TY - JOUR A1 - Hoernig, Robin A1 - Oberauer, Klaus A1 - Weidenfeld, Andrea T1 - Between reasoning JF - The quarterly journal of experimental psychology N2 - In two experiments we investigated three-term reasoning with spatial relational assertions using the preposition between as compared to projective prepositions (such as to the left of). For each kind of assertion we distinguish the referent expression (i.e., the grammatical subject) from the relatum expression (i.e., the internal argument of the preposition; e.g., [The hedgehog](referent)_(expression) is to the left of [the frog](relatum)_(expression); [the snake](referent)_(expression) is between [the donkey and the deer](relatum)_(expression)). Previous research has shown that integrating premises with projective prepositions is easier (a) when the relatum expression of the second premise denotes an element already given by the first premise (relatum = given), and (b) when the term denoting a given element precedes the term denoting a new element (given - new). Experiment 1 extended this finding to second premises with the preposition between. In Experiment 2, between figured in the first premise. In this case, participants built an initial preferred model already from the first premise, although such a premise is indeterminate with respect to the array that it describes. Since there is no need left for integrating the second premise, this premise is instead used to verify the initial model and to modify it when necessary. A further investigation of conclusion evaluation times showed that conclusions were evaluated faster when they first mentioned the element that was included most recently into the mental model of the premises. The use of premises with between permitted the separation of recency of model inclusion from recency of appearance of an element in a premise. Y1 - 2006 U6 - https://doi.org/10.1080/17470210500416151 SN - 1747-0218 VL - 59 IS - 10 SP - 1805 EP - 1825 PB - SAGE Publishing CY - Thousand Oaks, CA ER - TY - JOUR A1 - Oberauer, Klaus A1 - Weidenfeld, Andrea A1 - Hörnig, Robin T1 - Working memory capacity and the construction of spatial mental models in comprehension and deductive reasoning N2 - We asked 149 high-school students who were pretested for their working memory capacity (WMC) to read spatial descriptions relating to five objects and to evaluate conclusions asserting an unmentioned relationship between two of the objects. Unambiguous descriptions were compatible with a single spatial arrangement, whereas ambiguous descriptions permitted two arrangements; a subset of the ambiguous descriptions still determined the relation asserted in the conclusion, whereas another subset did not. Two groups of participants received different instructions: The deduction group should accept conclusions only if they followed with logical necessity from the description, whereas the comprehension group should accept a conclusion if it agreed with their representation of the arrangement. Self-paced reading times increased on sentences that introduced an ambiguity, replicating previous findings in deductive reasoning experiments. This effect was also found in the comprehension group, casting doubt on the interpretation that people consider multiple possible arrangements online. Responses to conclusions could be modelled by a multinomial processing model with four parameters: the probability of constructing a correct mental model, the probability of detecting an ambiguity, and two guessing parameters. Participants with high and with low WMC differed mainly in the probability of successfully constructing a mental model Y1 - 2006 UR - http://www.informaworld.com/openurl?genre=journal&issn=1747-0218 U6 - https://doi.org/10.1080/17470210500151717 ER - TY - JOUR A1 - Oberauer, Klaus A1 - Weidenfeld, Andrea A1 - Hornig, R. T1 - Logical reasoning and probabilities: A comprehensive test of Oaksford and Chater (2001) N2 - We report two experiments testing a central prediction of the probabilistic account of reasoning provided by Oaksford and Chater (2001): Acceptance of standard conditional inferences, card choices in the Wason selection task, and quantifiers chosen for conclusions from syllogisms should vary as a function of the frequency of the concepts involved. Frequency was manipulated by a probability-learning phase preceding the reasoning tasks to simulate natural sampling. The effects predicted by Oaksford and Chater (2001) were not obtained with any of the three paradigms Y1 - 2004 SN - 1069-9384 ER - TY - JOUR A1 - Oberauer, Klaus A1 - Hornig, R. A1 - Weidenfeld, Andrea A1 - Wilhelm, Oliver T1 - Effects of directionality in deductive