Conjunctive Rule Research Articles

Information search and decision making: The effects of information displays

Information display boards may be used to test assumptions about underlying cognitive processes in decision situations. However, the question may be raised whether information processing in a complex decision situation is indepemdent of the structure of the information display board used. In a study employing 96 subjects, the design of the information display board, the number of alternatives, and the number of attributes were varied. Twelve groups of eight subjects were presented with one hypothetical choice among riskless multiattribute decision alternatives (apartments). Results showed that information search patterns were not influenced by the design of the information display board, but that the relative number of attributes included in the decision process was. The number of available attributes appeared to be the strongest determinant of information search patterns. A higher number of attributes induced information search patterns consistent with the noncompensatory conjunctive decision rule. It is suggested that the decision situation employed, which forced the decision maker to remember each piece of information acquired, underlies the difference between the results in the present study and previous findings.

Rationality in Decision Making: An Investigation into a Satisficing Model of Search and Choice

Semi‐structured focused interviews were used to analyse the supposedly extended decision process involved in the choice of video recorder. The results suggested that the proposed three‐stage model was a meaningful reflection of the decision‐making process. First the respondents clarified the problems and benefits of video recorders. Next they created consideration and choice sets excluding more extensive searching. Conjunctive decision rules (weirs) were used to simplify the final decision. The implications for manufacturers are discussed.

MINIMAX APPROXIMATIONS FOR ERF(X)

Minimax approximations for erf(x) in the intervals [0, 1], [1, 2], and [2, 6] were developed a priori. The minimax absolute errors of the approximations in these intervals were, respectively, 0.57 × 10−9, 0.21 × 10−10, and 0.11 × 10−9. Erf(x) was approximated directly in [0, 1] and [1, 2] and indirectly as 1-erfc(x) in [2, 6]. The minimax errors of these approximations are three orders of magnitude lower than the commonly used Hastings' minimax approximation to erf(x). True values for erf(x) needed in developing the approximations were obtained by numerical integration using the trapezoid rule in conjunction with the Romberg extrapolation to the limit. Remez‘ algorithm was used to determine the parameters of the approximations and their associated minimax error. Practical computational details are provided for the approximations, which are useful for computers with no manufacturer-supplied library subprogram for calculating erf(x).

Effort and Accuracy in Choice

Individuals often use several different strategies such as the expected value rule, conjunctive rule, and elimination-by-aspects, to make decisions. It has been hypothesized that strategy selection is, in part, a function of (1) the ability of a strategy to produce an accurate response and (2) the strategy's demand for mental resources or effort. We examine effort and accuracy and their role in strategy selection. Several strategies that may be used to make choices under risk are simulated using a production system framework. This framework allows the estimation of the effort required to use the strategy in a choice environment, while simultaneously measuring its accuracy relative to a normative model. A series of Monte-Carlo studies varied several aspects of the choice environments, including the complexity of the task and the presence or absence of dominated alternatives. These simulations identify strategies which approximate the accuracy of normative procedures while requiring substantially less effort. These results, however, are highly contingent upon characteristics of the task environment. The potential of production system models in understanding task effects in decisions is stressed.

