Reasoning about Minimal Belief and Negation as Failure

We investigate the problem of reasoning in the propositional fragment of MBNF, the logic of minimal belief and negation as failure introduced by Lifschitz, which can be considered as a unifying framework for several nonmonotonic formalisms, including default logic, autoepistemic logic, circumscription, epistemic queries, and logic programming. We characterize the complexity and provide algorithms for reasoning in propositional MBNF. In particular, we show that entailment in propositional MBNF lies at the third level of the polynomial hierarchy, hence it is harder than reasoning in all the above mentioned propositional formalisms for nonmonotonic reasoning. We also prove the exact correspondence between negation as failure in MBNF and negative introspection in Moore's autoepistemic logic

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

In Defence of Modest Doxasticism About Delusions

Here I reply to the main points raised by the commentators on the arguments put forward in my Delusions and Other Irrational Beliefs (OUP, 2009). My response is aimed at defending a modest doxastic account of clinical delusions, and is articulated in three sections. First, I consider the view that delusions are in-between perceptual and doxastic states, defended by Jacob Hohwy and Vivek Rajan, and the view that delusions are failed attempts at believing or not-quite-beliefs, proposed by Eric Schwitzgebel and Maura Tumulty. Then, I address the relationship between the doxastic account of delusions and the role, nature, and prospects of folk psychology, which is discussed by Dominic Murphy, Keith Frankish, and Maura Tumulty in their contributions. In the final remarks, I turn to the continuity thesis and suggest that, although there are important differences between clinical delusions and non-pathological beliefs, these differences cannot be characterised satisfactorily in epistemic terms. \u

From here to human-level AI

AbstractHuman-level AI will be achieved, but new ideas are almost certainly needed, so a date cannot be reliably predicted—maybe five years, maybe five hundred years. I'd be inclined to bet on this 21st century.It is not surprising that human-level AI has proved difficult and progress has been slow—though there has been important progress. The slowness and the demand to exploit what has been discovered has led many to mistakenly redefine AI, sometimes in ways that preclude human-level AI—by relegating to humans parts of the task that human-level computer programs would have to do. In the terminology of this paper, it amounts to settling for a bounded informatic situation instead of the more general common sense informatic situation.Overcoming the “brittleness” of present AI systems and reaching human-level AI requires programs that deal with the common sense informatic situation—in which the phenomena to be taken into account in achieving a goal are not fixed in advance.We discuss reaching human-level AI, emphasizing logical AI and especially emphasizing representation problems of information and of reasoning. Ideas for reasoning in the common sense informatic situation include nonmonotonic reasoning, approximate concepts, formalized contexts and introspection

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

Logic, self-awareness and self-improvement: The metacognitive loop and the problem of brittleness

This essay describes a general approach to building perturbation-tolerant autonomous systems, based on the conviction that artificial agents should be able notice when something is amiss, assess the anomaly, and guide a solution into place. We call this basic strategy of self-guided learning the metacognitive loop; it involves the system monitoring, reasoning about, and, when necessary, altering its own decision-making components. In this essay, we (a) argue that equipping agents with a metacognitive loop can help to overcome the brittleness problem, (b) detail the metacognitive loop and its relation to our ongoing work on time-sensitive commonsense reasoning, (c) describe specific, implemented systems whose perturbation tolerance was improved by adding a metacognitive loop, and (d) outline both short-term and long-term research agendas

Place Based Education as a Tool for Rural Career Development

Rural career development is rarely studied despite a large portion of American students attending school in a rural area. Rural career development is affected by factors such as student attachment to place, access to professional role models, local economic development, school funding, and geographic proximity to professional industries and higher education. A Critical Pedagogy of Place (Gruenewald, 2003) empowers students to critical explore the spacial and social constructs of their local area.Given that school counselors are in a unique position as career development and social justice advocates, this article explores the use of a Critical Pedagogy of Place as an approach to rural career development