reasoning : II. Premise integration and conclusion evaluation N2 - Previous research (Oberauer & Wilhelm, 2000) has shown an inherent directionality between the two terms linked in premises of typical deductive reasoning tasks. With three experiments we investigated the effect of inherent directionality on the time to integrate two premises and for the derivation of a conclusion. We varied figure (i.e., order of terms in the premises) and direction of inference (i.e., order of terms in the conclusion) in deduction tasks from various domains (propositional reasoning, syllogisms, spatial, temporal, and linear order reasoning). Effects of figure on premise reading times varied with the directionality of the relations. Effects of direction of inference reflected the same directionality for a subset of relations. We propose that two factors are jointly responsible for a large part of observed directionality effects in premise integration: the inherent directionality of relational statements and a general advantage for a given-new order of terms in the second premise. Difficulty of deriving a conclusion is affected by the directionality or relations if and only if the relation is semantically asymmetric, so that the directionality must be preserved in the integrated mental model Y1 - 2005 SN - 0272-4987 ER - TY - JOUR A1 - Hornig, R. A1 - Oberauer, Klaus A1 - Weidenfeld, Andrea T1 - Two principles of premise integration in spatial reasoning N2 - We propose two principles that facilitate integration of two relational premises in spatial reasoning. Integration is easier if the anaphor in the second premise, P2, bears the role of the relatum (relatum = given). Moreover, integration is easier if, in P2, the anaphor is mentioned before the new element (given-new). In premises with canonical word order (grammatical subjects mentioned first), these principles always conflict with one another. In topicalized statements mentioning the prepositional phrase first, the two principles work in tandem. By varying word order, we tested the two principles by measuring P2 comprehension times. Comprehension times indicated that integration was easiest when P2 obeyed both principles and most difficult when both principles were violated. Canonical premises were of intermediate difficulty. This pattern emerged regardless of whether the anaphor was a definite description or a pronoun Y1 - 2005 ER - TY - JOUR A1 - Weidenfeld, Andrea A1 - Oberauer, Klaus A1 - Hornig, R T1 - Causal and noncausal conditionals : an integrated model of interpretation and reasoning N2 - We present an integrated model for the understanding of and the reasoning from conditional statements. Central assumptions from several approaches are integrated into a causal path model. According to the model, the cognitive availability of exceptions to a conditional reduces the subjective conditional probability of the consequent, given the antecedent. This conditional probability determines people's degree of belief in the conditional, which in turn affects their willingness to accept logically valid inferences. In addition to this indirect pathway, the model contains a direct pathway: Availability of exceptional situations directly reduces the endorsement of valid inferences. We tested the integrated model with three experiments using conditional statements embedded in pseudonaturalistic cover stories. An explicitly mentioned causal link between antecedent and consequent was either present (causal conditionals) or absent (arbitrary conditionals). The model was supported for the causal but not for the arbitrary conditional statements Y1 - 2005 ER - TY - THES A1 - Weidenfeld, Andrea T1 - Interpretation of and reasoning with conditionals : probabilities, mental models, and causality T1 - Interpretation von und Schlussfolgern mit Konditionalaussagen : Wahrscheinlichkeiten, Mentale Modelle und Kausalität N2 - In everyday conversation "if" is one of the most frequently used conjunctions. This dissertation investigates what meaning an everyday conditional transmits and what inferences it licenses. It is suggested that the nature of the relation between the two propositions in a conditional might play a major role for both questions. Thus, in the experiments reported here conditional statements that describe a causal relationship (e.g., "If you touch that wire, you will receive an electric shock") were compared to arbitrary conditional statements in which there is no meaningful relation between the antecedent and the consequent proposition (e.g., "If Napoleon is dead, then Bristol is in England"). Initially, central assumptions from several approaches to the meaning