Formulaicity, frame semantics, and pragmatics in German binomial expressions

FORMULAICITY, FRAME SEMANTICS, AND PRAGMATICS IN GERMAN BINOMIAL EXPRESSIONS Knud Lambrecht University of California, Berkeley The analysis of formulaic German binomial expressions of the form N und N reveals the following characteristics. The absence of determiners, along with other morphosyntactic and semantic anomalies, makes these phrases non-compositional and thus similar to idioms; but they differ from fixed idiomatic expressions in that their structural pattern can be productively used for the creation of new pairs. These bare binomials are not exhaustively listable lexical items, nor can they be generated by a syntactic conjunction rule. Their formal properties suggest that they are complex word-like expressions— comparable in many ways to nominal compounds and, like compounds, describable by lexical rules. Their creation and use is subject to semantic and pragmatic constraints which can be subsumed under a general principle offrame structure. They can be divided into three main types: (a) lexicalized and irreversible, (b) novel but semantically motivated , and (c) semantically unmotivated but pragmatically constrained. However, sharp lines between lexicalized and novel instances, or between semantically and pragmatically motivated types, cannot be drawn on principled grounds. Bare binomials lend support to a view of language in which the 'generative' and the 'idiomatic' components are two extremes on a continuum, rather than fundamentally distinct phenomena.* Introduction 1. This paper deals with a class of phrases often encountered in German at a certain stylistic level, the basic form of which can be characterized as N(oun) und N(oun). Ex. 1 contains samples of such phrases in actual usage (emphasis supplied): (1) Wallraffs "unerwünschte Reportagen"'Wallraffs "undesirable news reports" are sind unerwünscht nur für die Nutznießerundesirable only for the beneficiaries ofauautorit ärer Strukturen in Arbeitswelt undthoritarian structures in (the) working Sozialgefuge, für die Verteidiger vonworld and (the) social system, for the deRecht und Ordnung auf Kosten vonfenders of law and order at the expense of Freiheit und Gleichheit. (Wallrafffreedom and equality.' 1975:2) The emphasized phrases are short versions of stylistically somewhat lessmarked noun (or prepositional) phrases in which the nouns are preceded by determiners, usually the definite or the generic indefinite article. Ex. G contains the relevant parts of ex. 1 in their ordinary form, i.e. preceded by the appropriate determiners:1 (I') ... in der Arbeitswelt und im Sozialgefüge ... des Rechtes und der Ordnung ... der Freiheit und der Gleichheit. Following an old tradition, revived by Malkiel 1959, 1 will refer to these pairings * This study owes a great deal to the teaching and writings of Charles J. Fillmore; without his influence and advice, it would not have been written. I would also like to thank Pamela Downing, John Haiman, Paul Kay, Edith Moravcsik, and Karl Zimmer for many helpful comments. 1 The fact that, in ex. 1, the second and third noun pairs are preceded by von, whereas in ex. 1 ' the definite article appears in the genitive case without a preposition, results from a case-marking constraint of modern German which is irrelevant for the present example (cf. §2.2). 753 754LANGUAGE, VOLUME 60, NUMBER 4 (1984) of two nouns as binomials. But unlike Malkiel and other writers, who apply the term to paired items of any lexical category (e.g. Eng. bright and rosy, on and off, here and there), I will restrict my attention to sequences of two conjoined nouns. As for the particular binomial construction illustrated in ex. 1, where no determiner precedes the nouns, I will refer to it as a bare binomial (BB).2 There are several reasons for BB's to be of interest to the theoretical linguist. First is the striking fact—to my knowledge neither explained, nor even dealt with, in modern linguistics—that the emphasized phrases in ex. 1 are grammatical only as long as they occur in conjunction. Thus, next to the grammatical BB's in 1, we do not have the corresponding mononomials of the form noun: (2) ... für die Nutznießer autoritärer Strukturen in *Arbeitswelt, für die Verteidiger von *Recht auf Kosten von *Freiheit. From a generative point of view, this entails that the binomials in question cannot be generated by the same mechanism that produces the pairings in...

An Analysis of Conjunctive Choice: Theory and Experiments

This paper develops a theoretical framework in which the conjunctive choice rule can be analyzed and reports on a set of laboratory experiments designed to test that theory. Initially the conjunctive choice rule is formulated as a constrained optimization problem. The solution to this problem is then used to identify simpler versions of the rule that require less computational sophistication. In experiments designed to test this theory, all subject pools conformed to a particular simplified conjunctive rule.

Helical flow of plastic materials

An exact closed form solution is given for steady helical flow of plastic materials. Material behaviour is governed by the von-Mises flow rule in conjunction with a rigid/linear-hardening stress-strain characteristic. A restricted version of the general solution is used, as an example, for simulating the helical motion of a rough rigid tool through a circular cylindrical tunnel which is embedded in an infinite plastic medium. It is shown that wall friction induces a plastic boundary layer into the medium. The influence of wall pressure, wall friction and material properties on the behaviour within the boundary layer is discussed. It is also pointed out that no such helical flow pattern is possible for a rigid/perfectly-plastic material.

Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment.

Perhaps the simplest and the most basic qualitative law of probability is the conjunction rule: The probability of a conjunction, P (A&B) cannot exceed the probabilities of its constituents, P (A) and P (B), because the extension (or the possibility set) of the conjunction is included in the extension of its constituents. Judgments under uncertainty, however, are often mediated by intuitive heuristics that are not bound by the conjunction rule. A conjunction can be more representative than one of its constituents, and instances of a specific category can be easier to imagine or to retrieve than instances of a more inclusive category. The representativeness and availability heuristics therefore can make a conjunction appear more probable than one of its constituents. This phenomenon is demonstrated in a variety of contexts including estimation of word frequency, personality judgment, medical prognosis, decision under risk, suspicion of criminal acts, and political forecasting. Systematic violations of the conjunction rule are observed in judgments of lay people and of experts in both between-subjects and within-subjects comparisons. Alternative interpretations of the conjunction fallacy are discussed and attempts to combat it are explored.

Thermo-elastic/plastic behaviour of a strain-hardening thick-walled sphere

An exact solution is presented for the thermo-elastic/plastic problem of a thick-walled sphere subjected to a radial temperature gradient. Material behaviour is described by the von-Mises flow rule in conjunction with a modified Ramberg-Osgood stress-strain characteristic. The problem is formulated within the framework of small strain plasticity. Contact is made with earlier studies for elastic/perfectly-plastic and pure power-hardening materials. Also given are a few basic results for elastic/linear-hardening materials.

