by Hwang Hoi Yee Cothan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 68-70). / Abstract --- p.ii / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Objectives of the Thesis --- p.1 / Chapter 1.2 --- Overview of the Thesis --- p.7 / Chapter 2 --- Background and Related Work --- p.8 / Chapter 2.1 --- Deductive Databases --- p.8 / Chapter 2.2 --- Disjunctive Deductive Databases --- p.10 / Chapter 2.3 --- Model tree for disjunctive deductive databases --- p.11 / Chapter 3 --- Preliminary --- p.13 / Chapter 3.1 --- Disjunctive Logic Program --- p.13 / Chapter 3.2 --- Data-disjunctive Logic Program --- p.14 / Chapter 4 --- Semantics of Data-disjunctive Logic Program --- p.17 / Chapter 4.1 --- Model-theoretic semantics --- p.17 / Chapter 4.2 --- Fixpoint semantics --- p.20 / Chapter 4.2.1 --- Fixpoint operators corresponding to the MMSpDD --- p.22 / Chapter 4.2.2 --- "Fixpoint operator corresponding to the contingency model, CMP" --- p.25 / Chapter 4.3 --- Equivalence between the model-theoretic and fixpoint semantics --- p.26 / Chapter 4.4 --- Operational Semantics --- p.30 / Chapter 4.5 --- Correspondence with the I-table --- p.31 / Chapter 5 --- Disjunctive Deductive Databases --- p.33 / Chapter 5.1 --- Disjunctions in deductive databases --- p.33 / Chapter 5.2 --- Relation between predicates --- p.35 / Chapter 5.3 --- Transformation of Disjunctive Deductive Data-bases --- p.38 / Chapter 5.4 --- Query answering for Disjunctive Deductive Data-bases --- p.40 / Chapter 6 --- Magic for Data-disjunctive Deductive Database --- p.44 / Chapter 6.1 --- Magic for Relevant Answer Set --- p.44 / Chapter 6.1.1 --- Rule rewriting algorithm --- p.46 / Chapter 6.1.2 --- Bottom-up evaluation --- p.49 / Chapter 6.1.3 --- Examples --- p.49 / Chapter 6.1.4 --- Discussion on the rewriting algorithm --- p.52 / Chapter 6.2 --- Alternative algorithm for Traditional Answer Set --- p.54 / Chapter 6.2.1 --- Rule rewriting algorithm --- p.54 / Chapter 6.2.2 --- Examples --- p.55 / Chapter 6.3 --- Contingency answer set --- p.56 / Chapter 7 --- Experiments and Comparison --- p.57 / Chapter 7.1 --- Experimental Results --- p.57 / Chapter 7.1.1 --- Results for the Traditional answer set --- p.58 / Chapter 7.1.2 --- Results for the Relevant answer set --- p.61 / Chapter 7.2 --- Comparison with the evaluation method for Model tree --- p.63 / Chapter 8 --- Conclusions and Future Work --- p.66 / Bibliography --- p.68

This work is concerned generally with the relationship between logic and psychology, and in particular with the psychophilosophical foundations of deductive reasoning. This is against the recurrent background of logicians and psychologists knowing of the existence of each other but ignoring each others' work. However, cognitive psychology needs logic, not only as all sciences do to ensure coherence and consistency, but as an essential element of a general theory of cognition. This is a substantive claim, yet in its narrower form it highlights the need to study the precise way in which logic enters the theory of cognition. The contention here is that a theory of mental logic may satisfy both requirements: namely, to be the best explanation for everyday deductive reasoning and to offer an insight into the cognitive architecture. The theory maintains that deductive, reasoning consists of operations on internal representations in accordance with logical rules implemented in procedures activated by the forms of mental representation. Thus, the foundations of the logic(s) at which logicians aim, viz. the logical precepts and ideals, must be psychologically real in the sense of being instantiated in some form in the mind. The discussion is organised into three parts. The first part deals with several issues: arguments for and against the centrality of deduction, desiderata for a theory of deductive competence, and taxonomy of reasoning theories and topics. The second part considers the mental logic hypothesis from its inception to its latest formations. It reconstructs the mental logic paradigm and its transition from a general philosophical commonplace to a psychological hypothesis. The third part looks at the philosophical connections and consequences of the mental logic theory. The first connection is with the language of thought: the hypothesis seems naturally to commit itself to a language of thought on whose formulas abstract rules apply. Another connection is with the syntactic theory of mind and the question is whether mental logic is committed to it or not. Among the consequences, the notion of rationality and the significance of deduction for discovery and justification in science are examined

