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

An algebraic approach for action based default reasoning

Often, we assume that an action is permitted simply because it is not explicitly forbidden; or, similarly, that an action is forbidden simply because it is not explicitly permitted. This kind of assumptions appear, e.g., in autonomous computing systems where decisions must be taken in the presence of an incomplete set of norms regulating a particular scenario. Combining default and deontic reasoning over actions allows us to formally reason about such assumptions. With this in mind, we propose a logical formalism for default reasoning over a deontic action logic. The novelty of our approach is twofold. First, our formalism for default reasoning deals with actions and action operators, and it is based on the deontic action logic originally proposed by Segerberg in [27]. Second, inspired by Segerberg?s approach, we use tools coming from the theory of Boolean Algebra. These tools allow us to extend Segerberg?s algebraic completeness result to the setting of Default Logics.Fil: Castro, Pablo Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rio Cuarto. Facultad de Cs.exactas Fisicoquímicas y Naturales. Departamento de Computación. Grupo de Ingeniería de Software; ArgentinaFil: Cassano, Valentin. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Fervari, Raul Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; ArgentinaFil: Areces, Carlos Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Grip Suppression using a Machine-Learned Technique

This publication describes techniques for grip suppression of a touchscreen display of a computing device using a machine-learned technique. When a user intentionally or unintentionally touches the display (e.g., with a hand or a finger), a Touch Manager of the computing device performs operations to determine a user intent associated with the touch input to prevent false triggering of the display (e.g., by a grip of a hand holding the device). A machine-learned (ML) model calculates the likeliness of an intentional touch input (e.g., a tap, a swipe, or a scroll of a hand or a finger to input or manage information on the device) by identifying and assigning weights to features of the touch input. A total weight is calculated for each touch input and compared to a default threshold (e.g., an accepted threshold associated with an intentional touch input), which may be adjusted to ensure accuracy of user-intent predictions. After the Touch Manager verifies the user-intent predictions using heuristic and/or hysteresis logic, the computing device may perform operations to suppress or enable the touch input

Implementing Default and Autoepistemic Logics via the Logic of GK

The logic of knowledge and justified assumptions, also known as logic of grounded knowledge (GK), was proposed by Lin and Shoham as a general logic for nonmonotonic reasoning. To date, it has been used to embed in it default logic (propositional case), autoepistemic logic, Turner's logic of universal causation, and general logic programming under stable model semantics. Besides showing the generality of GK as a logic for nonmonotonic reasoning, these embeddings shed light on the relationships among these other logics. In this paper, for the first time, we show how the logic of GK can be embedded into disjunctive logic programming in a polynomial but non-modular translation with new variables. The result can then be used to compute the extension/expansion semantics of default logic, autoepistemic logic and Turner's logic of universal causation by disjunctive ASP solvers such as claspD(-2), DLV, GNT and cmodels.Comment: Proceedings of the 15th International Workshop on Non-Monotonic Reasoning (NMR 2014

Expressive Policy Analysis with Enhanced System Dynamicity

Despite several research studies, the effective analysis of policy based systems remains a significant challenge. Policy analysis should at least (i) be expressive (ii) take account of obligations and authorizations, (iii) include a dynamic system model, and (iv) give useful diagnostic information. We present a logic-based policy analysis framework which satisfies these requirements, showing how many significant policy-related properties can be analysed, and we give details of a prototype implementation. Copyright 2009 ACM