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

Multiple Revision on Horn Belief Bases

In logic programming, Horn clauses play a basic role, and in many logical constructs their consideration is important. In this paper we study the multiple revision of a belief base where the underlying logic is composed by Horn clauses. The main di culties as to restricting to the Horn fragment for revision operators by a single sentence are analyzed, and general results are presented about multiple revision operators on belief bases. We de ne prioritized multiple revision operators under a more restricted logic than classical propositional logic, i.e. Horn logic. We propose a set of postulates and representation theorems for each operation. This work is relevant for multiple revision in areas that employ Horn clauses, such as logic programming and deductive databases applications.XVII Workshop Agentes y Sistemas Inteligentes (WASI).Red de Universidades con Carreras en Informática (RedUNCI

Multiple Revision on Horn Belief Bases

In logic programming, Horn clauses play a basic role, and in many logical constructs their consideration is important. In this paper we study the multiple revision of a belief base where the underlying logic is composed by Horn clauses. The main di culties as to restricting to the Horn fragment for revision operators by a single sentence are analyzed, and general results are presented about multiple revision operators on belief bases. We de ne prioritized multiple revision operators under a more restricted logic than classical propositional logic, i.e. Horn logic. We propose a set of postulates and representation theorems for each operation. This work is relevant for multiple revision in areas that employ Horn clauses, such as logic programming and deductive databases applications.XVII Workshop Agentes y Sistemas Inteligentes (WASI).Red de Universidades con Carreras en Informática (RedUNCI

Redundancy in Logic I: CNF Propositional Formulae

A knowledge base is redundant if it contains parts that can be inferred from the rest of it. We study the problem of checking whether a CNF formula (a set of clauses) is redundant, that is, it contains clauses that can be derived from the other ones. Any CNF formula can be made irredundant by deleting some of its clauses: what results is an irredundant equivalent subset (I.E.S.) We study the complexity of some related problems: verification, checking existence of a I.E.S. with a given size, checking necessary and possible presence of clauses in I.E.S.'s, and uniqueness. We also consider the problem of redundancy with different definitions of equivalence.Comment: Extended and revised version of a paper that has been presented at ECAI 200

Multiple Revision on Horn Belief Bases

In logic programming, Horn clauses play a basic role, and in many logical constructs their consideration is important. In this paper we study the multiple revision of a belief base where the underlying logic is composed by Horn clauses. The main di culties as to restricting to the Horn fragment for revision operators by a single sentence are analyzed, and general results are presented about multiple revision operators on belief bases. We de ne prioritized multiple revision operators under a more restricted logic than classical propositional logic, i.e. Horn logic. We propose a set of postulates and representation theorems for each operation. This work is relevant for multiple revision in areas that employ Horn clauses, such as logic programming and deductive databases applications.XVII Workshop Agentes y Sistemas Inteligentes (WASI).Red de Universidades con Carreras en Informática (RedUNCI

Knowledge compilation for online decision-making : application to the control of autonomous systems = Compilation de connaissances pour la décision en ligne : application à la conduite de systèmes autonomes

La conduite de systèmes autonomes nécessite de prendre des décisions en fonction des observations et des objectifs courants : cela implique des tâches à effectuer en ligne, avec les moyens de calcul embarqués. Cependant, il s'agit généralement de tâches combinatoires, gourmandes en temps de calcul et en espace mémoire. Réaliser ces tâches intégralement en ligne dégrade la réactivité du système ; les réaliser intégralement hors ligne, en anticipant toutes les situations possibles, nuit à son embarquabilité. Les techniques de compilation de connaissances sont susceptibles d'apporter un compromis, en déportant au maximum l'effort de calcul avant la mise en situation du système. Ces techniques consistent à traduire un problème dans un certain langage, fournissant une forme compilée de ce problème, dont la résolution est facile et la taille aussi compacte que possible. La traduction peut être très longue, mais n'est effectuée qu'une seule fois, hors ligne. Il existe de nombreux langages-cible de compilation, notamment le langage des diagrammes de décision binaires (BDDs), qui ont été utilisés avec succès dans divers domaines (model-checking, configuration, planification). L'objectif de la thèse était d'étudier l'application de la compilation de connaissances à la conduite de systèmes autonomes. Nous nous sommes intéressés à des problèmes réels de planification, qui impliquent souvent des variables continues ou à grand domaine énuméré (temps ou mémoire par exemple). Nous avons orienté notre travail vers la recherche et l'étude de langages-cible de compilation assez expressifs pour permettre de représenter de tels problèmes.Controlling autonomous systems requires to make decisions depending on current observations and objectives. This involves some tasks that must be executed online-with the embedded computational power only. However, these tasks are generally combinatory; their computation is long and requires a lot of memory space. Entirely executing them online thus compromises the system's reactivity. But entirely executing them offline, by anticipating every possible situation, can lead to a result too large to be embedded. A tradeoff can be provided by knowledge compilation techniques, which shift as much as possible of the computational effort before the system's launching. These techniques consists in a translation of a problem into some language, obtaining a compiled form of the problem, which is both easy to solve and as compact as possible. The translation step can be very long, but it is only executed once, and offline. There are numerous target compilation languages, among which the language of binary decision diagrams (BDDs), which have been successfully used in various domains of artificial intelligence, such as model-checking, configuration, or planning. The objective of the thesis was to study how knowledge compilation could be applied to the control of autonomous systems. We focused on realistic planning problems, which often involve variables with continuous domains or large enumerated domains (such as time or memory space). We oriented our work towards the search for target compilation languages expressive enough to represent such problems

