Reasoning about relations

Inferences about spatial, temporal, and other relations are ubiquitous. This article presents a novel model-based theory of such reasoning. The theory depends on 5 principles. (a) The structure of mental models is iconic as far as possible. (b) The logical consequences of relations emerge from models constructed from the meanings of the relations and from knowledge. (c) Individuals tend to construct only a single, typical model. (d) They spontaneously develop their own strategies for relational reasoning. (e) Regardless of strategy, the difficulty of an inference depends on the process of integration of the information from separate premises, the number of entities that have to be integrated to form a model, and the depth of the relation. The article describes computer implementations of the theory and presents experimental results corroborating its main principle.     

Reasoning about visibility

We consider properties of sequences of spatial regions, as seen from a viewpoint. In particular, we concentrate on two types of regions: (1) general domains in which a region is any subset of the space, and (2) axis-parallel domains, where the regions are boxes in an N-dimensional space. We introduce binary relations allowing to express properties of these sequences and present two approaches to process them. First, we show that constraints on these relations can be solved in polynomial time for general domain and that the same problem is NP-complete in the axis-parallel case. Second, we introduce a modal logic on these relations, called Visibility Logic, and show that model-checking on a finite sequence of regions can be done in polynomial time (both in the general and axis-parallel cases). Finally, we present applications to image processing and firewall filtering.     

Reasoning about geography

To understand the nature and etiology of biases in geographical judgments, the authors asked people to estimate latitudes (Experiments 1 and 2) and longitudes (Experiments 3 and 4) of cities throughout the Old and New Worlds. They also examined how people's biased geographical judgments change after they receive accurate information ("seeds") about actual locations. Location profiles constructed from the pre- and postseeding location estimates conveyed detailed information about the representations underlying geography knowledge, including the subjective positioning and subregionalization of regions within continents; differential seeding effects revealed between-region dependencies. The findings implicate an important role for conceptual knowledge and plausible-reasoning processes in tasks that use subjective geographical information.     

Reasoning about evidence

Bayesians understand the notion of evidential support in terms of probability raising. Little is known about the logic of the evidential support relation, thus understood. We investigate a number of prima facie plausible candidate logical principles for the evidential support relation and show which of these principles the Bayesian evidential support relation does and which it does not obey. We also consider the question which of these principles hold for a stronger notion of evidential support.     

Reasoning defeasibly about probabilities

In concrete applications of probability, statistical investigation gives us knowledge of some probabilities, but we generally want to know many others that are not directly revealed by our data. For instance, we may know prob(P/Q) (the probability of P given Q) and prob(P/R), but what we really want is prob(P/Q&;R), and we may not have the data required to assess that directly. The probability calculus is of no help here. Given prob(P/Q) and prob(P/R), it is consistent with the probability calculus for prob(P/Q&;R) to have any value between 0 and 1. Is there any way to make a reasonable estimate of the value of prob(P/Q&;R)? A related problem occurs when probability practitioners adopt undefended assumptions of statistical independence simply on the basis of not seeing any connection between two propositions. This is common practice, but its justification has eluded probability theorists, and researchers are typically apologetic about making such assumptions. Is there any way to defend the practice? This paper shows that on a certain conception of probability—nomic probability—there are principles of “probable probabilities” that license inferences of the above sort. These are principles telling us that although certain inferences from probabilities to probabilities are not deductively valid, nevertheless the second-order probability of their yielding correct results is 1. This makes it defeasibly reasonable to make the inferences. Thus I argue that it is defeasibly reasonable to assume statistical independence when we have no information to the contrary. And I show that there is a function Y(r, s, a) such that if prob(P/Q) = r, prob(P/R) = s, and prob(P/U) = a (where U is our background knowledge) then it is defeasibly reasonable to expect that prob(P/Q&;R) = Y(r, s, a). Numerous other defeasible inferences are licensed by similar principles of probable probabilities. This has the potential to greatly enhance the usefulness of probabilities in practical application.     

Reasoning about update logic

Logical frameworks for analysing the dynamics of information processing abound [4, 5, 8, 10, 12, 14, 20, 22]. Some of these frameworks focus on the dynamics of the interpretation process, some on the dynamics of the process of drawing inferences, and some do both of these. Formalisms galore, so it is felt that some conceptual streamlining would pay off.This paper is part of a larger scale enterprise to pursue the obvious parallel between information processing and imperative programming. We demonstrate that logical tools from theoretical computer science are relevant for the logic of information flow. More specifically, we show that the perspective of Hoare logic [13, 18] can fruitfully be applied to the conceptual simplification of information flow logics.     

