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

A proposed psychological model of driving automation

This paper considers psychological variables pertinent to driver automation. It is anticipated that driving with automated systems is likely to have a major impact on the drivers and a multiplicity of factors needs to be taken into account. A systems analysis of the driver, vehicle and automation served as the basis for eliciting psychological factors. The main variables to be considered were: feed-back, locus of control, mental workload, driver stress, situational awareness and mental representations. It is expected that anticipating the effects on the driver brought about by vehicle automation could lead to improved design strategies. Based on research evidence in the literature, the psychological factors were assembled into a model for further investigation

A decidable quantified fragment of set theory with ordered pairs and some undecidable extensions

In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field of knowledge representation. We will also show that the decision problem for our language has a non-deterministic exponential time complexity. However, for the restricted case of formulae whose quantifier prefixes have length bounded by a constant, the decision problem becomes NP-complete. We also observe that in spite of such restriction, several useful set-theoretic constructs, mostly related to maps, are expressible. Finally, we present some undecidable extensions of our language, involving any of the operators domain, range, image, and map composition. [4] Michael Breban, Alfredo Ferro, Eugenio G. Omodeo and Jacob T. Schwartz (1981): Decision procedures for elementary sublanguages of set theory. II. Formulas involving restricted quantifiers, together with ordinal, integer, map, and domain notions. Communications on Pure and Applied Mathematics 34, pp. 177-195Comment: In Proceedings GandALF 2012, arXiv:1210.202

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

The development of reasoning heuristics in autism and in typical development

Reasoning and judgment under uncertainty are often based on a limited number of simplifying heuristics rather than formal logic or rule-based argumentation. Heuristics are low-effort mental shortcuts, which save time and effort, and usually result in accurate judgment, but they can also lead to systematic errors and biases when applied inappropriately. In the past 40 years hundreds of papers have been published on the topic of heuristics and biases in judgment and decision making. However, we still know surprisingly little about the development and the cognitive underpinnings of heuristics and biases. The main aim of my thesis is to examine these questions. Another aim is to evaluate the applicability of dual-process theories of reasoning to the development of reasoning. Dual-process theories claim that there are two types of process underlying higher order reasoning: fast, automatic, and effortless (Type 1) processes (which are usually associated with the use of reasoning heuristics), and slow, conscious and effortful (Type 2) processes (which are usually associated with rule-based reasoning). This thesis presents eight experiments which investigated the development of reasoning heuristics in three different populations: typically developing children and adolescents between the age of 5 and 16, adolescents with autism, and university students. Although heuristic reasoning is supposed to be basic, simple, and effortless, we have found evidence that responses that are usually attributed to heuristic processes are positively correlated with cognitive capacity in the case of young children (even after controlling for the effects of age). Moreover, we have found that adolescents with autism are less susceptible to a number of reasoning heuristics than typically developing children. Finally, our experiments with university students provided evidence that education in statistics increases the likelihood of the inappropriate use of a certain heuristic (the equiprobability bias). These results offer a novel insight into the development of reasoning heuristics. Additionally, they have interesting implications for dual-process theories of reasoning, and they can also inform the debates about the rationality of reasoning heuristics and biases

The Body In Avant Garde Poetry

This thesis examines the use of the body in avant-garde poetics, relating it to both theory and contemporary culture. An outline of how the body has been depicted, represented, and formalized in modernism is made, and contemporary issues involving the body, from what Meredith M. Render calls the “alienability” of the body to posthuman hybridity and technological transcendence. Language poetry, including the works of M. SourbeSe Philip, Clark Coolidge, Steve McCaffery, Charles Bernstein, Karen Mac Cormack, Lyn Hejinian, and Bruce Andrews is then examined for the body’s fraught usage in a generally non-referential poetics. The body’s place in conceptual writing combines contemporary technologies with a look back at Antonin Artaud’s corps sans organes

A comparative survey of integrated learning systems

This paper presents the duction framework for unifying the three basic forms of inference - deduction, abduction, and induction - by specifying the possible relationships and influences among them in the context of integrated learning. Special assumptive forms of inference are defined that extend the use of these inference methods, and the properties of these forms are explored. A comparison to a related inference-based learning frame work is made. Finally several existing integrated learning programs are examined in the perspective of the duction framework