COLAB : a hybrid knowledge representation and compilation laboratory

Knowledge bases for real-world domains such as mechanical engineering require expressive and efficient representation and processing tools. We pursue a declarative-compilative approach to knowledge engineering. While Horn logic (as implemented in PROLOG) is well-suited for representing relational clauses, other kinds of declarative knowledge call for hybrid extensions: functional dependencies and higher-order knowledge should be modeled directly. Forward (bottom-up) reasoning should be integrated with backward (top-down) reasoning. Constraint propagation should be used wherever possible instead of search-intensive resolution. Taxonomic knowledge should be classified into an intuitive subsumption hierarchy. Our LISP-based tools provide direct translators of these declarative representations into abstract machines such as an extended Warren Abstract Machine (WAM) and specialized inference engines that are interfaced to each other. More importantly, we provide source-to-source transformers between various knowledge types, both for user convenience and machine efficiency. These formalisms with their translators and transformers have been developed as part of COLAB, a compilation laboratory for studying what we call, respectively, "vertical\u27; and "horizontal\u27; compilation of knowledge, as well as for exploring the synergetic collaboration of the knowledge representation formalisms. A case study in the realm of mechanical engineering has been an important driving force behind the development of COLAB. It will be used as the source of examples throughout the paper when discussing the enhanced formalisms, the hybrid representation architecture, and the compilers

The ghosts of forgotten things: A study on size after forgetting

Forgetting is removing variables from a logical formula while preserving the constraints on the other variables. In spite of being a form of reduction, it does not always decrease the size of the formula and may sometimes increase it. This article discusses the implications of such an increase and analyzes the computational properties of the phenomenon. Given a propositional Horn formula, a set of variables and a maximum allowed size, deciding whether forgetting the variables from the formula can be expressed in that size is $D^p$-hard in $\Sigma^p_2$. The same problem for unrestricted propositional formulae is $D^p_2$-hard in $\Sigma^p_3$. The hardness results employ superredundancy: a superirredundant clause is in all formulae of minimal size equivalent to a given one. This concept may be useful outside forgetting

TOPIC SENSITIVE BELIEF REVISION

When asked to change one's beliefs in the face of new information, or to revise a book given errata, we commonly strive to keep our changes relevant, that is, we try to restrict the beliefs (or chapters) we change to those that bear some content relation to the new information. One kind of relevance, topicality, is interesting for two reasons: First, topicality tends to be strongly encapsulating, e.g., we shouldn't make any off-topic changes. Second, topicality tends to be weaker than strict relevance. Consider a panel of three papers on the topic of Kant's life and works. It would be entirely possible for each of the papers to have no bearing on the truth of any sentence in any of the other papers, and yet for all of the papers to be on topic. In this dissertation, I explore theories of logical topicality and their effect on formal theories of belief revision. Formal theories of belief revision (in the Alchourrón, Gärdenfors, and Makinson (AGM) tradition) model the object of change (my beliefs, a book) as a collection of formulae in a supra-classical logic and provide a set of postulates which express constraints on the sorts of change that are, in principle, formally rational. In 1999, Rohit Parikh proposed that signature disjointness captured a reasonable notion of topicality but that taking topicality into account required changes in the standard AGM postulates (and thus, the notion of rational change). He, and subsequent theorists, abandoned this notion of topicality in order to deal with the revision of inconsistent objects of change. In this thesis, I show 1) that a disjoint signature account of topicality does not require changes to the AGM rationality postulates and 2) a disjoint signature account of topicality can apply to inconsistent objects of change. Additionally, I argue that signature disjointness has a strong claim to being at least a sufficient condition of logical topicality