and the reasoning from causal conditionals will be integrated into a common model. In the model the availability of exceptional situations that have the power to generate exceptions to the rule described in the conditional (e.g., the electricity is turned off), reduces the subjective conditional probability of the consequent, given the antecedent (e.g., the probability of receiving an electric shock when touching the wire). This conditional probability determines people's degree of belief in the conditional, which in turn affects their willingness to accept valid inferences (e.g., "Peter touches the wire, therefore he receives an electric shock") in a reasoning task. Additionally to this indirect pathway, the model contains a direct pathway: Cognitive availability of exceptional situations directly reduces the readiness to accept valid conclusions. The first experimental series tested the integrated model for conditional statements embedded in pseudo-natural cover stories that either established a causal relation between the antecedent and the consequent event (causal conditionals) or did not connect the propositions in a meaningful way (arbitrary conditionals). The model was supported for the causal, but not for the arbitrary conditional statements. Furthermore, participants assigned lower degrees of belief to arbitrary than to causal conditionals. Is this effect due to the presence versus absence of a semantic link between antecedent and consequent in the conditionals? This question was one of the starting points for the second experimental series. Here, the credibility of the conditionals was manipulated by adding explicit frequency information about possible combinations of presence or absence of antecedent and consequent events to the problems (i.e., frequencies of cases of 1. true antecedent with true consequent, 2. true antecedent with false consequent, 3. false antecedent with true consequent, 4. false antecedent with false consequent). This paradigm allows testing different approaches to the meaning of conditionals (Experiment 4) as well as theories of conditional reasoning against each other (Experiment 5). The results of Experiment 4 supported mainly the conditional probability approach to the meaning of conditionals (Edgington, 1995) according to which the degree of belief a listener has in a conditional statement equals the conditional probability that the consequent is true given the antecedent (e.g., the probability of receiving an electric shock when touching the wire). Participants again assigned lower degrees of belief to the arbitrary than the causal conditionals, although the conditional probability of the consequent given the antecedent was held constant within every condition of explicit frequency information. This supports the hypothesis that the mere presence of a causal link enhances the believability of a conditional statement. In Experiment 5 participants solved conditional reasoning tasks from problems that contained explicit frequency information about possible relevant cases. The data favored the probabilistic approach to conditional reasoning advanced by Oaksford, Chater, and Larkin (2000). The two experimental series reported in this dissertation provide strong support for recent probabilistic theories: for the conditional probability approach to the meaning of conditionals by Edgington (1995) and the probabilistic approach to conditional reasoning by Oaksford et al. (2000). In the domain of conditional reasoning, there was additionally support for the modified mental model approaches by Markovits and Barrouillet (2002) and Schroyens and Schaeken (2003). Probabilistic and mental model approaches could be reconciled within a dual-process-model as suggested by Verschueren, Schaeken, and d'Ydewalle (2003). N2 - Im Laufe eines Tages verwenden die meisten Menschen mehrfach Konditionalsätze: Das Wörtchen "wenn" gehört zu den häufigsten Konjunktionen in Alltag, Wissenschaft und Literatur. Die vorliegende Dissertation beschäftigt sich mit der Frage, welche Bedeutung ein Konditionalsatz im alltäglichen Sprachgebrauch übermittelt und welche Inferenzen er erlaubt. Es wird die Vermutung aufgestellt, dass dabei die Art der Relation zwischen den zwei Propositionen in einem Konditional eine bedeutsame Rolle spielen könnte. Daher werden in den Experimenten Konditionalsätze, die eine kausale Beziehung beschreiben (z.B. "Wenn Du das Kabel berührst, bekommst Du einen elektrischen Schlag") mit arbiträren Konditionalen verglichen, in denen keinerlei sinnvolle Relation zwischen Antezedens und Konsequens besteht (z.B. "Wenn Napoleon tot ist, liegt Bristol in England"). Als erstes werden