Complexity of Nested Circumscription and Nested Abnormality Theories

The need for a circumscriptive formalism that allows for simple yet elegant modular problem representation has led Lifschitz (AIJ, 1995) to introduce nested abnormality theories (NATs) as a tool for modular knowledge representation, tailored for applying circumscription to minimize exceptional circumstances. Abstracting from this particular objective, we propose L_{CIRC}, which is an extension of generic propositional circumscription by allowing propositional combinations and nesting of circumscriptive theories. As shown, NATs are naturally embedded into this language, and are in fact of equal expressive capability. We then analyze the complexity of L_{CIRC} and NATs, and in particular the effect of nesting. The latter is found to be a source of complexity, which climbs the Polynomial Hierarchy as the nesting depth increases and reaches PSPACE-completeness in the general case. We also identify meaningful syntactic fragments of NATs which have lower complexity. In particular, we show that the generalization of Horn circumscription in the NAT framework remains CONP-complete, and that Horn NATs without fixed letters can be efficiently transformed into an equivalent Horn CNF, which implies polynomial solvability of principal reasoning tasks. Finally, we also study extensions of NATs and briefly address the complexity in the first-order case. Our results give insight into the ``cost'' of using L_{CIRC} (resp. NATs) as a host language for expressing other formalisms such as action theories, narratives, or spatial theories.Comment: A preliminary abstract of this paper appeared in Proc. Seventeenth International Joint Conference on Artificial Intelligence (IJCAI-01), pages 169--174. Morgan Kaufmann, 200

Postdictive Reasoning in Epistemic Action Theory

If an agent executes an action, this will not only change the world physically, but also the agent's knowledge about the world. Therefore the occurrence of an action can be modeled as an epistemic state transition which maps the knowledge state of an agent to a successor knowledge state. For example, consider that an agent in a state s_0 executes an action a. This causes a transition to a state s_1. Subsequently, the agent executes a sensing action a_s, which produces knowledge and causes a transition to a state s_2. With the information which is gained by the sensation, the agent can not only extend its knowledge about s_2, but also infer additional knowledge about the initial state s_0. That is, the agent uses knowledge about the present to retrospectively acquire additional information about the past. We refer to this temporal form of epistemic inference as postdiction. Existing action theories are not capable of efficiently performing postdictive reasoning because they require an exponential number of state variables to represent an agent's knowledge state. The contribution of this thesis is an approximate epistemic action theory which is capable of postdictive reasoning while it requires only a linear number of state variables to represent an agent's knowledge state. In addition, the theory is able to perform a more general temporal form of postdiction, which most existing approaches do not support. We call the theory the h-approximation (HPX) because it explicitly represents historical knowledge about past world states. In addition to the operational semantics of HPX, we present its formalization in terms of Answer Set Programming (ASP) and provide respective soundness results. The ASP implementation allows us to apply HPX in real robotic applications by using off-the-shelf ASP solvers. Specifically, we integrate of HPX in an online planning framework for Cognitive Robotics where planning, plan execution and abductive explanation tasks are interleaved. As a proof-of-concept, we provide a case-study which demonstrates the application of HPX for high-level robot control in a Smart Home. The case-study emphasizes the usefulness of postdiction for abnormality detection in robotics: actions which are performed by robots are often not successful due to unforeseen practical problems. A solution is to verify action success by observing the effects of the action. If the desired effects do not hold after action execution, then one can postdict the existence of an abnormality

Using Extended Logic Programs to Formalize Commonsense Reasoning

In this dissertation, we investigate how commonsense reasoning can be formalized by using extended logic programs. In this investigation, we first use extended logic programs to formalize inheritance hierarchies with exceptions by adopting McCarthy's simple abnormality formalism to express uncertain knowledge. In our representation, not only credulous reasoning can be performed but also the ambiguity-blocking inheritance and the ambiguity-propagating inheritance in skeptical reasoning are simulated. In response to the anomalous extension problem, we explore and discover that the intuition underlying commonsense reasoning is a kind of forward reasoning. The unidirectional nature of this reasoning is applied by many reformulations of the Yale shooting problem to exclude the undesired conclusion. We then identify defeasible conclusions in our representation based on the syntax of extended logic programs. A similar idea is also applied to other formalizations of commonsense reasoning to achieve such a purpose

The Role of preferences in logic programming: nonmonotonic reasoning, user preferences, decision under uncertainty

