Special Issue on Higher-Level Cognition and Computation

Lecture Notes in Computer Science, 1998

2003

We provide a model for reasoning about knowledge anti probability together. We a.llow explicit mention of probabilities in formulas, so that our language has formulas tha.t essentia.lly say "a.ccording to agent i, formula. (p holds with probability a.t least o~." The language is powerfid enough to allow reasoning a~bout higher-order probabilities, as well as allowing explicit comparisons of the probabilities an agent places on distinct events. We present a general framework for interpreting such formulas, a.nd consider various properties that might hold of the interrelationship between agents' subjective probability spaces at different states. We provide a. complete a.xiomatiza.tion for rea.soning about knowledge a.nd probability, prove a. small model property, and obtain decision procedures. We then consider the effects of adding common knowledge and a. probabilistic va.ria.nt of common knowledge to the language.

A review of the literature on evaluating reasoning systems reveals that it is a very broad area with wide variation in depth and breadth of research on metrics and tests. This is the second of a two-part series that begins to bring order to the area by categorizing reasoning systems according to their capabilities. These can be used as a basis for evaluating and testing reasoning systems claiming to be in each category. Capabilities are analyzed along the dimensions of representation languages and inference. The first part introduces information metrology, model theory, and inference to facilitate understanding of the reasoning categories presented. It also groups representation languages by their relation to first-order logic, and model-theoretic properties, such as soundness and completeness. This part examines inference procedures, dividing them into deduction, induction, abduction, and analogical reasoning. It explains the subcategories and characteristics of each, and concludes with recommendations for future work.

Journal of Applied Logic, 2007

2009

As already mentioned in several places, in the search for a proof there are almost always many (depending on the calculus, potentially infinitely many) possibilities for the application of inference rules at every step. The result is the aforementioned explosive growth of the search space ( .1 on page 58). In the worst case, all of these possibilities must be tried in order to find the proof, which is usually not possible in a reasonable amount of time.

2000

We suggest an axiomatic approach to the way in which past cases, or observations, are or should be used for making predictions and for learning. In our model, a predictor is asked to rank eventualities based on possible memories. A \memory" consists of repetitions of past cases, and can be identi ̄ed with a vector, attaching a nonnegative integer (number of occurrences) to each case. Mild consistency requirements on these rankings imply that they have a numerical representation that is linear in the number of case repetitions. That is, there exists a matrix assigning numbers to eventuality-case pairs, such that, for every memory vector, multiplication of the matrix by the vector yields a numerical representation of the ordinal plausibility ranking given that memory. Interpreting this result for the ranking of theories or hypotheses, rather than of speci ̄c eventualities, it is shown that one may ascribe to the predictor subjective conditional probabilities of cases given theori...

2004

Logics have, for many years, laid claim to providing a formal basis for the study of artificial intelligence. With the depth and maturity of methodologies, formalisms, procedures, implementations, and their applications available today, this claim is stronger than ever, as witnessed by increasing amount and range of publications in the area, to which the present proceedings accrue. The European series of Workshops on Logics in Artificial Intelligence (or Journées Européennes sur la Logique en Intelligence Artificielle-JELIA) began in response to the need for a European forum for the discussion of emerging work in this burgeoning field. JELIA 2000 is the seventh such workshop in the

arXiv (Cornell University), 2019

Evidence-based reasoning is at the core of many problemsolving and decision-making tasks in a wide variety of domains. Generalizing from the research and development of cognitive agents in several such domains, this paper presents progress toward a computational theory for the development of instructable cognitive agents for evidence-based reasoning tasks. The paper also illustrates the application of this theory to the development of four prototype cognitive agents in domains that are critical to the government and the public sector. Two agents function as cognitive assistants, one in intelligence analysis, and the other in science education. The other two agents operate autonomously, one in cybersecurity and the other in intelligence, surveillance, and reconnaissance. The paper concludes with the directions of future research on the proposed computational theory. Evidence-Based Reasoning as Discovery of Evidence, Hypotheses, and Arguments Developed in the framework of the scientific method, the computational approach to evidence-based reasoning views this process as ceaseless discovery of evidence, hypotheses, and arguments in a non-stationary world, involving collaborative computational processes of evidence in search of hypotheses, hypotheses in search of evidence, and evidentiary testing of hypotheses (see Figure 1). First, through abductive (imaginative) reasoning that shows that something is possibly true, one generates alternative hypotheses that may explain an observation of interest or answer an important question. Next, through deductive reasoning that shows that something is ______________________________________________________________________

Journal of Experimental & Theoretical Artificial Intelligence, 2006

It is sad but true that most people in AI and related fields, upon hearing the word 'reasoning', imagine a sequence of purely linguistic expressions which follow standard rules of deductive inference for elementary two-valued logic. (Other similarly one-dimensional schemes may come to mind at the mention of this word. For example, so-called 'Bayesian reasoning' is probabilistic, but relative to the issue at hand, this is of no help because, compared with the human case, probabilistic formalisms are also thoroughly one-dimensional; they make no use, for example, of diagrams or other pictographic representations, or of semantic models.) Human reasoners greatly exceed such rigid, inflexible modes of reasoning. The present issue is devoted to taking seriously the brute fact that human reasoning is 'heterogeneous'; it involves not just declarative formulae of the classical sort, processed in the classical way, but also diagrams, images, models, underlying semantic relationships between propositions (e.g. intuitive similarity), etc., and non-deductive procedures (e.g. abduction) for processing such things. In addition, when (untrained) human reasoning involves linguistic information, it often departs radically from the canon of what is normatively correct reasoning over such standard information, and the departure is sometimes very effective for the particular task at hand. Johnson-Laird has long held that human reasoning extends well beyond standard logic, and he stands as a seminal figure in the history of heterogeneous reasoning, as it is uncovered and studied via empirical techniques, and rendered at least to some degree in computational form. According to his mental models theory (which by now is supported by a large amount of empirical data), logically untrained people predominantly reason not over formulae or their relatives (e.g. declarative sentences in some natural language), but rather over 'mental models'. His paper explains the mental models theory in connection with spatial reasoning, and shows that this theory predicts something that some other contributors to the volume have presupposed-diagrams facilitate human reasoning. Although mental models theory appeared on the scene long ago, another scheme (minus experiments in psychology that support mental models) predates Johnson-Laird's theory by many years: Peirce's alpha, beta, and gamma systems