zentrale Annahmen von mehreren Ansätzen zur Bedeutung und zum Schlußfolgern mit kausalen Konditionalsätzen in ein gemeinsames Modell integriert. In dem Modell reduziert die kognitive Verfügbarkeit von Situationen, die zu Ausnahmen von der Regel im Konditionalsatz führen können (z.B. der Strom ist abgestellt), die subjektive bedingte Wahrscheinlichkeit des Konsequens gegeben das Antezedens (z.B. die Wahrscheinlichkeit, einen Schlag zu bekommen gegeben, dass man das Kabel berührt). Diese subjektive bedingte Wahrscheinlichkeit bestimmt die Glaubwürdigkeit des Konditionals, die wiederum die Bereitwilligkeit beeinflußt, mit der gültige Schlußfolgerungen (z.B. "Peter berührt das Kabel, daher erhält er einen elektrischen Schlag") in einer Schlußfolgerungsaufgabe akzeptiert werden. Zusätzlich zu dem gerade beschriebenen indirekten Pfad enthält das integrierte Modell zusätzlich einen direkten Pfad: Die kognitive Verfügbarkeit von Ausnahme-Situationen reduziert unmittelbar die Bereitschaft, gültige Schlüsse zu akzeptieren. Die erste Experimentalreihe testete das entwickelte integrierte Model für Konditionalsätze, die in pseudo-natürliche Kontextgeschichten eingebettet wurden. Die Kontextgeschichten stellten entweder eine kausale Relation zwischen Antezedens und Konsequens her (kausale Konditionale) oder stellten die Propositionen in keinerlei sinnvollen Zusammenhang (arbiträre Konditionale). Die empirischen Daten stützen das Modell für die kausalen, aber nicht für die arbiträren Konditionale. Außerdem schätzten die TeilnehmerInnen die arbiträren Konditionalsätzen als weniger glaubwürdig ein als die kausalen Konditionale. Es stellt sich die Frage, ob dieser Unterschied in der Glaubwürdigkeit auf die An- bzw. Abwesenheit einer bedeutungshaltigen Relation zwischen Antezedens und Konsequens im Konditional zurückgeführt werden kann. Diese Frage war einer der Ausgangspunkte für die zweite Experimentalreihe. In dieser wurde die Glaubwürdigkeit der Konditionalsätze kontrolliert manipuliert, indem in den Kontextgeschichten explizite Häufigkeitsinformationen über die vier möglichen Kombinationen von An- bzw. Abwesenheit von Antezedens und Konsequens gegeben wurden (d.h. die Häufigkeit von Fällen mit 1. wahrem Antezedens und wahrem Konsequens, 2. wahrem Antezedens und falschem Konsequens, 3. falschem Antezedens und wahrem Konsequens, 4. falschem Antezedens und falschem Konsequens). Dieses Paradigma ermöglichte ferner, unterschiedliche Ansätze zur Bedeutung des Konditionals (Experiment 4) ebenso wie Theorien zum konditionalen Schlußfolgern gegeneinander zu testen (Experiment 5). Die Befunde aus Experiment 4 stützen im wesentlichen Edgingtons Ansatz zur Bedeutung von Konditionalen (Edgington, 1995). Nach diesem Ansatz entspricht die Glaubwürdigkeit, die ein Zuhörer einem Konditionalsatz einräumt, der bedingten Wahrscheinlichkeit, dass das Konsequens wahr ist gegeben das Antezedens (z.B. die Wahrscheinlichkeit, einen Schlag zu bekommen gegeben, dass man das Kabel berührt). Erneut schrieben die TeilnehmerInnen den arbiträren Konditionalsätzen geringere Glaubwürdigkeit zu als den kausalen Sätzen, obwohl diesmal innerhalb jeder Häufigkeitsbedingung die bedingte Wahrscheinlichkeit des Konsequens gegeben das Antezedens konstant gehalten wurde. Dieses Ergebnis stützt die Hypothese, dass die bloße Anwesenheit einer kausalen Beziehung die Glaubwürdigkeit eines Konditionalsatzes erhöht. In Experiment 5 lösten die TeilnehmerInnen konditionale Schlußfolgerungsaufgaben, dabei wurden die Kontextgeschichten um explizite Häufigkeitsangaben ergänzt. Die Ergebnisse favorisieren die probabilistische Theorie zum konditionalen Schließen, die von Oaksford, Chater, und Larkin (2000) vorgeschlagen wurde. Beide Experimentalreihen lieferten deutliche Evidenz für probabilistische Theorien: für Edgingtons Ansatz zur Bedeutung von Konditionalsätzen (Edgington, 1995) und für die probabilistische Theorie des konditionalen Schließens von Oaksford et al. (2000). Im Bereich des konditionalen Schließens stützen die Daten gleichzeitig die modifizierten mentalen Modell-Theorien von Markovits und Barrouillet (2002) und Schroyens und Schaeken (2003). Probabilistische und mentale Modell-Theorien könnten im Rahmen eines Dualen-Prozeß-Modells wie es von Verschueren, Schaeken und d'Ydewalle (2003) vorgeschlagen wurde, miteinander versöhnt werden. KW - Konditional KW - Konditionalsatz KW - Kausalität KW - Bedeutung KW - Glaubwürdigkeit KW - Schlussfolgern KW - bedingte Wahrscheinlichkeit KW - mentale Modelle KW - probabilistisch KW - Mental Models Theory KW - conditional reasoning KW - probabilistic Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-5207 ER -