Intelligent systems that assist users in fulfilling complex tasks need a concise and processable representation of incomplete and uncertain information. In order to be able to choose among different options, these systems also need a compact and processable representation of the concept of preference. Preferences can provide an effective way to choose the best solutions to a given problem. These solutions can represent the most plausible states of the world when we model incomplete information, the most satisfactory states of the world when we express user preferences, or optimal decisions when we make decisions under uncertainty. Several domains, such as, reasoning under incomplete and uncertain information, user preference modeling, and qualitative decision making under uncertainty, have benefited from advances on preference representation. In the literature, several symbolic approaches of nonclassical reasoning have been proposed. Among them, logic programming under answer set semantics offers a good compromise between symbolic representation and computation of knowledge and several extensions for handling preferences. Nevertheless, there are still some open issues to be considered in logic programming. In nonmonotonic reasoning, first, most approaches assume that exceptions to logic program rules are already specified. However, sometimes, it is possible to consider implicit preferences based on the specificity of the rules to handle incomplete information. Secondly, the joint handling of exceptions and uncertainty has received little attention: when information is uncertain, the selection of default rules can be a matter of explicit preferences and uncertainty. In user preference modeling, although existing logic programming specifications allow to express user preferences which depend both on incomplete and contextual information, in some applications, some preferences in some context may be more important than others. Furthermore, more complex preference expressions need to be supported. In qualitative decision making under uncertainty, existing logic programming-based methodologies for making decisions seem to lack a satisfactory handling of preferences and uncertainty. The aim of this dissertation is twofold: 1) to tackle the role played by preferences in logic programming from different perspectives, and 2) to contribute to this novel field by proposing several frameworks and methods able to address the above issues. To this end, we will first show how preferences can be used to select default rules in logic programs in an implicit and explicit way. In particular, we propose (i) a method for selecting logic program rules based on specificity, and (ii) a framework for selecting uncertain default rules based on explicit preferences and the certainty of the rules. Then, we will see how user preferences can be modeled and processed in terms of a logic program (iii) in order to manage user profiles in a context-aware system and (iv) in order to propose a framework for the specification of nested (non-flat) preference expressions. Finally, in the attempt to bridge the gap between logic programming and qualitative decision under uncertainty, (v) we propose a classical- and a possibilistic-based logic programming methodology to compute an optimal decision when uncertainty and preferences are matters of degrees.Els sistemes intel.ligents que assisteixen a usuaris en la realització de tasques complexes necessiten una representació concisa i formal de la informació que permeti un raonament nomonòton en condicions d’incertesa. Per a poder escollir entre les diferents opcions, aquests sistemes solen necessitar una representació del concepte de preferència. Les preferències poden proporcionar una manera efectiva de triar entre les millors solucions a un problema. Aquestes solucions poden representar els estats del món més plausibles quan es tracta de modelar informació incompleta, els estats del món més satisfactori quan expressem preferències de l’usuari, o decisions òptimes quan estem parlant de presa de decisió incorporant incertesa. L’ús de les preferències ha beneficiat diferents dominis, com, el raonament en presència d’informació incompleta i incerta, el modelat de preferències d’usuari, i la presa de decisió sota incertesa. En la literatura, s’hi troben diferents aproximacions al raonament no clàssic basades en una representació simbòlica de la informació. Entre elles, l’enfocament de programació lògica, utilitzant la semàntica de answer set, ofereix una bona aproximació entre representació i processament simbòlic del coneixement, i diferents extensions per gestionar les preferències. No obstant això, en programació lògica es poden identificar diferents problemes pel que fa a la gestió de les preferències. Per exemple, en la majoria d’enfocaments de raonament no-monòton s’assumeix que les excepcions a default rules d’un programa lògic ja estan expressades. Però de vegades es poden considerar preferències implícites basades en l’especificitat de les regles per gestionar la informació incompleta. A més, quan la informació és també incerta, la selecció de default rules pot dependre de preferències explícites i de la incertesa. En el modelatge de preferències del usuari, encara que els formalismes existents basats en programació lògica permetin expressar preferències que depenen d’informació contextual i incompleta, en algunes aplicacions, donat un context, algunes preferències poden ser més importants que unes altres. Per tant, resulta d’interès un llenguatge que permeti capturar preferències més complexes. En la presa de decisions sota incertesa, les metodologies basades en programació lògica creades fins ara no ofereixen una solució del tot satisfactòria pel que fa a la gestió de les preferències i la incertesa. L’objectiu d’aquesta tesi és doble: 1) estudiar el paper de les preferències en la programació lògica des de diferents perspectives, i 2) contribuir a aquesta jove àrea d’investigació proposant diferents marcs teòrics i mètodes per abordar els problemes anteriorment citats. Per a aquest propòsit veurem com les preferències es poden utilitzar de manera implícita i explícita per a la selecció de default rules proposant: (i) un mètode basat en l’especificitat de les regles, que permeti seleccionar regles en un programa lògic; (ii) un marc teòric per a la selecció de default rules incertes basat en preferències explícites i la incertesa de les regles. També veurem com les preferències de l’usuari poden ser modelades i processades usant un enfocament de programació lògica (iii) que suporti la creació d’un mecanisme de gestió dels perfils dels usuaris en un sistema amb reconeixement del context; (iv) que permeti proposar un marc teòric capaç d’expressar preferències amb fòrmules imbricades. Per últim, amb l’objectiu de disminuir la distància entre programació lògica i la presa de decisió amb incertesa proposem (v) una metodologia basada en programació lògica clàssica i en una extensió de la programació lògica que incorpora lògica possibilística per modelar un problema de presa de decisions i per inferir una decisió òptima.Los sistemas inteligentes que asisten a usuarios en tareas complejas necesitan una representación concisa y procesable de la información que permita