The Automation of Syllogistic II. Optimization and Complexity Issues

In the first paper of this series it was shown that any unquantified formula p in the collection MLSSF (multilevel syllogistic extended with the singleton operator and the predicate Finite) can be decomposed as a disjunction of set-theoretic formulae called syllogistic schemes. The syllogistic schemes are satisfiable and no two of them have a model in common, therefore the previous result already implied the decidability of the class MLSSF by simply checking if the set of syllogistic schemes associated with the given formula is empty. In the first section of this paper a new and improved searching algorithm for syllogistic schemes is introduced, based on a proof of existence of a 'minimum effort' scheme for any given satisfiable formula in MLSF. The algorithm addressed above can be piloted quite effectively even though it involves backtracking. In the second part of the paper, complexity issues are studied by showing that the class of ( 00)o1-simple prenex formulae (an extension of MLS) has a decision problem which is NP-complete. The decision algorithm that proves the membership of this decision problem to NP can be seen as a different decision algorithm for ML

Designing Software Architectures As a Composition of Specializations of Knowledge Domains

This paper summarizes our experimental research and software development activities in designing robust, adaptable and reusable software architectures. Several years ago, based on our previous experiences in object-oriented software development, we made the following assumption: ‘A software architecture should be a composition of specializations of knowledge domains’. To verify this assumption we carried out three pilot projects. In addition to the application of some popular domain analysis techniques such as use cases, we identified the invariant compositional structures of the software architectures and the related knowledge domains. Knowledge domains define the boundaries of the adaptability and reusability capabilities of software systems. Next, knowledge domains were mapped to object-oriented concepts. We experienced that some aspects of knowledge could not be directly modeled in terms of object-oriented concepts. In this paper we describe our approach, the pilot projects, the experienced problems and the adopted solutions for realizing the software architectures. We conclude the paper with the lessons that we learned from this experience

A critical rationalist approach to organizational learning: testing the theories held by managers

The common wisdom is that Popper's critical rationalism, a method aimed at knowledge validation through falsification of theories, is inadequate for managers in organizations. This study falsifies this argument in three phases: first, it specifies the obstructers that prevent the method from being employed; second, the critical rationalist method is adapted for strategic management purposes; last, the method and the hypotheses are tested via action research. Conclusions are that once the obstructers are omitted the method is applicable and effective

Individual differences and strategies for human reasoning

Theories of human reasoning have tended to assume cognitive universality, i. e. that all individuals reason in basically the same way. However, some research (e. g. that of Ford. 1995) has found evidence of individual differences in the strategies people use for syllogistic reasoning. This thesis presents a series of experiments which aimed to identify individual differences in strategies for human reasoning and investigate their nature and aetiology. Experiment 1 successfully replicated and extended Ford (1995) and provided further evidence that most individuals prefer to reason with either verbal-propositional or visuo-spatial representations. Data from verbal and written protocols showed that verbal reasoners tended to use a method of substitution whereby they obtain a value for the common term from one premise and then simply substitute it in the other premise to obtain a conclusion. Spatial reasoners, on the other hand, presented protocols which resembled Euler circles and described the syllogistic premises in terms of sets and subsets. Experiment 2 provided some further qualitative evidence about the nature of such strategies, especially the verbal reasoners, showing that within strategy variations occurred. Experiment 3 extended this line of research, identifying a strong association between verbal and spatial strategies for syllogistic reasoning and abstract and concrete strategies for transitive inference (the latter having originally been identified by Egan and Grimes- Farrow, 1982). Experiments 1-3 also showed that inter-strategic differences in accuracy are generally not observed, hence, reasoners present an outward appearance of ubiquity despite underlying differences in reasoning processes. Experiments 5 and 6 investigated individual differences in cognitive factors which may underpin strategy preference. Whilst no apparent effects of verbal and spatial ability or cognitive style were found, reasoners did appear to draw differentially on the verbal and spatial components of working memory. Confirmatory factor analysis showed that whilst verbal reasoners draw primarily on the verbal memory resource, spatial reasoners draw both on this and on spatial resource. Overall, these findings have important implications for theories of human reasoning, which need to take into account possible individual differences in strategies if they are to present a truly comprehensive account of how people reason.Economic and Social Research Counci

Information enforcement in learning with graphics : improving syllogistic reasoning skills

This thesis is an investigation into the factors that contribute to good choices among graphical systems used in teaching, and the feasibility of implementing teaching software that uses this knowledge.The thesis describes a mathematical metric derived from a cognitive theory of human diagram processing. The theory characterises differences among representations by their ability to express information. The theory provides the factors and relationships needed to build the metric. It says that good representations are easily processed because they are more vivid, more tractable and less expressive, than poor representations.The metric is applied to abstract systems for teaching and learning syllogistic reasoning, TARSKI'S WORLD, EULER CIRCLES, VENN DIAGRAMS and CARROLL'S GAME OF LOGIC. A rank ordering reflects the value of each system predicted by the theory and the metric. The theory, the metric and the systems are then tested in empirical studies. Five studies involving sixty-eight learners, examined the benefit of software based on these abstract systems.Studies showed the theory correctly predicted learners' success with the circle systems and poorer performance with TARSKI'S WORLD. The metric showed small but clear differences in expressivity between the circle systems. Differences between results of the learners using the circle systems contradicted the predictions of the metric.Learners with mathematical training were better equipped and more successful at learning syllogistic reasoning with the systems. Performance of learners without mathematical training declined after using the software systems. Diagrams drawn by learners together with video footage collected during problem solving, led to a catalogue of errors, misconceptions and some helpful strategies for learning from graphical systems.A cognitive style test investigated the poor performance of non-mathematically trained learners. Learners with mathematics training showed serialist and versatile learning styles while learners without this training showed a holist learning style. This is consistent with the hypothesis that non-mathematically trained learners emphasise the use of semantic cues during learning and problem solving.A card-sorting task investigated learners' preferences for parts of the graphical lexicon used in the diagram systems. Preferences for the EULER lexicon increased difficulty in explaining the system's poor results in earlier studies. Video footage of learners using the systems in the final study illustrated useful learning strategies and improved performance with EULER while individual instruction was available.Further work describes a preliminary design for an adaptive syllogism tutor and other related work

Real Islamic Logic

Four options for assigning a meaning to Islamic Logic are surveyed including a new proposal for an option named "Real Islamic Logic" (RIL). That approach to Islamic Logic should serve modern Islamic objectives in a way comparable to the functionality of Islamic Finance. The prospective role of RIL is analyzed from several perspectives: (i) parallel distributed systems design, (ii) reception by a community structured audience, (iii) informal logic and applied non-classical logics, and (iv) (in)tractability and artificial intelligence

A cognitive theory of graphical and linguistic reasoning: Logic and implementation

We discuss external and internal graphical and linguistic representational systems. We argue that a cognitive theory of peoples' reasoning performance must account for (a) the logical equivalence of inferences expressed in graphical and linguistic form; and (b) the implementational differences that affect facility of inference. Our theory proposes that graphical representations limit abstraction and thereby aid processibility. We discuss the ideas of specificity and abstraction, and their cognitive relevance. Empirical support comes from tasks involving (i) the manipulation of external graphics; and (ii) no external graphics. For (i), we take Euler's Circles, provide a novel computational reconstruction, show how it captures abstractions, and contrast it with earlier construals, and with Mental Models' representations. We demonstrate equivalence of the graphical Euler system, and the non-graphical Mental Models system. For (ii), we discuss text comprehension, and the mental ..