A simple logic for reasoning about incomplete knowledge

International audienceThe semantics of modal logics for reasoning about belief or knowledge is often described in terms of accessibility relations, which is too expressive to account for mere epistemic states of an agent. This paper proposes a simple logic whose atoms express epistemic attitudes about formulae expressed in another basic propositional language, and that allows for conjunctions, disjunctions and negations of belief or knowledge statements. It allows an agent to reason about what is known about the beliefs held by another agent. This simple epistemic logic borrows its syntax and axioms from the modal logic KD. It uses only a fragment of the S5 language, which makes it a two-tiered propositional logic rather than as an extension thereof. Its semantics is given in terms of epistemic states understood as subsets of mutually exclusive propositional interpretations. Our approach offers a logical grounding to uncertainty theories like possibility theory and belief functions. In fact, we define the most basic logic for possibility theory as shown by a completeness proof that does not rely on accessibility relations

Investigations in Belnap's Logic of Inconsistent and Unknown Information

Nuel Belnap schlug 1977 eine vierwertige Logik vor, die -- im Gegensatz zur klassischen Logik -- die Faehigkeit haben sollte, sowohl mit widerspruechlicher als auch mit fehlender Information umzugehen. Diese Logik hat jedoch den Nachteil, dass sie Saetze der Form 'wenn ..., dann ...' nicht ausdruecken kann. Ausgehend von dieser Beobachtung analysieren wir die beiden nichtklassischen Aspekte, Widerspruechlichkeit und fehlende Information, indem wir eine dreiwertige Logik entwickeln, die mit widerspruechlicher Information umgehen kann und eine Modallogik, die mit fehlender Information umgehen kann. Beide Logiken sind nicht monoton. Wir untersuchen Eigenschaften, wie z.B. Kompaktheit, Entscheidbarkeit, Deduktionstheoreme und Berechnungkomplexitaet dieser Logiken. Es stellt sich heraus, dass die dreiwertige Logik, nicht kompakt und ihre Folgerungsmenge im Allgemeinen nicht rekursiv aufzaehlbar ist. Beschraenkt man sich hingegen auf endliche Formelmengen, so ist die Folgerungsmenge rekursiv entscheidbar, liegt in der Klasse $\Sigma_2^P$ der polynomiellen Zeithierarchie und ist DIFFP-schwer. Wir geben ein auf semantischen Tableaux basierendes, korrektes und vollstaendiges Berechnungsverfahren fuer endliche Praemissenmengen an. Darueberhinaus untersuchen wir Abschwaechungen der Kompaktheitseigenschaft. Die nichtmonotone auf S5-Modellen basierende Modallogik stellt sich als nicht minder komplex heraus. Auch hier untersuchen wir eine sinnvolle Abschwaechung der Kompaktheitseigenschaft. Desweiteren studieren wir den Zusammenhang zu anderen nichtmonotonen Modallogiken wie Moores autoepistemischer Logik (AEL) und McDermotts NML-2. Wir zeigen, dass unsere Logik zwischen AEL und NML-2 liegt. Schliesslich koppeln wir die entworfene Modallogik mit der dreiwertigen Logik. Die dabei enstehende Logik MKT ist eine Erweiterung des nichtmonotonen Fragments von Belnaps Logik. Wir schliessen unsere Betrachtungen mit einem Vergleich von MKT und verschiedenen informationstheoretischen Logiken, wie z.B. Nelsons N und Heytings intuitionistischer Logik ab

Active Logics: A Unified Formal Approach to Episodic Reasoning

Artificial intelligence research falls roughly into two categories: formal and implementational. This division is not completely firm: there are implementational studies based on (formal or informal) theories (e.g., CYC, SOAR, OSCAR), and there are theories framed with an eye toward implementability (e.g., predicate circumscription). Nevertheless, formal/theoretical work tends to focus on very narrow problems (and even on very special cases of very narrow problems) while trying to get them ``right'' in a very strict sense, while implementational work tends to aim at fairly broad ranges of behavior but often at the expense of any kind of overall conceptually unifying framework that informs understanding. It is sometimes urged that this gap is intrinsic to the topic: intelligence is not a unitary thing for which there will be a unifying theory, but rather a ``society'' of subintelligences whose overall behavior cannot be reduced to useful characterizing and predictive principles. Here we describe a formal architecture that is more closely tied to implementational constraints than is usual for formalisms, and which has been used to solve a number of commonsense problems in a unified manner. In particular, we address the issue of formal, integrated, and longitudinal reasoning: inferentially-modeled behavior that incorporates a fairly wide variety of types of commonsense reasoning within the context of a single extended episode of activity requiring keeping track of ongoing progress, and altering plans and beliefs accordingly. Instead of aiming at optimal solutions to isolated, well-specified and temporally narrow problems, we focus on satisficing solutions to under-specified and temporally-extended problems, much closer to real-world needs. We believe that such a focus is required for AI to arrive at truly intelligent mechanisms with the ability to behave effectively over considerably longer time periods and range of circumstances than is common in AI today. While this will surely lead to less elegant formalisms, it also surely is requisite if AI is to get fully out of the blocks-world and into the real world. (Also cross-referenced as UMIACS-TR-99-65