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The ‘belief bias’ effect is one of the most pervasive findings in the study of syllogistic reasoning. Here, participants respond “valid” to more believable than unbelievable conclusions, regardless of the actual validity of the conclusion. There is also an interaction characteristic of the belief bias effect, in that conclusion believability plays a greater role when conclusions are invalid than when they are valid. The experiments reported in this thesis had two goals: first, to determine how individual differences in working memory (WM) capacity influence belief bias in reasoning; and second, to indentify which WM systems are involved in syllogistic deductive reasoning. To this end, both experiments employed a dual task paradigm. In Experiment 1, participants remembered spatial arrays whilst reasoning through syllogisms in order to load the visuospatial sketchpad. Results demonstrated that performance on the secondary spatial memory task suffered when participants reasoned through syllogisms of which the validity and believability of conclusions were incongruent (i.e., “conflict” problems), indicating that reasoning through conflict problems utilized limited visuospatial WM resources. Also, only participants with high WM capacities showed the typical belief-bias effect, with greater effects of conclusion believability on invalid than on valid conclusions. This interaction was not present for low WM span participants, because they made greater errors on problems with invalid, unbelievable conclusions. In Experiment 2, participants remembered digit sequences whilst reasoning in order to load the phonological loop. Both of the major results from Experiment 1 were replicated. Accuracy on the secondary digit recall task was impaired when participants reasoned through conflict problems, demonstrating that limited verbal WM resources were directed toward reasoning. Again, only high WM span participant showed the interaction between conclusion validity and believability characteristic of the belief bias effect. Effects were additive for low WM span participants because they made more errors on invalid, unbelievable syllogisms. Results from both experiments demonstrate first, that both visuospatial and verbal WM resources are involved in syllogistic reasoning, and second, that individuals with different amounts of available WM resources demonstrate differential belief bias. These results are discussed in terms of the mental models and mental logic theories of reasoning and in terms of dual process accounts of reasoning.

The ‘belief bias’ effect is one of the most pervasive findings in the study of syllogistic reasoning. Here, participants respond “valid” to more believable than unbelievable conclusions, regardless of the actual validity of the conclusion. There is also an interaction characteristic of the belief bias effect, in that conclusion believability plays a greater role when conclusions are invalid than when they are valid. The experiments reported in this thesis had two goals: first, to determine how individual differences in working memory (WM) capacity influence belief bias in reasoning; and second, to indentify which WM systems are involved in syllogistic deductive reasoning. To this end, both experiments employed a dual task paradigm. In Experiment 1, participants remembered spatial arrays whilst reasoning through syllogisms in order to load the visuospatial sketchpad. Results demonstrated that performance on the secondary spatial memory task suffered when participants reasoned through syllogisms of which the validity and believability of conclusions were incongruent (i.e., “conflict” problems), indicating that reasoning through conflict problems utilized limited visuospatial WM resources. Also, only participants with high WM capacities showed the typical belief-bias effect, with greater effects of conclusion believability on invalid than on valid conclusions. This interaction was not present for low WM span participants, because they made greater errors on problems with invalid, unbelievable conclusions. In Experiment 2, participants remembered digit sequences whilst reasoning in order to load the phonological loop. Both of the major results from Experiment 1 were replicated. Accuracy on the secondary digit recall task was impaired when participants reasoned through conflict problems, demonstrating that limited verbal WM resources were directed toward reasoning. Again, only high WM span participant showed the interaction between conclusion validity and believability characteristic of the belief bias effect. Effects were additive for low WM span participants because they made more errors on invalid, unbelievable syllogisms. Results from both experiments demonstrate first, that both visuospatial and verbal WM resources are involved in syllogistic reasoning, and second, that individuals with different amounts of available WM resources demonstrate differential belief bias. These results are discussed in terms of the mental models and mental logic theories of reasoning and in terms of dual process accounts of reasoning.

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Student Number : 0001241N - M Industrial Psychology dissertation - School of Human and Community Development - Faculty of Humanities / The following thesis explores the variables of math anxiety, deductive reasoning and career appraisal. This dissertation investigates whether there is a relationship between math anxiety and deductive reasoning. A relationship is found to exist between these two variables and the relationship is of an indirectly proportional nature. As a result, when “math anxiety is high, deductive reasoning is low” and visa viz. 74 participants were used in this research study to assess whether their appraisal of various careers differed or were homogenous in nature. This thesis discusses how various careers were appraised heterogeneously and others homogenously between people with different levels of math anxiety and deductive reasoning. This phenomenon is also explained through the possibility of extraneous factors, influencing these results.

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Thesis (Ed.D.)--Boston University