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 from connectives and relations between entities

This article reports investigations of inferences that depend both on connectives between clauses, such as or else, and on relations between entities, such as in the same place as. Participants made more valid inferences from biconditionals—for instance, Ann is taller than Beth if and only if Beth is taller than Cath—than from exclusive disjunctions (Exp. 1). They made more valid transitive inferences from a biconditional when a categorical premise affirmed rather than denied one of its clauses, but they made more valid transitive inferences from an exclusive disjunction when a categorical premise denied rather than affirmed one of its clauses (Exp. 2). From exclusive disjunctions, such as Either Ann is not in the same place as Beth or else Beth is not in the same place as Cath, individuals tended to infer that all three individuals could be in different places, whereas in fact this was impossible (Exps. 3a and 3b). The theory of mental models predicts all of these results.     

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 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.     

Causal judgments about relations between multilevel variables

Three experiments presented stimulus information about cause and effect variables taking 3 quantitative values. Judgments tended to vary in accordance with considerations of conditions affecting the validity of causal inference from correlational data: whether causal candidates were presented simultaneously or in a temporal order such that one could affect the other and whether candidates were confounded with each other. The results supported a general hypothesis that causal judgments are moderated in accordance with acquired methodological intuitions. The fourth experiment showed that tendencies in correlation judgment were different from those in causal judgment, further supporting the hypothesis that causal judgment from multilevel variable information is, to some extent, determined by processes or conceptual frameworks specific to the domain of causal cognition.     

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.     

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 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 a rule

Two experiments were carried out to investigate the difficulty of making the contra-positive inference from conditional sentences of the form, “if P then Q.” This inference, that not-P follows from not-Q, requires the transformation of the information presented in the conditional sentence. It is suggested that the difficulty is due to a mental set for expecting a relation of truth, correspondence, or match to hold between sentences and states of affairs. The elicitation of the inference was not facilitated by attempting to induce two kinds of therapy designed to break this set. It is argued that the subjects did not give evidence of having acquired the characteristics of Piaget's “formal operational thought.”     

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.     

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 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 the future: Doom and Beauty

According to the Doomsday Argument we have to rethink the probabilities we assign to a soon or not so soon extinction of mankind when we realize that we are living now, rather early in the history of mankind. Sleeping Beauty finds herself in a similar predicament: on learning the date of her first awakening, she is asked to re-evaluate the probabilities of her two possible future scenarios. In connection with Doom, I argue that it is wrong to assume that our ordinary probability judgements do not already reflect our place in history: we justify the predictive use we make of the probabilities yielded by science (or other sources of information) by our knowledge of the fact that we live now, a certain time before the possible occurrence of the events the probabilities refer to. Our degrees of belief should change drastically when we forget the date—importantly, this follows without invoking the “Self Indication Assumption”. Subsequent conditionalization on information about which year it is cancels this probability shift again. The Doomsday Argument is about such probability shifts, but tells us nothing about the concrete values of the probabilities—for these, experience provides the only basis. Essentially the same analysis applies to the Sleeping Beauty problem. I argue that Sleeping Beauty “thirders” should be committed to thinking that the Doomsday Argument is ineffective; whereas “halfers” should agree that doom is imminent—but they are wrong.     

会通与更新:基督宗教伦理道德观与社会工作专业价值观的关系

基督宗教伦理道德既是欧美历史发展与社会文化的深厚渊源,又为社会服务和利他助人专业行为提供价值基础,还能广泛深刻影响世人的社会生活模式与行为规范取向.基督宗教伦理反映欧美社会主流文化模式,为社会福利与社会工作专业的发展奠定价值基础.在社会结构转型与非基督宗教社会处境下,关键是如何发展中国的社会工作专业的价值观.     

Proof Systems for Reasoning about Computation Errors

In the paper we examine the use of non-classical truth values for dealing with computation errors in program specification and validation. In that context, 3-valued McCarthy logic is suitable for handling lazy sequential computation, while 3-valued Kleene logic can be used for reasoning about parallel computation. If we want to be able to deal with both strategies without distinguishing between them, we combine Kleene and McCarthy logics into a logic based on a non-deterministic, 3-valued matrix, incorporating both options as a non-deterministic choice. If the two strategies are to be distinguished, Kleene and McCarthy logics are combined into a logic based on a 4-valued deterministic matrix featuring two kinds of computation errors which correspond to the two computation strategies described above. For the resulting logics, we provide sound and complete calculi of ordinary, two-valued sequents. Presented by Yaroslav Shramko and Heinrich Wansing