un razonamiento nomonótono e incierto. Para poder escoger entre las diferentes opciones, estos sistemas suelen necesitar una representación del concepto de preferencia. Las preferencias pueden proporcionar una manera efectiva para elegir entre las mejores soluciones a un problema. Dichas soluciones pueden representar los estados del mundo más plausibles cuando hablamos de representación de información incompleta, los estados del mundo más satisfactorios cuando hablamos de preferencias del usuario, o decisiones óptimas cuando estamos hablando de toma de decisión con incertidumbre. El uso de las preferencias ha beneficiado diferentes dominios, como, razonamiento en presencia de información incompleta e incierta, modelado de preferencias de usuario, y toma de decisión con incertidumbre. En la literatura, distintos enfoques simbólicos de razonamiento no clásico han sido creados. Entre ellos, la programación lógica con la semántica de answer set ofrece un buen acercamiento entre representación y procesamiento simbólico del conocimiento, y diferentes extensiones para manejar las preferencias. Sin embargo, en programación lógica se pueden identificar diferentes problemas con respecto al manejo de las preferencias. Por ejemplo, en la mayoría de enfoques de razonamiento no-monótono se asume que las excepciones a default rules de un programa lógico ya están expresadas. Pero, a veces se pueden considerar preferencias implícitas basadas en la especificidad de las reglas para manejar la información incompleta. Además, cuando la información es también incierta, la selección de default rules pueden depender de preferencias explícitas y de la incertidumbre. En el modelado de preferencias, aunque los formalismos existentes basados en programación lógica permitan expresar preferencias que dependen de información contextual e incompleta, in algunas aplicaciones, algunas preferencias en un contexto puede ser más importantes que otras. Por lo tanto, un lenguaje que permita capturar preferencias más complejas es deseable. En la toma de decisiones con incertidumbre, las metodologías basadas en programación lógica creadas hasta ahora no ofrecen una solución del todo satisfactoria al manejo de las preferencias y la incertidumbre. El objectivo de esta tesis es doble: 1) estudiar el rol de las preferencias en programación lógica desde diferentes perspectivas, y 2) contribuir a esta joven área de investigación proponiendo diferentes marcos teóricos y métodos para abordar los problemas anteriormente citados. Para este propósito veremos como las preferencias pueden ser usadas de manera implícita y explícita para la selección de default rules proponiendo: (i) un método para seleccionar reglas en un programa basado en la especificad de las reglas; (ii) un marco teórico para la selección de default rules basado en preferencias explícitas y incertidumbre. También veremos como las preferencias del usuario pueden ser modeladas y procesadas usando un enfoque de programación lógica (iii) para crear un mecanismo de manejo de los perfiles de los usuarios en un sistema con reconocimiento del contexto; (iv) para crear un marco teórico capaz de expresar preferencias con formulas anidadas. Por último, con el objetivo de disminuir la distancia entre programación lógica y la toma de decisión con incertidumbre proponemos (v) una metodología para modelar un problema de toma de decisiones y para inferir una decisión óptima usando un enfoque de programación lógica clásica y uno de programación lógica extendida con lógica posibilística.Sistemi intelligenti, destinati a fornire supporto agli utenti in processi decisionali complessi, richiedono una rappresentazione dell’informazione concisa, formale e che permetta di ragionare in maniera non monotona e incerta. Per poter scegliere tra le diverse opzioni, tali sistemi hanno bisogno di disporre di una rappresentazione del concetto di preferenza altrettanto concisa e formale. Le preferenze offrono una maniera efficace per scegliere le miglior soluzioni di un problema. Tali soluzioni possono rappresentare gli stati del mondo più credibili quando si tratta di ragionamento non monotono, gli stati del mondo più soddisfacenti quando si tratta delle preferenze degli utenti, o le decisioni migliori quando prendiamo una decisione in condizioni di incertezza. Diversi domini come ad esempio il ragionamento non monotono e incerto, la strutturazione del profilo utente, e i modelli di decisione in condizioni d’incertezza hanno tratto beneficio dalla rappresentazione delle preferenze. Nella bibliografia disponibile si possono incontrare diversi approcci simbolici al ragionamento non classico. Tra questi, la programmazione logica con answer set semantics offre un buon compromesso tra rappresentazione simbolica e processamento dell’informazione, e diversi estensioni per la gestione delle preferenze sono state proposti in tal senso. Nonostante ció, nella programmazione logica esistono ancora delle problematiche aperte. Prima di tutto, nella maggior parte degli approcci al ragionamento non monotono, si suppone che nel programma le eccezioni alle regole siano già specificate. Tuttavia, a volte per trattare l’informazione incompleta è possibile prendere in considerazione preferenze implicite basate sulla specificità delle regole. In secondo luogo, la gestione congiunta di eccezioni e incertezza ha avuto scarsa attenzione: quando l’informazione è incerta, la scelta di default rule può essere una questione di preferenze esplicite e d’incertezza allo stesso tempo. Nella creazione di preferenze dell’utente, anche se le specifiche di programmazione logica esistenti permettono di esprimere preferenze che dipendono sia da un’informazione incompleta che da una contestuale, in alcune applicazioni talune preferenze possono essere più importanti di altre, o espressioni più complesse devono essere supportate. In un processo decisionale con incertezza, le metodologie basate sulla programmazione logica viste sinora, non offrono una gestione soddisfacente delle preferenze e dell’incertezza. Lo scopo di questa dissertazione è doppio: 1) chiarire il ruolo che le preferenze giocano nella programmazione logica da diverse prospettive e 2) contribuire proponendo in questo nuovo settore di ricerca, diversi framework e metodi in grado di affrontare le citate problematiche. Per prima cosa, dimostreremo come le preferenze possono essere usate per selezionare default rule in un programma in maniera implicita ed esplicita. In particolare proporremo: (i) un metodo per la selezione delle regole di un programma logico basato sulla specificità dell’informazione; (ii) un framework per la selezione di default rule basato sulle preferenze esplicite e sull’incertezza associata alle regole del programma. Poi, vedremo come le preferenze degli utenti possono essere modellate attraverso un programma logico, (iii) per creare il profilo dell’utente in un sistema context-aware, e (iv) per proporre un framework che supporti la definizione di preferenze complesse. Infine, per colmare le lacune in programmazione logica applicata a un processo di decisione con incertezza (v) proporremo una metodologia basata sulla programmazione logica classica e una metodologia basata su un’estensione della programmazione logica con logica possibilistica