The semantics of Hoare's Iteration Rule

Hoare's Iteration Rule is a principle of reasoning that is used to derive correctness assertions about the effects of implementing a while-command. We show that the propositional modal logic of this type of command is axiomatised by Hoare's rule in conjunction with two additional axioms. The proof also establishes decidability of the logic. The paper concludes with a discussion of the relationship between the logic of “while” and Segerberg's axiomatisation of propositional dynamic logic.

The role of memory aids in two instructional paradigms: Learning and utilization of logical rules

One hundred and thirty-two 10th graders performed either a conjunetive or biconditional rule task in one of six conditions defined by a 2 (tasks: attribute-identification versus rule-learning) by 3 (memory aids: 0 versus 3 versus 6) factorial design. Learners' attribute-identification was facilitated when six memory aids were made available, especially given the biconditional rule, but not when three aids were available. This effect was attributed to the facilitative role of six memory aids in the process of eliminating irrelevant dimensions. The acquisition of the biconditional rule was a linear function of the number of memory aids; but that of the conjunctive rule was not differentially affected by the memory aids. This interaction was attributed to the facilitative role of memory aids in the formation of a relatively complex one, not in the identification of a familiar, easy one.

Efficient sets, decision heuristics, and single-peaked preferences

The origins of single-peaked preferences in multiattribute choice behavior are analyzed. The starting point is Coombs and Avrunin's ( Psychological Review, 1977, 84, 216–230; Journal of Mathematical Psychology, 1977 , 16, 261–266) theory which explains single-peakedness as the joint effect of task and behavior characteristics. Whereas the task conditions—so-called efficient sets—are retained, and their importance is even more stressed, it is argued that Coombs and Avrunin's behavioral assumptions—classical marginally decreasing preference functions—may not be representative of actually displayed choice behavior. Rather, the information processing approach to decision research has shown that multiattribute choices are often based on simplifying heuristic rules which, due to their possible intransitivity, are inconsistent with Coombs and Avrunin's behavioral requirements. Tversky's ( Psychological Review, 1969 , 76, 31–48) additive difference model is used as an algebraic framework for analyzing such so-called attribute-based choice rules. Sufficient (and in the continuous case also necessary) conditions are presented which guarantee that the additive difference model will also be single-peaked on efficient sets. These conditions show that the behavioral principles yielding single-peaked preferences are far more general than Coombs and Avrunin assumed and include most of the empirically substantiated forms of attribute-based choice rules. Further, a necessary and sufficient condition is derived which insures that elimination rules, like the conjunctive rule, for instance, and generalizations thereof are single-peaked. Finally, making use of a result by Edgeworth, ( Mathematical Psychics, London, Paul, 1881 ), it is shown that efficient sets per se may originate in quite different ways. It is concluded that the phenomenon of single-peakedness is mainly a function of the task rather than of some specific behavior.

Le langage du cinema en tant que langage artistique

The author deals with the following question; to what extent film - considered in terms of language communication - can be characterized by features allowing for classification on an artistic order. This is based on traditional literary research, especially the achievements of the Russian Formalists and the Prague School of Linguistics. The author specifies the characteristics of artistic language as individualization, emotional appeal, violation of standard rules, excessive organization of the language, and the weakening of the referential function. Then, accepting the thesis of the massive heterogeneousness of the film sign, she searches for the rules governing the artisticness on the level of the image, spoken language, music, etc., and tries to support her stetements through psychological perception. There are two basic conclusions to the article: 1) systemic relations in filming, distribution, and conjunction rules, are generated on the level of a particular film (the thesis based on the semiotics of film), and 2) artisticness, understood as rule-breaking, is achieved through devices violating semantic cohesion (e.g. shots) and conspicuous particularity of presentation.

Rule Differences, Practice, and Response Label in Complete Learning

Summary Rule differences in a complete learning (CL) task were investigated over practice and conditions of neutral and directional response labels. The Ss were forty 13- to 14-year-old paid volunteers, 20 males and 20 females. Ss were given 20 problems, in four blocks of five problems each. Within each block, problems representing the Affirmative (Af), Conjunctive (Cj), Conditional (Cd), Inclusive Disjunctive (Id), and Biconditional (Bd) rules were presented. The order of rule difficulty was found to be Af < Cj = Cd = Id < Bd. Performance improved after the first block of five rules with no further change over the next three blocks of problems. No significant effect was obtained for Label, and there were no significant interactions. These results for rule difficulty and practice were concluded to be generally consistent with both Neisser and Weene's and Hunt, Marin, and Stone's models of CL, and to clarify previous results concerning Rule by Practice interactions. The absence of a Label effect is inconsistent with previous findings in attribute indentification and rule learning, and may be unique to the CL selection paradigm.