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

Self-Modelling in Inference about Absence

Representing the absence of an object requires one to know that they would know if it were present. This form of second-order, counterfactual reasoning critically relies on access to a mental self-model, specifying expected perceptual and cognitive states under different world states. This thesis addresses open questions regarding inference about absence in perceptual decision making: its reliance on prior metacognitive knowledge, relative encapsulation from metacognitive monitoring, neural underpinning, and relation with default-reasoning. I start by showing that in visual search, implicit metacognitive knowledge about spatial attention supports inference about the absence in the first trial of an experiment, and that this knowledge is dissociable from explicit metacognitive knowledge. Further underscoring the richness and complexity of this knowledge, I find that people are able to accurately predict their future search times, even for complex, unfamiliar displays. Participants’ predictions were better aligned with their own search times than with those of other participants, suggesting that this self-knowledge is person-specific. I then ask what factors contribute to confidence in decisions about presence and absence. Reverse-correlation analysis reveals stimulus features that contribute to detection decisions and confidence. I discuss these findings in the context of sensory noise estimation. Using functional MRI, I find that a network of frontal and parietal regions that are implicated in decision confidence are mostly invariant to whether subjective confidence is rated with respect to decisions about presence or absence. In interpreting these results, I formulate computational models that monitor fluctuations in external stimulus strength and in internal attentional states. Finally, in six behavioural experiments, different levels of the cognitive hierarchy are found to be sensitive to different notions of absence. I conclude with a discussion of ways in which inference about absence can be used by cognitive scientists for probing implicit metacognitive beliefs and studying the mental self-model

Artificial general intelligence: Proceedings of the Second Conference on Artificial General Intelligence, AGI 2009, Arlington, Virginia, USA, March 6-9, 2009

Artificial General Intelligence (AGI) research focuses on the original and ultimate goal of AI – to create broad human-like and transhuman intelligence, by exploring all available paths, including theoretical and experimental computer science, cognitive science, neuroscience, and innovative interdisciplinary methodologies. Due to the difficulty of this task, for the last few decades the majority of AI researchers have focused on what has been called narrow AI – the production of AI systems displaying intelligence regarding specific, highly constrained tasks. In recent years, however, more and more researchers have recognized the necessity – and feasibility – of returning to the original goals of the field. Increasingly, there is a call for a transition back to confronting the more difficult issues of human level intelligence and more broadly artificial general intelligence

Contemporary Natural Philosophy and Philosophies - Part 1

This book is a printed edition of the Special Issue titled "Contemporary Natural Philosophy and Philosophies" - Part 1 that was published in the journal Philosophies

Advances in Human-Robot Interaction

Rapid advances in the field of robotics have made it possible to use robots not just in industrial automation but also in entertainment, rehabilitation, and home service. Since robots will likely affect many aspects of human existence, fundamental questions of human-robot interaction must be formulated and, if at all possible, resolved. Some of these questions are addressed in this collection of papers by leading HRI researchers

Irreversible Noise: The Rationalisation of Randomness and the Fetishisation of Indeterminacy

This thesis aims to elaborate the theoretical and practical significance of the concept of noise with regard to current debates concerning realism, materialism, and rationality. The scientific conception of noise follows from the developments of thermodynamics, information theory, cybernetics, and dynamic systems theory; hence its qualification as irreversible. It is argued that this conceptualization of noise is entangled in several polemics that cross the arts and sciences, and that it is crucial to an understanding of their contemporary condition. This thesis draws on contemporary scientific theories to argue that randomness is an intrinsic functional aspect at all levels of complex dynamic systems, including higher cognition and reason. However, taking randomness or noise as given, or failing to distinguish between different descriptive levels, has led to misunderstanding and ideology. After surveying the scientific and philosophical context, the practical understanding of randomness in terms of probability theory is elaborated through a history of its development in the field of economics, where its idealization has had its most pernicious effects. Moving from the suppression of noise in economics to its glorification in aesthetics, the experience of noise in the sonic sense is first given a naturalistic neuro-phenomenological explanation. Finally, the theoretical tools developed over the course of the inquiry are applied to the use of noise in music. The rational explanation of randomness in various specified contexts, and the active manipulation of probability that this enables, is opposed to the political and aesthetic tendencies to fetishize indeterminacy. This multi-level account of constrained randomness contributes to the debate by demystifying noise, showing it to be an intrinsic and functionally necessary condition of reason and consequently of freedom

Proceedings of the 11th Workshop on Nonmonotonic Reasoning

These are the proceedings of the 11th Nonmonotonic Reasoning Workshop. The aim of this series is to bring together active researchers in the broad area of nonmonotonic reasoning, including belief revision, reasoning about actions, planning, logic programming, argumentation, causality, probabilistic and possibilistic approaches to KR, and other related topics. As part of the program of the 11th workshop, we have assessed the status of the field and discussed issues such as: Significant recent achievements in the theory and automation of NMR; Critical short and long term goals for NMR; Emerging new research directions in NMR; Practical applications of NMR; Significance of NMR to knowledge representation and AI in general