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Thesis (M.Soc.Sc.)--University of Hong Kong, 2006. / Title from title page (viewed Apr. 19, 2007) Includes bibliographical references (p. 37-40)

One aspect of Automated Reasoning (AR) deals with writing computer programs that can answer questions using logical reasoning. An Automated Theorem Proving system (ATP system) translates a question to be answered to a first-order logic conjecture, and attempts to prove the conjecture from a set of axioms provided, thereby leading to a proof. If a proof is found an answer extraction method can be applied to answer the original question. If more than one proof is possible, more than one answer may need to be extracted. For ATP systems that can find only one answer at a time, to answer questions that yield multiple answers, the ATP system can be re-invoked with a modified question to find other possible answers. In this thesis, an answer extraction method has been designed to extract more than one answer when an ATP system is used to answer a question that has multiple answers. The method is implemented in an interactive computer program and the process is called multiple-answer extraction. The answer extraction software, called the multi-answer system, is a three layered software architecture model. SNARK, at the bottom-most layer, serves as the ATP system that finds single answers. The answer extractor, in the middle layer, extracts possible answers by re-invoking the ATP system. The top layer compares the answers extracted to the user's expected answers. The software is command line driven. Keywords such as all, some, n (where n is a number), while and until are specified on the command line to limit the number of answers to be extracted. The top layer allows the user to check properties of the answer, e.g., if a specific element belongs to the set of answers obtained, or if the user's set of answers is a subset of the answers returned by the multi-answer system. This is done using set operations, such as subset, element of, union, difference, intersection, on the user's set of answers and the extracted set of answers.

Deductive reasoning is a fundamental cognitive skill, and consequently has been the focus of much research over the past several decades. In the realm of syllogistic reasoning—judging the validity of a conclusion given two premises—a robust finding is the belief bias effect: broadly, the tendency for reasoners to judge as valid more believable than unbelievable conclusions. How the content believability of conclusions influences syllogistic reasoning has been the subject of hundreds of experiments and has informed several theories of deductive reasoning; however, how the content of premises influences the reasoning processes has been largely overlooked. In this thesis, I present 5 experiments that examine how premise content influences reasoning about categorical (i.e., statements with the words ‘some’ and ‘not’) and conditional (i.e., ‘if/then’ statements) syllogisms, which tend to be treated as interchangeable in deductive reasoning literature. It is demonstrated that premise content influences reasoning in these two types of syllogisms in fundamentally different ways. Specifically, Experiment 1 replicates and extends previous findings and demonstrates that for conditional syllogisms, belief bias results when premises are both believable and unbelievable; however, reasoners are more likely to judge that a conclusion is valid when it follows from believable than from unbelievable premises. Conversely, belief bias for categorical syllogisms results only when premises are believable; conclusion believability does not influence conclusion endorsement when premises are unbelievable. Based on these preliminary findings, I propose a theory that categorical and conditional syllogisms differ in the extent to which reasoners initially assume the premises to be true, and that this difference influences when in the reasoning process reasoners evaluate the believability of premises. Specifically, I propose that reasoners automatically assume that conditional, but not categorical, premises are true. It is proposed that, because the word “if” in conditional statements elicits hypothetical thinking, conditional premises are assumed to be true for the duration of the reasoning process. Subsequent to reasoning, premises can be “disbelieved” in a time-consuming process, and initial judgments about the conclusion may be altered, with a bias to respond that conclusions following from believable premises are valid. On the other hand, because categorical premises are phrased as factual propositions, reasoners initially judge the believability of categorical premises prior to reasoning about the conclusion. Unbelievable premises trigger the reasoner to disregard content from the rest of the syllogism, perhaps because the reasoner believes that the information in the problem will not be helpful in solving the problem. This theory is tested and supported by four additional experiments. Experiment 2 demonstrates that reasoners take longer to reason about conditional syllogisms with unbelievable than believable premises, consistent with the theory that unbelievable premises are “disbelieved” in a time-consuming process. Further, participants demonstrate belief bias for categorical syllogisms with unbelievable premises when they are instructed to assume that premises are true (Experiment 3) or when the word ‘if’ precedes the categorical premises (Experiment 4). Finally, Experiment 5 uses eye-tracking to demonstrate that premise believability influences post-conclusion premise looking durations for conditional syllogisms and pre-conclusion premise looking durations for categorical syllogisms. This finding supports the hypothesis that reasoners evaluate the believability of conditional premises after reasoning about the conclusion but that they evaluate the believability of categorical premises before reasoning about the conclusion. Further, Experiment 5 reveals that participants have poorer memory for the content of categorical syllogisms with unbelievable than believable premises, but memory did not differ for conditional syllogisms with believable and unbelievable premises. This suggests that unbelievable premise content in categorical syllogism is suppressed or ignored. These results and the theory of premise evaluation that I propose are discussed in the context of contemporary theories of deductive reasoning.

Thesis (Ph. D.)--Calcutta University. / Includes bibliographical references and index.

Thesis (M.A.)--California State University, Chico. / Includes abstract. "Located in the Chico Digital Repository." Includes bibliographical references (p. 40 - 43 ).

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This project investigated the impact of sustained disconfirmation on an acquired belief in a covariation judgment task. Both epistemology and the philosophy of science suggest that data which oppose a hypothesis might not dictate the revision of the hypothesis unless an alternative hypothesis can explain the negative evidence and replace the previous hypothesis. As well, the literature on human categorization and reasoning documents a preference for examples and test instances which confirm rather than disconfirm a prior hypothesis. It was therefore predicted that upon the presentation of negative data for an acquired correlational expectation, subjects would abandon their disconfirmed hypothesis with greater ease if the negative evidence was supplemented with alternative hypotheses. A series of four experiments examined this prediction. Using a within-subjects design, subjects first learned that certain predictor variables signalled the presence of certain outcome variables. In a second phase, the outcomes were systematically presented in the absence of the predictors. Adjustment to the negative evidence was measured on the basis of estimates of correlation and the subjects' tendency to predict the presence of the outcomes on trials where the predictors were present. There were three experimental conditions. In the first, an alternative predictor was present on all trials where the outcomes occurred in the absence of the original predictor. In a second, an alternative outcome was present on all trials where the original outcome was absent. In a third, the negative evidence was not framed in terms of either alternative predictors nor alternative outcomes. While all three conditions produced the same reductions in correlation estimates, the condition without alternatives produced perseverance in outcome predictions in the presence of the predictors. This pattern of adjustment was observed in a simulated medical diagnostic task (Experiment 1), and in a nonmedical s