Decision making with texts: Information analysis and schema acquisition.

SUMMARY While making decisions in a semantically rich natural situation, people encounter information, such as in texts, that is often massive and at the same time imprecise. Yet the desired information is extracted and decisions are made. In an attempt to study the characteristics of performance in such a situation, we created a laboratory analogue of the stock market. Subjects acting as stockbrokers acquired a conjunctive decision rule for predicting the market performance of a fictitious stock. After receiving suitable training, subjects read 20 quarterly reports containing information about six market information categories, of which only two were relevant to correct decisions. In each trial, subjects recorded their hypotheses about the categories in the the decision rule. Feedback was given following each decision, and the subjects were able to reread each text in order to decide if and how to modify their hypothesis about the rule. On some trials, following the decisions, the subjects were asked to free recall the texts they had just read. Decision performance distinguished between learners (subjects who discovered the decision rule) and nonlearners. The characteristics of hypothesis-selection behavior were similar to those observed in simpler concept-learning problems. Learners displayed a more global approach to the problem, were more sensitive to the given feedback, and utilized the available information more effectively than nonlearners. The category-recall patterns reflected the observed hypothesis-selection and decision behavior and the subjects' overall category-identification strategies. These data were congruent with a model of text comprehension, a result suggesting an equivalence between some of the comprehension and the hypothesis-selection operators. Effective decision in this task was viewed as the ability to acquire an appropriate control schema to guide the comprehension and the analysis of complex, often unreliable, text inputs.

Attractiveness of decision rules

Four groups of fifteen subjects were each presented with a hypothetical choice situation (job offers or apartments). Before choosing, the subjects were informed about three compensatory and three non-compensatory decision rules and were asked to rate the applicability of each rule in the given situation. Means of the applicability ratings were highest for two compensatory rules. The response distributions across individuals and situations indicated that the subjects could distinguish among the rules in a meaningful way. Reported usage of decision rules was closely related to the applicability ratings, particularly for the conjunctive rule. Factors favoring certain rules were discussed, as well as the validity of retrospective reports on decision rules.

Making “Relevant Attributes” Relevant in Rule Learning

Subjects in a rule-learning task learned either Conjunction, Exclusion, or Joint denial concepts with the relevant attributes presented in either their positive form (“red” and “square”) or in the form in which they are expressed in the rule to be learned (“red” and “not square” for Exclusion; “not red” and “not square” for Joint denial). Presenting relevant attributes in their rule-relevant form significantly improved rule learning. In addition, when rule-relevant attributes were used the Exclusion and Joint-denial rules were not significantly different in difficulty from the Conjunction rule, as predicted by a model of rule learning developed by Salatas and Bourne (1974).

Stimulus-Rule Interactions in Concept Verification

The difficulty of learning a conceptual rule has been shown to depend upon the stimulus attributes which that rule conjoins. For what appear to be separable attributes, the disjunctive rule is easier than the conjunctive. In contrast, for what appear to be integrable attributes, the conjunctive rule is easier. This paper reports six experiments designed to determine whether the integrality of stimulus attributes affects the speed of verification of the stimulus, as positive or negative, with respect to a given conjunctive or disjunctive concept. The pattern of reaction times is not consistent with the result of rule-learning experiments and does not support an integrality hypothesis. Verification times seem to be more a function of the perceptual salience of the relevant attributes of the concept. Thus, a perceptual-integrality hypothesis is an unlikely explanation of rule learning results.

Stimulus-Rule Interaction in Concept Learning

The acquisition and use of conceptual or categorical rules has heretofore been treated theoretically as a stimulus-independent process, involving the establishment of mental procedures that are equally applicable to any collection of stimulus attributes or within any stimulus population. The results of two experiments are inconsistent with this principle, at least for subjects who are relatively naive in the use of logical rules. The procedures that subjects employ initially, and therefore the relative difficulty of conjunctive and disjunctive rules, depend on the pair of attributes integrated by the rule in any concrete concept problem. The differences among attribute pairs reflect an underlying variable identified as local integrality. Integrable attributes conduce to conjunctive procedures, and separable attributes conduce to disjunctive procedures.

Rule-specific dimensional interaction effects in concept learning

Garner (1976) has identified two main types of dimensional interactions, integrality and separability, which are likely to affect concept learning. Evidence available to Garner suggested that integral stimuli facilitate concept learning, but these studies investigated only concepts based on the conjunctive or some simpler rule. The present experiment assessed the integrality-separability effect in concept learning over a variety of bidimensional rules. The results indicate that integral dimensions facilitate conjunctive rule learning but that separable dimensions facilitate the acquisition of conditional and biconditional rules. Thus, dimensional interaction effects are rule specific. In particular, any rule which requires a precise discrimination of the truth table class structure of the stimulus population will be facilitated when stimulus dimensions are separable.