Complexity of Non-Monotonic Logics

Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been considered, e.g., extension with default rules, extension with modal belief operators, or modification of the semantics. In this survey we consider a logical formalism from each of the above possibilities, namely Reiter's default logic, Moore's autoepistemic logic and McCarthy's circumscription. Additionally, we consider abduction, where one is not interested in inferences from a given knowledge base but in computing possible explanations for an observation with respect to a given knowledge base. Complexity results for different reasoning tasks for propositional variants of these logics have been studied already in the nineties. In recent years, however, a renewed interest in complexity issues can be observed. One current focal approach is to consider parameterized problems and identify reasonable parameters that allow for FPT algorithms. In another approach, the emphasis lies on identifying fragments, i.e., restriction of the logical language, that allow more efficient algorithms for the most important reasoning tasks. In this survey we focus on this second aspect. We describe complexity results for fragments of logical languages obtained by either restricting the allowed set of operators (e.g., forbidding negations one might consider only monotone formulae) or by considering only formulae in conjunctive normal form but with generalized clause types. The algorithmic problems we consider are suitable variants of satisfiability and implication in each of the logics, but also counting problems, where one is not only interested in the existence of certain objects (e.g., models of a formula) but asks for their number.Comment: To appear in Bulletin of the EATC

Technology assessment of advanced automation for space missions

Six general classes of technology requirements derived during the mission definition phase of the study were identified as having maximum importance and urgency, including autonomous world model based information systems, learning and hypothesis formation, natural language and other man-machine communication, space manufacturing, teleoperators and robot systems, and computer science and technology

Parameterized aspects of team-based formalisms and logical inference

Parameterized complexity is an interesting subfield of complexity theory that has received a lot of attention in recent years. Such an analysis characterizes the complexity of (classically) intractable problems by pinpointing the computational hardness to some structural aspects of the input. In this thesis, we study the parameterized complexity of various problems from the area of team-based formalisms as well as logical inference. In the context of team-based formalism, we consider propositional dependence logic (PDL). The problems of interest are model checking (MC) and satisfiability (SAT). Peter Lohmann studied the classical complexity of these problems as a part of his Ph.D. thesis proving that both MC and SAT are NP-complete for PDL. This thesis addresses the parameterized complexity of these problems with respect to a wealth of different parameterizations. Interestingly, SAT for PDL boils down to the satisfiability of propositional logic as implied by the downwards closure of PDL-formulas. We propose an interesting satisfiability variant (mSAT) asking for a satisfiable team of size m. The problem mSAT restores the ‘team semantic’ nature of satisfiability for PDL-formulas. We propose another problem (MaxSubTeam) asking for a maximal satisfiable team if a given team does not satisfy the input formula. From the area of logical inference, we consider (logic-based) abduction and argumentation. The problem of interest in abduction (ABD) is to determine whether there is an explanation for a manifestation in a knowledge base (KB). Following Pfandler et al., we also consider two of its variants by imposing additional restrictions over the size of an explanation (ABD and ABD=). In argumentation, our focus is on the argument existence (ARG), relevance (ARG-Rel) and verification (ARG-Check) problems. The complexity of these problems have been explored already in the classical setting, and each of them is known to be complete for the second level of the polynomial hierarchy (except for ARG-Check which is DP-complete) for propositional logic. Moreover, the work by Nord and Zanuttini (resp., Creignou et al.) explores the complexity of these problems with respect to various restrictions over allowed KBs for ABD (ARG). In this thesis, we explore a two-dimensional complexity analysis for these problems. The first dimension is the restrictions over KB in Schaefer’s framework (the same direction as Nord and Zanuttini and Creignou et al.). What differentiates the work in this thesis from an existing research on these problems is that we add another dimension, the parameterization. The results obtained in this thesis are interesting for two reasons. First (from a theoretical point of view), ideas used in our reductions can help in developing further reductions and prove (in)tractability results for related problems. Second (from a practical point of view), the obtained tractability results might help an agent designing an instance of a problem come up with the one for which the problem is tractable