Reasoning about data and information

Cognitive states as well as cognitive commodities play central though distinct roles in our epistemological theories. By being attentive to how a difference in their roles affects our way of referring to them, we can undoubtedly accrue our understanding of the structure and functioning of our main epistemological theories. In this paper we propose an analysis of the dichotomy between states and commodities in terms of the method of abstraction, and more specifically by means of infomorphisms between different ways to classify states of information, information-bases, and evidential situations.     

Reasoning about Arbitrary Natural Numbers from a Carnapian Perspective

Journal of Philosophical Logic - Inspired by Kit Fine’s theory of arbitrary objects, we explore some ways in which the generic structure of the natural numbers can be presented. Following a...     

Moral Reasoning about the Environment

ABSTRACT This paper deals in the main with the problem of delimiting the classes of beings to which we have moral duties when making environmental decisions, and of how to balance their interests fairly. The relation between having interests, having desires and having value (intrinsic or other) is discussed, and a distinction made between entities which can themselves value and those which can have value. Its conclusion is that duties are owed directly to, and only to, sentient beings, and that these duties can be ascertained by weighing their interests impartially strength for strength. It ends with some suggestions about procedures for doing this. Examples are taken from proposals to develop a beach commercially, and to construct a new road in an environmentally sensitive area [1].     

Representation and Reasoning about Evolutions of the World in the Context of Reasoning about Actions

The first step in reasoning about actions and change involves reasoning about how the world would evolve if a certain action is executed in a certain state. Most research on this assumes the evolution to be only a single step and focus on formulating the transition function that defines changes between states due to actions. In this paper we consider cases where the evolution is more than just a single change between one state and another. This is manifested when the execution of an action may trigger execution of other actions, or when multiple agents act on the environment following certain strategies.     

Reasoning about partial functions with the aid of a computer

Partial functions are ubiquitous in both mathematics and computer science. Therefore, it is imperative that the underlying logical formalism for a general-purpose mechanized mathematics system provide strong support for reasoning about partial functions. Unfortunately, the common logical formalisms — first-order logic, type theory, and set theory — are usually only adequate for reasoning about partial functionsin theory. However, the approach to partial functions traditionally employed by mathematicians is quite adequatein practice. This paper shows how the traditional approach to partial functions can be formalized in a range of formalisms that includes first-order logic, simple type theory, and Von-Neumann—Bernays—Gödel set theory. It argues that these new formalisms allow one to directly reason about partial functions; are based on natural, well-understood, familiar principles; and can be effectively implemented in mechanized mathematics systems.Supported by the MITRE-Sponsored Research program. This paper is a written version (with references) of an address given at the Partial Functions and Programming: Foundational Questions conference held 17 February 1995 at the University ol California at Irvine.     

On Reasoning Morally about the Environment

ABSTRACT R. M. Hare argues that moral reasoning about the environment requires the setting out of the various interests at stake and adjudication between them, strength for strength. Though there are possible objections to some aspects of his programme, it is clearly intended to be fair. However, it is not clear that in his concluding discussion, of the building of new roads, the interests at stake are set out with total impartiality. Some further relevant interests are listed, in an attempt to redress the balance.     

Reasoning about conventional time as a function of conventional time systems

This study investigated how reasoning about conventional time information varied as a function of conventional time systems by using the Chinese month and Jieqi systems. Twenty Chinese students were asked to answer month-related questions and another 20 were asked to answer Jieqi-related questions. Reaction time and accuracy were the dependent measures. A cross-boundary effect was observed in processing months, and distance and direction effects were obtained when participants judged the interval of Jieqi. These results suggested that arithmetic operations were used in Chinese reasoning about months and verbal-articulatory processes were used for the Jieqi. The effects of mode of language representation on cognition and the strategies for cross-linguistic study are discussed.     

类比推理研究综述

类比推理是哲学、逻辑学和心理学等学科研究的重要内容,是人类能够进行整合思维活动的重要机制,也是保证个体有效学习的工具。它的产生、发展和成熟是个体认知活动顺利完成的主要保障。近年来,类比推理机制研究已经逐渐成为探讨认知过程和机能的一个十分活跃的研究领域。为此,本文拟从以下四个方面对类比推理研究加以综述。