EMIL: Extracting Meaning from Inconsistent Language

Developments in formal and computational theories of argumentation reason with inconsistency. Developments in Computational Linguistics extract arguments from large textual corpora. Both developments head in the direction of automated processing and reasoning with inconsistent, linguistic knowledge so as to explain and justify arguments in a humanly accessible form. Yet, there is a gap between the coarse-grained, semi-structured knowledge-bases of computational theories of argumentation and fine-grained, highly-structured inferences from knowledge-bases derived from natural language. We identify several subproblems which must be addressed in order to bridge the gap. We provide a direct semantics for argumentation. It has attractive properties in terms of expressivity and complexity, enables reasoning by cases, and can be more highly structured. For language processing, we work with an existing controlled natural language (CNL), which interfaces with our computational theory of argumentation; the tool processes natural language input, translates them into a form for automated inference engines, outputs argument extensions, then generates natural language statements. The key novel adaptation incorporates the defeasible expression ‘it is usual that’. This is an important, albeit incremental, step to incorporate linguistic expressions of defeasibility. Overall, the novel contribution of the paper is an integrated, end-to-end argumentation system which bridges between automated defeasible reasoning and a natural language interface. Specific novel contributions are the theory of ‘direct semantics’, motivations for our theory, results with respect to the direct semantics, an implementation, experimental results, the tie between the formalisation and the CNL, the introduction into a CNL of a natural language expression of defeasibility, and an ‘engineering’ approach to fine-grained argument analysis

Time-Situated Metacognitive Agency and Other Aspects of Commonsense Reasoning

Much research in commonsense reasoning (CSR) involves use of external representations of an agent's reasoning, based on compelling features of classical logic. However, these advantages come with severe costs, including: omniscience, consistency, static semantics, frozen deadlines, lack of self-knowledge, and lack of expressive power to represent the reasoning of others. Active logic was developed to address many of these, but work to date still leaves serious gaps. The present work focuses on major extensions of active logic to deal with self-knowledge, and their implementation into a newly-developed automated reasoner for commonsense active logic. Dealing with self-knowledge has been designed and implemented in the reasoner via a new treatment of quotation as a form of nesting. More sophisticated varieties of nesting, particularly quasi-quotation mechanisms, have also been developed to extend the basic form of quotation. Active logic and the reasoner are applied to classical issues in CSR, including a treatment of one agent having the knowledge and inferential mechanisms to reason about another's time-situated reasoning