is overshadowed by problems such as the `order puzzle' that are not satisfactorily resolved by existing approaches. The paper provides a new proposal as to how these problems may be overcome.

A consistency default is a propositional inference rule that asserts the consistency of a formula in its consequence. Consistency defaults allow for a straightforward encoding of domains in which it is explicitely known when something is possible. The logic of consistency defaults can be seen as a variant of cumulative default logic or as a generalization of justified default logic; it is also able to simulate Reiter default logic in the seminormal case. A semantical characterization of consistency defaults in terms of processes and in terms of a fixpoint equation is given, as well as a normal form.

International audience; The paper investigates the relation between inconsistencytolerant semantics (AR-semantics and Brave-semantics) and a class of default theories in Reiter’s Default Logic called semi-monotonic default theories. We show that any inconsistent knowledge base can be interpreted as a normal closed default theory by means of a polynomial mapping that maps every fact to a default. As result we prove a relation between inference in Reiter’s Default Logic (sceptical and credulous entailment) and inconsistency-tolerant semantics (AR and Brave entailment). In addition, by means of such relation we prove certain properties that will serve as a basis for an anytime algorithm that provides an approximate solution to AR-entailment whenever interrupted.

© 2015 Cambridge University Press. Recent advances in knowledge compilation introduced techniques to compile positive logic programs into propositional logic, essentially exploiting the constructive nature of the least fixpoint computation. This approach has several advantages over existing approaches: it maintains logical equivalence, does not require (expensive) loop-breaking preprocessing or the introduction of auxiliary variables, and significantly outperforms existing algorithms. Unfortunately, this technique is limited to negation-free programs. In this paper, we show how to extend it to general logic programs under the well-founded semantics. We develop our work in approximation fixpoint theory, an algebraical framework that unifies semantics of different logics. As such, our algebraical results are also applicable to autoepistemic logic, default logic and abstract dialectical frameworks. ispartof: pages:464-480 ispartof: Theory and Practice of Logic Programming vol:15 issue:4 pages:464-480 ispartof: location:Cork, Ireland status: published

In various domains of logic, researchers have made use of a similar intuition: that facts (or models) can be derived from the ground up. They typically phrase this intuition by saying, e.g., that the facts should be grounded, or that they should not be unfounded, or that they should be supported by cycle-free arguments, et cetera. In this paper, we formalise this intuition in the context of algebraical fixpoint theory. We define when a lattice element x ∈ L is grounded for lattice operator O : L → L. On the algebraical level, we investigate the relationship between grounded fixpoints and the various classes of fixpoints of approximation fixpoint theory, including supported, minimal, Kripke-Kleene, stable and well-founded fixpoints. On the logical level, we investigate groundedness in the context of logic programming, autoepistemic logic, default logic and argumentation frameworks. We explain what grounded points and fixpoints mean in these logics and show that this concept indeed formalises intuitions that existed in these fields. We investigate which existing semantics are grounded. We study the novel semantics for these logics that is induced by grounded fixpoints, which has some very appealing properties, not in the least its mathematical simplicity and generality. Our results unveil a remarkable uniformity in intuitions and mathematics in these fields. publisher: Elsevier articletitle: Grounded fixpoints and their applications in knowledge representation journaltitle: Artificial Intelligence articlelink: http://dx.doi.org/10.1016/j.artint.2015.03.006 content_type: article copyright: Copyright © 2015 Elsevier B.V. All rights reserved. ispartof: Artificial Intelligence vol:224 pages:51-71 status: published

Gerhard Brewka has made a remarkable impact on artificial intelligence, especially in the area of knowledge representation, through his ideas, collaborations and mentoring, always amazing those close to him with his ability to inspire. This short paper offers a glimpse into four areas of research where Gerd's imprint has been particularly distinct, intertwined with personal recollections of the authors, and with comments on those of Gerd's personal characteristics that make his research perspectives so appealing to others.

Commonsense reasoning requires default reasoning. As one engage in commonsense reasoning, one makes certain assumptions so that he can proceed. This chapter discusses default reasoning in general, temporal default reasoning, and then temporal default reasoning. Further, it also describes a general method for default reasoning about time based on the circumscription of abnormality predicates and how this method can be used to address the qualification problem. Then, explains the representation of default events and properties. The event calculus assumes by default that unexpected events do not occur and events have no unexpected effects. In addition, default reasoning can be used to address the qualification problem. Default reasoning provides a more elaboration-tolerant way of specifying qualifications that prevent events from having their intended effects.