Razonamiento abductivo aplicado al diagnóstico de PyMEs

Las pequeñas y medianas empresas tienen un rol preponderante en las economías de todos los países. Este sector se caracteriza por proveer productos y servicios singulares, a diferencia de las grandes empresas que suelen enfocarse hacia soluciones más estandarizadas. Estas empresas padecen problemáticas específicas que pueden afectar desde su funcionamiento hasta su permanencia en el mercado. Para tener éxito en este ámbito, son indispensables habilidades gerenciales adicionales. Sin embargo, a menudo no cuentan con personal calificado en esas áreas por lo que deben contratar servicios de consultoría. El proyecto MAEOS viene desarrollando herramientas que permiten modelar esta realidad para asistir al consultor en su práctica cotidiana. Por un lado, mediante la formalización del conocimiento teórico disponible en la materia. Por otro, construyendo software que permite realizar inferencias con dicho conocimiento para asistir en el proceso de análisis. Estas inferencias corresponden a razonamiento de tipo deductivo. El presente trabajo completa el proceso de asesoramiento brindado a pequeñas y medianas empresas en el marco del proyecto MAEOS mediante la incorporación de un módulo de diagnóstico. En el proceso de diagnóstico utilizamos otro tipo de razonamiento denominado abductivo. En el desarrollo de esta nueva funcionalidad aplicamos razonamiento abductivo al conocimiento formalizado existente, para obtener una representación de la situación de la empresa, a partir de la cual el experto puede generar recomendaciones acerca de las acciones a realizar para que la misma alcance los objetivos deseados. Para poder llevar a cabo lo anterior tuvimos que implementar nuevamente parte de las aplicaciones que conformaban el proyecto. Con la utilización del mismo lenguaje en los diferentes módulos logramos una mejor integración entre los mismos.FCEIA-UN

Advanced Automation for Space Missions

The feasibility of using machine intelligence, including automation and robotics, in future space missions was studied

L'abduction en conception architecturale : une sémiose hypostatique

Cette thèse développe un modèle sémiotique de l’abduction pour représenter un processus de conception architecturale. Elle formalise ce processus par une dualisation hypostatique du rapport sémiotique entre un problème de conception, saisi en tant que signe, et la possibilité de sa matérialisation géométrique. La dualisation réintègre ce signe dans le domaine des systèmes de savoir-concevoir utilisés en conception architecturale, et par conséquent, elle génère de nouvelles solutions architecturales. L’abduction modifie les connaissances préalables engagées dans la production d’une solution (l’hypothèse) et en introduit de nouvelles. La complexité du processus de conception implique, au niveau méthodologique et à partir d’une position épistémologique constructiviste, l’intégration de la subjectivité du concepteur dans le modèle. Ainsi résulte une incertitude des interactions entre problème de conception, production de solution, concepteur et contexte. La sémiotisation de l’abduction architecturale explicite le rôle central de l’interprétation dans la création d’une solution. D’ailleurs, la dualisation s’appuie sur la théorie des possibilités pour opérationnaliser le calcul interprétatif incertain et pour valider les hypothèses générées. En retour, la gestion de la propagation de cette incertitude, dans le modèle sémiotique, facilite l’identification et la formulation des solutions, et rend possible une émergence observationnelle de la nouveauté. Le modèle développé est appliqué à un cas de transformations architecturales géométriques dans un milieu urbain fortement caractérisé.This thesis develops a semiotic model of abduction to represent a process of architectural design. It formalizes this process by the means of a hypostatic dualization, applied to the semiotic relationship between, on the one hand, a design problem, considered as a sign, and on the other, the possibility of its geometric materialization. The dualization reintegrate this sign in the domain of know-how systems used in architectural design, and consequently, it generates new architectural solutions. Abduction modifies and augments the prior knowledge involved in producing the solution (the hypothesis). From a constructivist stance and the ensuing methodological viewpoint, the complexity of the design process implies embedding the designer’s subjectivity in the model. Thus arises an uncertainty about the interactions among design problem, solution production, designer and context. Semiotizing architectural abduction reveals the central role played by interpretation in creating a solution. Besides, dualization relies on possibility theory to formalize the resulting, and uncertain, interpretation calculus, and to validate the obtained hypotheses. In return, managing the uncertainty propagation within the semiotic model, facilitates the identification and the formulation of architectural solutions and allows for an observational emergence of novelty. The developed model is applied to a case of architectural geometric transformations in a heavily characterized neighborhood